1 | #region License Information
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2 | /* HeuristicLab
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3 | * Copyright (C) 2002-2010 Heuristic and Evolutionary Algorithms Laboratory (HEAL)
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4 | *
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5 | * This file is part of HeuristicLab.
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6 | *
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7 | * HeuristicLab is free software: you can redistribute it and/or modify
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8 | * it under the terms of the GNU General Public License as published by
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9 | * the Free Software Foundation, either version 3 of the License, or
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10 | * (at your option) any later version.
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11 | *
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12 | * HeuristicLab is distributed in the hope that it will be useful,
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13 | * but WITHOUT ANY WARRANTY; without even the implied warranty of
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14 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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15 | * GNU General Public License for more details.
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16 | *
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17 | * You should have received a copy of the GNU General Public License
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18 | * along with HeuristicLab. If not, see <http://www.gnu.org/licenses/>.
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19 | */
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20 | #endregion
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21 |
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22 | using System;
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23 | using System.Collections.Generic;
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24 | using System.Diagnostics;
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25 | using System.Linq;
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26 | using HeuristicLab.Common;
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27 | using HeuristicLab.Encodings.SymbolicExpressionTreeEncoding;
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28 | using HeuristicLab.Encodings.SymbolicExpressionTreeEncoding.Symbols;
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29 | using HeuristicLab.Problems.DataAnalysis.Symbolic.Symbols;
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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 | /// Simplistic simplifier for arithmetic expressions
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34 | /// </summary>
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35 | public class SymbolicSimplifier {
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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 |
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42 | public SymbolicExpressionTree Simplify(SymbolicExpressionTree originalTree) {
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43 | var clone = (SymbolicExpressionTreeNode)originalTree.Root.Clone();
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44 | // macro expand (initially no argument trees)
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45 | var macroExpandedTree = MacroExpand(clone, clone.SubTrees[0], new List<SymbolicExpressionTreeNode>());
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46 | SymbolicExpressionTreeNode rootNode = (new ProgramRootSymbol()).CreateTreeNode();
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47 | rootNode.AddSubTree(GetSimplifiedTree(macroExpandedTree));
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48 | return new SymbolicExpressionTree(rootNode);
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49 | }
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50 |
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51 | // the argumentTrees list contains already expanded trees used as arguments for invocations
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52 | private SymbolicExpressionTreeNode MacroExpand(SymbolicExpressionTreeNode root, SymbolicExpressionTreeNode node, IList<SymbolicExpressionTreeNode> argumentTrees) {
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53 | List<SymbolicExpressionTreeNode> subtrees = new List<SymbolicExpressionTreeNode>(node.SubTrees);
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54 | while (node.SubTrees.Count > 0) node.RemoveSubTree(0);
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55 | if (node.Symbol is InvokeFunction) {
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56 | var invokeSym = node.Symbol as InvokeFunction;
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57 | var defunNode = FindFunctionDefinition(root, invokeSym.FunctionName);
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58 | var macroExpandedArguments = new List<SymbolicExpressionTreeNode>();
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59 | foreach (var subtree in subtrees) {
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60 | macroExpandedArguments.Add(MacroExpand(root, subtree, argumentTrees));
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61 | }
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62 | return MacroExpand(root, defunNode, macroExpandedArguments);
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63 | } else if (node.Symbol is Argument) {
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64 | var argSym = node.Symbol as Argument;
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65 | // return the correct argument sub-tree (already macro-expanded)
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66 | return (SymbolicExpressionTreeNode)argumentTrees[argSym.ArgumentIndex].Clone();
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67 | } else {
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68 | // recursive application
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69 | foreach (var subtree in subtrees) {
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70 | node.AddSubTree(MacroExpand(root, subtree, argumentTrees));
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71 | }
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72 | return node;
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73 | }
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74 | }
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75 |
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76 | private SymbolicExpressionTreeNode FindFunctionDefinition(SymbolicExpressionTreeNode root, string functionName) {
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77 | foreach (var subtree in root.SubTrees.OfType<DefunTreeNode>()) {
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78 | if (subtree.FunctionName == functionName) return subtree.SubTrees[0];
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79 | }
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80 |
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81 | throw new ArgumentException("Definition of function " + functionName + " not found.");
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82 | }
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83 |
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84 |
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85 | #region symbol predicates
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86 | private bool IsDivision(SymbolicExpressionTreeNode original) {
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87 | return original.Symbol is Division;
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88 | }
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89 |
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90 | private bool IsMultiplication(SymbolicExpressionTreeNode original) {
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91 | return original.Symbol is Multiplication;
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92 | }
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93 |
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94 | private bool IsSubtraction(SymbolicExpressionTreeNode original) {
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95 | return original.Symbol is Subtraction;
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96 | }
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97 |
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98 | private bool IsAddition(SymbolicExpressionTreeNode original) {
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99 | return original.Symbol is Addition;
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100 | }
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101 |
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102 | private bool IsVariable(SymbolicExpressionTreeNode original) {
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103 | return original.Symbol is Variable;
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104 | }
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105 |
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106 | private bool IsConstant(SymbolicExpressionTreeNode original) {
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107 | return original.Symbol is Constant;
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108 | }
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109 |
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110 | private bool IsAverage(SymbolicExpressionTreeNode original) {
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111 | return original.Symbol is Average;
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112 | }
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113 | private bool IsLog(SymbolicExpressionTreeNode original) {
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114 | return original.Symbol is Logarithm;
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115 | }
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116 | private bool IsIfThenElse(SymbolicExpressionTreeNode original) {
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117 | return original.Symbol is IfThenElse;
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118 | }
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119 | #endregion
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120 |
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121 | /// <summary>
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122 | /// Creates a new simplified tree
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123 | /// </summary>
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124 | /// <param name="original"></param>
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125 | /// <returns></returns>
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126 | public SymbolicExpressionTreeNode GetSimplifiedTree(SymbolicExpressionTreeNode original) {
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127 | if (IsConstant(original) || IsVariable(original)) {
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128 | return (SymbolicExpressionTreeNode)original.Clone();
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129 | } else if (IsAddition(original)) {
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130 | return SimplifyAddition(original);
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131 | } else if (IsSubtraction(original)) {
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132 | return SimplifySubtraction(original);
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133 | } else if (IsMultiplication(original)) {
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134 | return SimplifyMultiplication(original);
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135 | } else if (IsDivision(original)) {
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136 | return SimplifyDivision(original);
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137 | } else if (IsAverage(original)) {
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138 | return SimplifyAverage(original);
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139 | } else if (IsLog(original)) {
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140 | // TODO simplify logarithm
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141 | return SimplifyAny(original);
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142 | } else if (IsIfThenElse(original)) {
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143 | // TODO simplify conditionals
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144 | return SimplifyAny(original);
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145 | } else if (IsAverage(original)) {
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146 | return SimplifyAverage(original);
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147 | } else {
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148 | return SimplifyAny(original);
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149 | }
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150 | }
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151 |
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152 | #region specific simplification routines
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153 | private SymbolicExpressionTreeNode SimplifyAny(SymbolicExpressionTreeNode original) {
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154 | // can't simplify this function but simplify all subtrees
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155 | List<SymbolicExpressionTreeNode> subTrees = new List<SymbolicExpressionTreeNode>(original.SubTrees);
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156 | while (original.SubTrees.Count > 0) original.RemoveSubTree(0);
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157 | var clone = (SymbolicExpressionTreeNode)original.Clone();
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158 | List<SymbolicExpressionTreeNode> simplifiedSubTrees = new List<SymbolicExpressionTreeNode>();
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159 | foreach (var subTree in subTrees) {
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160 | simplifiedSubTrees.Add(GetSimplifiedTree(subTree));
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161 | original.AddSubTree(subTree);
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162 | }
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163 | foreach (var simplifiedSubtree in simplifiedSubTrees) {
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164 | clone.AddSubTree(simplifiedSubtree);
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165 | }
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166 | if (simplifiedSubTrees.TrueForAll(t => IsConstant(t))) {
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167 | SimplifyConstantExpression(clone);
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168 | }
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169 | return clone;
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170 | }
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171 |
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172 | private SymbolicExpressionTreeNode SimplifyConstantExpression(SymbolicExpressionTreeNode original) {
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173 | // not yet implemented
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174 | return original;
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175 | }
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176 |
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177 | private SymbolicExpressionTreeNode SimplifyAverage(SymbolicExpressionTreeNode original) {
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178 | if (original.SubTrees.Count == 1) {
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179 | return GetSimplifiedTree(original.SubTrees[0]);
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180 | } else {
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181 | // simplify expressions x0..xn
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182 | // make sum(x0..xn) / n
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183 | Trace.Assert(original.SubTrees.Count > 1);
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184 | var sum = original.SubTrees
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185 | .Select(x => GetSimplifiedTree(x))
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186 | .Aggregate((a, b) => MakeSum(a, b));
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187 | return MakeFraction(sum, MakeConstant(original.SubTrees.Count));
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188 | }
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189 | }
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190 |
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191 | private SymbolicExpressionTreeNode SimplifyDivision(SymbolicExpressionTreeNode original) {
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192 | if (original.SubTrees.Count == 1) {
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193 | return Invert(GetSimplifiedTree(original.SubTrees[0]));
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194 | } else {
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195 | // simplify expressions x0..xn
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196 | // make multiplication (x0 * 1/(x1 * x1 * .. * xn))
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197 | Trace.Assert(original.SubTrees.Count > 1);
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198 | var simplifiedTrees = original.SubTrees.Select(x => GetSimplifiedTree(x));
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199 | return
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200 | MakeProduct(simplifiedTrees.First(), Invert(simplifiedTrees.Skip(1).Aggregate((a, b) => MakeProduct(a, b))));
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201 | }
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202 | }
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203 |
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204 | private SymbolicExpressionTreeNode SimplifyMultiplication(SymbolicExpressionTreeNode original) {
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205 | if (original.SubTrees.Count == 1) {
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206 | return GetSimplifiedTree(original.SubTrees[0]);
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207 | } else {
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208 | Trace.Assert(original.SubTrees.Count > 1);
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209 | return original.SubTrees
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210 | .Select(x => GetSimplifiedTree(x))
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211 | .Aggregate((a, b) => MakeProduct(a, b));
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212 | }
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213 | }
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214 |
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215 | private SymbolicExpressionTreeNode SimplifySubtraction(SymbolicExpressionTreeNode original) {
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216 | if (original.SubTrees.Count == 1) {
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217 | return Negate(GetSimplifiedTree(original.SubTrees[0]));
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218 | } else {
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219 | // simplify expressions x0..xn
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220 | // make addition (x0,-x1..-xn)
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221 | Trace.Assert(original.SubTrees.Count > 1);
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222 | var simplifiedTrees = original.SubTrees.Select(x => GetSimplifiedTree(x));
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223 | return simplifiedTrees.Take(1)
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224 | .Concat(simplifiedTrees.Skip(1).Select(x => Negate(x)))
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225 | .Aggregate((a, b) => MakeSum(a, b));
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226 | }
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227 | }
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228 |
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229 | private SymbolicExpressionTreeNode SimplifyAddition(SymbolicExpressionTreeNode original) {
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230 | if (original.SubTrees.Count == 1) {
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231 | return GetSimplifiedTree(original.SubTrees[0]);
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232 | } else {
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233 | // simplify expression x0..xn
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234 | // make addition (x0..xn)
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235 | Trace.Assert(original.SubTrees.Count > 1);
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236 | return original.SubTrees
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237 | .Select(x => GetSimplifiedTree(x))
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238 | .Aggregate((a, b) => MakeSum(a, b));
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239 | }
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240 | }
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241 | #endregion
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242 |
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243 |
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244 |
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245 | #region low level tree restructuring
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246 | // MakeFraction, MakeProduct and MakeSum take two already simplified trees and create a new simplified tree
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247 |
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248 | private SymbolicExpressionTreeNode MakeFraction(SymbolicExpressionTreeNode a, SymbolicExpressionTreeNode b) {
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249 | if (IsConstant(a) && IsConstant(b)) {
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250 | // fold constants
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251 | return MakeConstant(((ConstantTreeNode)a).Value / ((ConstantTreeNode)b).Value);
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252 | } if (IsConstant(a) && !((ConstantTreeNode)a).Value.IsAlmost(1.0)) {
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253 | return MakeFraction(MakeConstant(1.0), MakeProduct(b, Invert(a)));
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254 | } else if (IsVariable(a) && IsConstant(b)) {
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255 | // merge constant values into variable weights
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256 | var constB = ((ConstantTreeNode)b).Value;
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257 | ((VariableTreeNode)a).Weight /= constB;
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258 | return a;
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259 | } else if (IsAddition(a) && IsConstant(b)) {
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260 | return a.SubTrees
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261 | .Select(x => GetSimplifiedTree(x))
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262 | .Select(x => MakeFraction(x, b))
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263 | .Aggregate((c, d) => MakeSum(c, d));
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264 | } else if (IsMultiplication(a) && IsConstant(b)) {
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265 | return MakeProduct(a, Invert(b));
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266 | } else if (IsDivision(a) && IsConstant(b)) {
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267 | // (a1 / a2) / c => (a1 / (a2 * c))
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268 | Trace.Assert(a.SubTrees.Count == 2);
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269 | return MakeFraction(a.SubTrees[0], MakeProduct(a.SubTrees[1], b));
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270 | } else if (IsDivision(a) && IsDivision(b)) {
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271 | // (a1 / a2) / (b1 / b2) =>
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272 | Trace.Assert(a.SubTrees.Count == 2);
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273 | Trace.Assert(b.SubTrees.Count == 2);
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274 | return MakeFraction(MakeProduct(a.SubTrees[0], b.SubTrees[1]), MakeProduct(a.SubTrees[1], b.SubTrees[0]));
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275 | } else if (IsDivision(a)) {
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276 | // (a1 / a2) / b => (a1 / (a2 * b))
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277 | Trace.Assert(a.SubTrees.Count == 2);
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278 | return MakeFraction(a.SubTrees[0], MakeProduct(a.SubTrees[1], b));
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279 | } else if (IsDivision(b)) {
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280 | // a / (b1 / b2) => (a * b2) / b1
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281 | Trace.Assert(b.SubTrees.Count == 2);
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282 | return MakeFraction(MakeProduct(a, b.SubTrees[1]), b.SubTrees[0]);
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283 | } else {
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284 | var div = divSymbol.CreateTreeNode();
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285 | div.AddSubTree(a);
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286 | div.AddSubTree(b);
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287 | return div;
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288 | }
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289 | }
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290 |
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291 | private SymbolicExpressionTreeNode MakeSum(SymbolicExpressionTreeNode a, SymbolicExpressionTreeNode b) {
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292 | if (IsConstant(a) && IsConstant(b)) {
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293 | // fold constants
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294 | ((ConstantTreeNode)a).Value += ((ConstantTreeNode)b).Value;
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295 | return a;
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296 | } else if (IsConstant(a)) {
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297 | // c + x => x + c
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298 | // b is not constant => make sure constant is on the right
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299 | return MakeSum(b, a);
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300 | } else if (IsConstant(b) && ((ConstantTreeNode)b).Value.IsAlmost(0.0)) {
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301 | // x + 0 => x
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302 | return a;
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303 | } else if (IsAddition(a) && IsAddition(b)) {
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304 | // merge additions
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305 | var add = addSymbol.CreateTreeNode();
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306 | for (int i = 0; i < a.SubTrees.Count - 1; i++) add.AddSubTree(a.SubTrees[i]);
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307 | for (int i = 0; i < b.SubTrees.Count - 1; i++) add.AddSubTree(b.SubTrees[i]);
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308 | if (IsConstant(a.SubTrees.Last()) && IsConstant(b.SubTrees.Last())) {
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309 | add.AddSubTree(MakeSum(a.SubTrees.Last(), b.SubTrees.Last()));
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310 | } else if (IsConstant(a.SubTrees.Last())) {
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311 | add.AddSubTree(b.SubTrees.Last());
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312 | add.AddSubTree(a.SubTrees.Last());
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313 | } else {
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314 | add.AddSubTree(a.SubTrees.Last());
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315 | add.AddSubTree(b.SubTrees.Last());
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316 | }
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317 | MergeVariablesInSum(add);
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318 | return add;
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319 | } else if (IsAddition(b)) {
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320 | return MakeSum(b, a);
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321 | } else if (IsAddition(a) && IsConstant(b)) {
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322 | // a is an addition and b is a constant => append b to a and make sure the constants are merged
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323 | var add = addSymbol.CreateTreeNode();
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324 | for (int i = 0; i < a.SubTrees.Count - 1; i++) add.AddSubTree(a.SubTrees[i]);
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325 | if (IsConstant(a.SubTrees.Last()))
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326 | add.AddSubTree(MakeSum(a.SubTrees.Last(), b));
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327 | else {
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328 | add.AddSubTree(a.SubTrees.Last());
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329 | add.AddSubTree(b);
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330 | }
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331 | return add;
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332 | } else if (IsAddition(a)) {
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333 | // a is already an addition => append b
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334 | var add = addSymbol.CreateTreeNode();
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335 | add.AddSubTree(b);
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336 | foreach (var subTree in a.SubTrees) {
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337 | add.AddSubTree(subTree);
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338 | }
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339 | MergeVariablesInSum(add);
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340 | return add;
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341 | } else {
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342 | var add = addSymbol.CreateTreeNode();
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343 | add.AddSubTree(a);
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344 | add.AddSubTree(b);
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345 | MergeVariablesInSum(add);
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346 | return add;
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347 | }
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348 | }
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349 |
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350 | // makes sure variable symbols in sums are combined
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351 | // possible improvment: combine sums of products where the products only reference the same variable
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352 | private void MergeVariablesInSum(SymbolicExpressionTreeNode sum) {
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353 | var subtrees = new List<SymbolicExpressionTreeNode>(sum.SubTrees);
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354 | while (sum.SubTrees.Count > 0) sum.RemoveSubTree(0);
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355 | var groupedVarNodes = from node in subtrees.OfType<VariableTreeNode>()
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356 | where node.Symbol.Name == "Variable"
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357 | group node by node.VariableName into g
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358 | select g;
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359 | var unchangedSubTrees = subtrees.Where(t => t.Symbol.Name != "Variable");
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360 |
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361 | foreach (var variableNodeGroup in groupedVarNodes) {
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362 | var weightSum = variableNodeGroup.Select(t => t.Weight).Sum();
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363 | var representative = variableNodeGroup.First();
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364 | representative.Weight = weightSum;
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365 | sum.AddSubTree(representative);
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366 | }
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367 | foreach (var unchangedSubtree in unchangedSubTrees)
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368 | sum.AddSubTree(unchangedSubtree);
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369 | }
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370 |
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371 |
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372 | private SymbolicExpressionTreeNode MakeProduct(SymbolicExpressionTreeNode a, SymbolicExpressionTreeNode b) {
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373 | if (IsConstant(a) && IsConstant(b)) {
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374 | // fold constants
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375 | ((ConstantTreeNode)a).Value *= ((ConstantTreeNode)b).Value;
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376 | return a;
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377 | } else if (IsConstant(a)) {
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378 | // a * $ => $ * a
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379 | return MakeProduct(b, a);
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380 | } else if (IsConstant(b) && ((ConstantTreeNode)b).Value.IsAlmost(1.0)) {
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381 | // $ * 1.0 => $
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382 | return a;
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383 | } else if (IsConstant(b) && IsVariable(a)) {
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384 | // multiply constants into variables weights
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385 | ((VariableTreeNode)a).Weight *= ((ConstantTreeNode)b).Value;
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386 | return a;
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387 | } else if (IsConstant(b) && IsAddition(a)) {
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388 | // multiply constants into additions
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389 | return a.SubTrees.Select(x => MakeProduct(x, b)).Aggregate((c, d) => MakeSum(c, d));
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390 | } else if (IsDivision(a) && IsDivision(b)) {
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391 | // (a1 / a2) * (b1 / b2) => (a1 * b1) / (a2 * b2)
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392 | Trace.Assert(a.SubTrees.Count == 2);
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393 | Trace.Assert(b.SubTrees.Count == 2);
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394 | return MakeFraction(MakeProduct(a.SubTrees[0], b.SubTrees[0]), MakeProduct(a.SubTrees[1], b.SubTrees[1]));
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395 | } else if (IsDivision(a)) {
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396 | // (a1 / a2) * b => (a1 * b) / a2
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397 | Trace.Assert(a.SubTrees.Count == 2);
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398 | return MakeFraction(MakeProduct(a.SubTrees[0], b), a.SubTrees[1]);
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399 | } else if (IsDivision(b)) {
|
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400 | // a * (b1 / b2) => (b1 * a) / b2
|
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401 | Trace.Assert(b.SubTrees.Count == 2);
|
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402 | return MakeFraction(MakeProduct(b.SubTrees[0], a), b.SubTrees[1]);
|
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403 | } else if (IsMultiplication(a) && IsMultiplication(b)) {
|
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404 | // merge multiplications (make sure constants are merged)
|
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405 | var mul = mulSymbol.CreateTreeNode();
|
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406 | for (int i = 0; i < a.SubTrees.Count; i++) mul.AddSubTree(a.SubTrees[i]);
|
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407 | for (int i = 0; i < b.SubTrees.Count; i++) mul.AddSubTree(b.SubTrees[i]);
|
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408 | MergeVariablesAndConstantsInProduct(mul);
|
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409 | return mul;
|
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410 | } else if (IsMultiplication(b)) {
|
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411 | return MakeProduct(b, a);
|
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412 | } else if (IsMultiplication(a)) {
|
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413 | // a is already an multiplication => append b
|
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414 | a.AddSubTree(b);
|
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415 | MergeVariablesAndConstantsInProduct(a);
|
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416 | return a;
|
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417 | } else {
|
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418 | var mul = mulSymbol.CreateTreeNode();
|
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419 | mul.SubTrees.Add(a);
|
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420 | mul.SubTrees.Add(b);
|
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421 | MergeVariablesAndConstantsInProduct(mul);
|
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422 | return mul;
|
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423 | }
|
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424 | }
|
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425 | #endregion
|
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426 |
|
---|
427 | // helper to combine the constant factors in products and to combine variables (powers of 2, 3...)
|
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428 | private void MergeVariablesAndConstantsInProduct(SymbolicExpressionTreeNode prod) {
|
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429 | var subtrees = new List<SymbolicExpressionTreeNode>(prod.SubTrees);
|
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430 | while (prod.SubTrees.Count > 0) prod.RemoveSubTree(0);
|
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431 | var groupedVarNodes = from node in subtrees.OfType<VariableTreeNode>()
|
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432 | where node.Symbol.Name == "Variable"
|
---|
433 | group node by node.VariableName into g
|
---|
434 | orderby g.Count()
|
---|
435 | select g;
|
---|
436 | var constantProduct = (from node in subtrees.OfType<VariableTreeNode>()
|
---|
437 | where node.Symbol.Name == "Variable"
|
---|
438 | select node.Weight)
|
---|
439 | .Concat(from node in subtrees.OfType<ConstantTreeNode>()
|
---|
440 | select node.Value)
|
---|
441 | .DefaultIfEmpty(1.0)
|
---|
442 | .Aggregate((c1, c2) => c1 * c2);
|
---|
443 |
|
---|
444 | var unchangedSubTrees = from tree in subtrees
|
---|
445 | where !(tree is VariableTreeNode && tree.Symbol.Name == "Variable")
|
---|
446 | where !(tree is ConstantTreeNode)
|
---|
447 | select tree;
|
---|
448 |
|
---|
449 | foreach (var variableNodeGroup in groupedVarNodes) {
|
---|
450 | var representative = variableNodeGroup.First();
|
---|
451 | representative.Weight = 1.0;
|
---|
452 | if (variableNodeGroup.Count() > 1) {
|
---|
453 | var poly = mulSymbol.CreateTreeNode();
|
---|
454 | for (int p = 0; p < variableNodeGroup.Count(); p++) {
|
---|
455 | poly.AddSubTree((SymbolicExpressionTreeNode)representative.Clone());
|
---|
456 | }
|
---|
457 | prod.AddSubTree(poly);
|
---|
458 | } else {
|
---|
459 | prod.AddSubTree(representative);
|
---|
460 | }
|
---|
461 | }
|
---|
462 |
|
---|
463 | foreach (var unchangedSubtree in unchangedSubTrees)
|
---|
464 | prod.AddSubTree(unchangedSubtree);
|
---|
465 |
|
---|
466 | if (!constantProduct.IsAlmost(1.0)) {
|
---|
467 | prod.AddSubTree(MakeConstant(constantProduct));
|
---|
468 | }
|
---|
469 | }
|
---|
470 |
|
---|
471 |
|
---|
472 | #region helper functions
|
---|
473 | /// <summary>
|
---|
474 | /// x => x * -1
|
---|
475 | /// Doesn't create new trees and manipulates x
|
---|
476 | /// </summary>
|
---|
477 | /// <param name="x"></param>
|
---|
478 | /// <returns>-x</returns>
|
---|
479 | private SymbolicExpressionTreeNode Negate(SymbolicExpressionTreeNode x) {
|
---|
480 | if (IsConstant(x)) {
|
---|
481 | ((ConstantTreeNode)x).Value *= -1;
|
---|
482 | } else if (IsVariable(x)) {
|
---|
483 | var variableTree = (VariableTreeNode)x;
|
---|
484 | variableTree.Weight *= -1.0;
|
---|
485 | } else if (IsAddition(x)) {
|
---|
486 | // (x0 + x1 + .. + xn) * -1 => (-x0 + -x1 + .. + -xn)
|
---|
487 | foreach (var subTree in x.SubTrees) {
|
---|
488 | Negate(subTree);
|
---|
489 | }
|
---|
490 | } else if (IsMultiplication(x) || IsDivision(x)) {
|
---|
491 | // x0 * x1 * .. * xn * -1 => x0 * x1 * .. * -xn
|
---|
492 | Negate(x.SubTrees.Last()); // last is maybe a constant, prefer to negate the constant
|
---|
493 | } else {
|
---|
494 | // any other function
|
---|
495 | return MakeProduct(x, MakeConstant(-1));
|
---|
496 | }
|
---|
497 | return x;
|
---|
498 | }
|
---|
499 |
|
---|
500 | /// <summary>
|
---|
501 | /// x => 1/x
|
---|
502 | /// Doesn't create new trees and manipulates x
|
---|
503 | /// </summary>
|
---|
504 | /// <param name="x"></param>
|
---|
505 | /// <returns></returns>
|
---|
506 | private SymbolicExpressionTreeNode Invert(SymbolicExpressionTreeNode x) {
|
---|
507 | if (IsConstant(x)) {
|
---|
508 | return MakeConstant(1.0 / ((ConstantTreeNode)x).Value);
|
---|
509 | } else if (IsDivision(x)) {
|
---|
510 | Trace.Assert(x.SubTrees.Count == 2);
|
---|
511 | return MakeFraction(x.SubTrees[1], x.SubTrees[0]);
|
---|
512 | } else {
|
---|
513 | // any other function
|
---|
514 | return MakeFraction(MakeConstant(1), x);
|
---|
515 | }
|
---|
516 | }
|
---|
517 |
|
---|
518 | private SymbolicExpressionTreeNode MakeConstant(double value) {
|
---|
519 | ConstantTreeNode constantTreeNode = (ConstantTreeNode)(constSymbol.CreateTreeNode());
|
---|
520 | constantTreeNode.Value = value;
|
---|
521 | return (SymbolicExpressionTreeNode)constantTreeNode;
|
---|
522 | }
|
---|
523 |
|
---|
524 | private SymbolicExpressionTreeNode MakeVariable(double weight, string name) {
|
---|
525 | var tree = (VariableTreeNode)varSymbol.CreateTreeNode();
|
---|
526 | tree.Weight = weight;
|
---|
527 | tree.VariableName = name;
|
---|
528 | return tree;
|
---|
529 | }
|
---|
530 | #endregion
|
---|
531 | }
|
---|
532 | }
|
---|