1 | using System;
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2 | using System.Collections.Generic;
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3 | using System.Diagnostics;
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4 | using System.Linq;
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5 | using HeuristicLab.Algorithms.DataAnalysis.SymRegGrammarEnumeration.GrammarEnumeration;
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6 | using HeuristicLab.Common;
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7 | using HeuristicLab.Encodings.SymbolicExpressionTreeEncoding;
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8 | using HeuristicLab.Problems.DataAnalysis.Symbolic;
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9 |
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10 | namespace HeuristicLab.Algorithms.DataAnalysis.SymRegGrammarEnumeration {
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11 | public class Grammar {
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12 |
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13 | public Symbol StartSymbol;
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14 |
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15 | #region Symbols
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16 |
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17 | public VariableSymbol Var;
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18 |
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19 | public NonterminalSymbol Expr;
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20 | public NonterminalSymbol Term;
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21 | public NonterminalSymbol Factor;
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22 | public NonterminalSymbol LogFactor;
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23 | public NonterminalSymbol ExpFactor;
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24 | public NonterminalSymbol SinFactor;
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25 |
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26 | public NonterminalSymbol InvExpr;
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27 | public NonterminalSymbol InvTerm;
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28 | public NonterminalSymbol InvFactor;
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29 |
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30 | public NonterminalSymbol SimpleExpr;
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31 | public NonterminalSymbol SimpleTerm;
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32 |
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33 | public TerminalSymbol Addition;
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34 | public TerminalSymbol Multiplication;
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35 | public TerminalSymbol Log;
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36 | public TerminalSymbol Exp;
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37 | public TerminalSymbol Sin;
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38 | public TerminalSymbol Inv;
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39 |
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40 | // For infix notation
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41 | public TerminalSymbol OpeningBracket;
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42 | public TerminalSymbol ClosingBracket;
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43 |
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44 | #endregion
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45 |
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46 |
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47 | #region HL Symbols for Parsing ExpressionTrees
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48 |
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49 | private TypeCoherentExpressionGrammar symbolicExpressionGrammar;
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50 |
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51 | private ISymbol constSy;
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52 | private ISymbol varSy;
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53 |
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54 | private ISymbol addSy;
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55 | private ISymbol mulSy;
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56 | private ISymbol logSy;
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57 | private ISymbol expSy;
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58 | private ISymbol divSy;
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59 | private ISymbol sinSy;
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60 |
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61 | private ISymbol rootSy;
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62 | private ISymbol startSy;
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63 |
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64 | #endregion
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65 |
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66 | public Grammar(string[] variables) {
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67 | #region Define Symbols
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68 | Var = new VariableSymbol("var", variables);
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69 |
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70 | Expr = new NonterminalSymbol("Expr");
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71 | Term = new NonterminalSymbol("Term");
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72 | Factor = new NonterminalSymbol("Factor");
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73 | LogFactor = new NonterminalSymbol("LogFactor");
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74 | ExpFactor = new NonterminalSymbol("ExpFactor");
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75 | SinFactor = new NonterminalSymbol("SinFactor");
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76 |
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77 | InvExpr = new NonterminalSymbol("InvExpr");
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78 | InvTerm = new NonterminalSymbol("InvTerm");
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79 | InvFactor = new NonterminalSymbol("InvFactor");
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80 |
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81 | SimpleExpr = new NonterminalSymbol("SimpleExpr");
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82 | SimpleTerm = new NonterminalSymbol("SimpleTerm");
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83 |
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84 | Addition = new TerminalSymbol("+");
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85 | Multiplication = new TerminalSymbol("*");
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86 | Log = new TerminalSymbol("log");
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87 | Exp = new TerminalSymbol("exp");
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88 | Sin = new TerminalSymbol("sin");
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89 | Inv = new TerminalSymbol("inv");
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90 |
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91 | OpeningBracket = new TerminalSymbol("(");
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92 | ClosingBracket = new TerminalSymbol(")");
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93 | #endregion
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94 |
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95 |
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96 | #region Production rules
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97 | // order of production is important, since they are accessed via index
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98 | // in memoization.
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99 | StartSymbol = Expr;
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100 |
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101 | Expr.AddProduction(Term, Expr, Addition);
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102 | Expr.AddProduction(Term);
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103 |
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104 | Term.AddProduction(Factor, Term, Multiplication);
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105 | Term.AddProduction(Factor);
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106 | Term.AddProduction(InvExpr, Inv);
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107 |
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108 | Factor.AddProduction(Var);
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109 | Factor.AddProduction(LogFactor);
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110 | Factor.AddProduction(ExpFactor);
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111 | Factor.AddProduction(SinFactor);
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112 |
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113 | LogFactor.AddProduction(SimpleExpr, Log);
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114 | ExpFactor.AddProduction(SimpleTerm, Exp);
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115 | SinFactor.AddProduction(SimpleExpr, Sin);
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116 |
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117 | SimpleExpr.AddProduction(SimpleTerm, SimpleExpr, Addition);
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118 | SimpleExpr.AddProduction(SimpleTerm);
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119 |
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120 | SimpleTerm.AddProduction(Var, SimpleTerm, Multiplication);
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121 | SimpleTerm.AddProduction(Var);
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122 |
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123 | InvExpr.AddProduction(InvTerm, InvExpr, Addition);
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124 | InvExpr.AddProduction(InvTerm);
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125 |
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126 | InvTerm.AddProduction(InvFactor, InvTerm, Multiplication);
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127 | InvTerm.AddProduction(InvFactor);
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128 |
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129 | InvFactor.AddProduction(Var);
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130 | InvFactor.AddProduction(LogFactor);
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131 | InvFactor.AddProduction(SinFactor);
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132 | #endregion
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133 |
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134 | #region Parsing to SymbolicExpressionTree
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135 | symbolicExpressionGrammar = new TypeCoherentExpressionGrammar();
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136 | symbolicExpressionGrammar.ConfigureAsDefaultRegressionGrammar();
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137 |
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138 | constSy = symbolicExpressionGrammar.Symbols.OfType<Constant>().First();
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139 | varSy = symbolicExpressionGrammar.Symbols.OfType<Variable>().First();
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140 | addSy = symbolicExpressionGrammar.Symbols.OfType<Addition>().First();
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141 | mulSy = symbolicExpressionGrammar.Symbols.OfType<Multiplication>().First();
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142 | logSy = symbolicExpressionGrammar.Symbols.OfType<Logarithm>().First();
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143 | expSy = symbolicExpressionGrammar.Symbols.OfType<Exponential>().First();
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144 | divSy = symbolicExpressionGrammar.Symbols.OfType<Division>().First();
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145 | sinSy = symbolicExpressionGrammar.Symbols.OfType<Sine>().First();
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146 |
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147 | rootSy = symbolicExpressionGrammar.Symbols.OfType<ProgramRootSymbol>().First();
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148 | startSy = symbolicExpressionGrammar.Symbols.OfType<StartSymbol>().First();
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149 |
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150 | #endregion
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151 | }
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152 |
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153 | #region Hashing
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154 | public int CalcHashCode(SymbolString sentence) {
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155 | Debug.Assert(sentence.Any(), "Trying to evaluate empty sentence!");
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156 | // Debug.Assert(sentence.All(s => s is TerminalSymbol), "Trying to evaluate symbol sequence with nonterminalsymbols!");
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157 |
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158 | Stack<Symbol> parseStack = new Stack<Symbol>(sentence);
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159 |
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160 | Symbol peek = parseStack.Peek();
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161 | int[] subtreeHashes = GetSubtreeHashes(parseStack);
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162 | return AggregateHashes(peek, subtreeHashes);
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163 | }
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164 |
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165 | private int[] GetSubtreeHashes(Stack<Symbol> parseStack) {
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166 | Symbol currentSymbol = parseStack.Pop();
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167 |
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168 | // ADDITION
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169 | if (ReferenceEquals(currentSymbol, Addition)) {
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170 | HashSet<int> uniqueChildHashes = new HashSet<int>();
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171 |
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172 | // First subtree
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173 | if (ReferenceEquals(parseStack.Peek(), Addition)) {
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174 | uniqueChildHashes.UnionWith(GetSubtreeHashes(parseStack));
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175 | } else {
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176 | var peek = parseStack.Peek();
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177 | uniqueChildHashes.Add(AggregateHashes(peek, GetSubtreeHashes(parseStack)));
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178 | }
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179 | // Second subtree
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180 | if (ReferenceEquals(parseStack.Peek(), Addition)) {
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181 | uniqueChildHashes.UnionWith(GetSubtreeHashes(parseStack));
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182 | } else {
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183 | var peek = parseStack.Peek();
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184 | uniqueChildHashes.Add(AggregateHashes(peek, GetSubtreeHashes(parseStack)));
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185 | }
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186 |
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187 | var result = uniqueChildHashes.ToList();
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188 | result.Sort();
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189 | return result.ToArray();
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190 | }
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191 |
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192 | // MULTIPLICATION
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193 | if (ReferenceEquals(currentSymbol, Multiplication)) {
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194 | List<int> childHashes = new List<int>();
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195 |
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196 | // First subtree
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197 | if (ReferenceEquals(parseStack.Peek(), Multiplication)) {
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198 | childHashes.AddRange(GetSubtreeHashes(parseStack));
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199 | } else {
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200 | childHashes.Add(AggregateHashes(parseStack.Peek(), GetSubtreeHashes(parseStack)));
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201 | }
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202 | // Second subtree
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203 | if (ReferenceEquals(parseStack.Peek(), Multiplication)) {
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204 | childHashes.AddRange(GetSubtreeHashes(parseStack));
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205 | } else {
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206 | childHashes.Add(AggregateHashes(parseStack.Peek(), GetSubtreeHashes(parseStack)));
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207 | }
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208 |
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209 | // Sort due to commutativity
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210 | childHashes.Sort();
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211 |
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212 | // Cancel out inverse factors.
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213 | var inversChildHashes = childHashes
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214 | .Select(ch => AggregateHashes(Inv, ch.ToEnumerable()))
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215 | .ToList();
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216 |
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217 | return childHashes // If this factor cancels out another one, then remove BOTH. Otherwise, keep the factor.
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218 | .Where(ch => !inversChildHashes.Remove(ch))
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219 | .ToArray();
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220 | }
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221 |
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222 | // LOG, EXP, SIN, INV
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223 | if (ReferenceEquals(currentSymbol, Log) || ReferenceEquals(currentSymbol, Exp) ||
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224 | ReferenceEquals(currentSymbol, Sin) || ReferenceEquals(currentSymbol, Inv)) {
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225 | return AggregateHashes(parseStack.Peek(), GetSubtreeHashes(parseStack)).ToEnumerable().ToArray();
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226 | }
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227 |
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228 | // var or nonterminal symbol
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229 | return currentSymbol.StringRepresentation.GetHashCode().ToEnumerable().ToArray();
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230 | }
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231 |
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232 | private int AggregateHashes(Symbol operatorSym, IEnumerable<int> hashes) {
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233 | var hashesArray = hashes.ToArray();
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234 |
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235 | int start;
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236 | if ((ReferenceEquals(operatorSym, Addition) || ReferenceEquals(operatorSym, Multiplication)) && hashesArray.Count() <= 1) {
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237 | start = 0;
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238 | } else {
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239 | start = operatorSym.StringRepresentation.GetHashCode();
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240 | }
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241 |
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242 | return hashesArray.Aggregate(start, (result, ti) => ((result << 5) + result) ^ ti.GetHashCode());
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243 | }
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244 | #endregion
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245 |
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246 | #region Parse to SymbolicExpressionTree
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247 | public SymbolicExpressionTree ParseSymbolicExpressionTree(SymbolString sentence) {
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248 | Debug.Assert(sentence.Any(), "Trying to evaluate empty sentence!");
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249 | Debug.Assert(sentence.All(s => s is TerminalSymbol), "Trying to evaluate symbol sequence with nonterminalsymbols!");
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250 |
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251 | symbolicExpressionGrammar.ConfigureAsDefaultRegressionGrammar();
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252 |
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253 | var rootNode = rootSy.CreateTreeNode();
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254 | var startNode = startSy.CreateTreeNode();
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255 | rootNode.AddSubtree(startNode);
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256 |
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257 | Stack<TerminalSymbol> parseStack = new Stack<TerminalSymbol>(sentence.OfType<TerminalSymbol>());
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258 | startNode.AddSubtree(ParseSymbolicExpressionTree(parseStack));
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259 |
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260 | return new SymbolicExpressionTree(rootNode);
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261 | }
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262 |
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263 | public ISymbolicExpressionTreeNode ParseSymbolicExpressionTree(Stack<TerminalSymbol> parseStack) {
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264 | TerminalSymbol currentSymbol = parseStack.Pop();
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265 |
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266 | ISymbolicExpressionTreeNode parsedSubTree = null;
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267 |
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268 | if (ReferenceEquals(currentSymbol, Addition)) {
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269 | parsedSubTree = addSy.CreateTreeNode();
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270 | parsedSubTree.AddSubtree(ParseSymbolicExpressionTree(parseStack)); // left part
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271 | parsedSubTree.AddSubtree(ParseSymbolicExpressionTree(parseStack)); // right part
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272 |
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273 | } else if (ReferenceEquals(currentSymbol, Multiplication)) {
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274 | parsedSubTree = mulSy.CreateTreeNode();
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275 | parsedSubTree.AddSubtree(ParseSymbolicExpressionTree(parseStack)); // left part
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276 | parsedSubTree.AddSubtree(ParseSymbolicExpressionTree(parseStack)); // right part
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277 |
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278 | } else if (ReferenceEquals(currentSymbol, Log)) {
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279 | parsedSubTree = logSy.CreateTreeNode();
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280 | parsedSubTree.AddSubtree(ParseSymbolicExpressionTree(parseStack));
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281 |
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282 | } else if (ReferenceEquals(currentSymbol, Exp)) {
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283 | parsedSubTree = expSy.CreateTreeNode();
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284 | parsedSubTree.AddSubtree(ParseSymbolicExpressionTree(parseStack));
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285 |
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286 | } else if (ReferenceEquals(currentSymbol, Sin)) {
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287 | parsedSubTree = sinSy.CreateTreeNode();
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288 | parsedSubTree.AddSubtree(ParseSymbolicExpressionTree(parseStack));
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289 |
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290 | } else if (ReferenceEquals(currentSymbol, Inv)) {
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291 | parsedSubTree = divSy.CreateTreeNode();
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292 | ConstantTreeNode dividend = (ConstantTreeNode)constSy.CreateTreeNode();
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293 | dividend.Value = 1.0;
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294 | parsedSubTree.AddSubtree(dividend);
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295 | parsedSubTree.AddSubtree(ParseSymbolicExpressionTree(parseStack));
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296 |
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297 | } else if (Var.VariableTerminalSymbols.Contains(currentSymbol)) {
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298 | VariableTreeNode varNode = (VariableTreeNode)varSy.CreateTreeNode();
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299 | varNode.Weight = 1.0;
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300 | varNode.VariableName = currentSymbol.StringRepresentation;
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301 | parsedSubTree = varNode;
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302 | }
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303 |
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304 | Debug.Assert(parsedSubTree != null);
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305 | return parsedSubTree;
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306 | }
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307 | #endregion
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308 |
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309 | #region Parse to Infix string
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310 |
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311 | public SymbolString PostfixToInfixParser(SymbolString phrase) {
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312 | Stack<Symbol> parseStack = new Stack<Symbol>(phrase);
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313 |
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314 | return PostfixToInfixSubtreeParser(parseStack);
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315 | }
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316 |
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317 | private SymbolString PostfixToInfixSubtreeParser(Stack<Symbol> parseStack) {
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318 | Symbol head = parseStack.Pop();
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319 |
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320 | SymbolString result = new SymbolString();
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321 |
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322 | if (ReferenceEquals(head, Addition) || ReferenceEquals(head, Multiplication)) {
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323 | // right part
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324 | SymbolString rightPart = PostfixToInfixSubtreeParser(parseStack);
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325 | SymbolString leftPart = PostfixToInfixSubtreeParser(parseStack);
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326 |
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327 | result.AddRange(leftPart);
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328 | result.Add(head);
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329 | result.AddRange(rightPart);
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330 |
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331 | } else if (ReferenceEquals(head, Log) || ReferenceEquals(head, Exp)
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332 | || ReferenceEquals(head, Sin) || ReferenceEquals(head, Inv)) {
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333 | result.Add(head);
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334 | result.Add(OpeningBracket);
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335 | result.AddRange(PostfixToInfixSubtreeParser(parseStack));
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336 | result.Add(ClosingBracket);
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337 |
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338 | } else {
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339 | result.Add(head);
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340 | }
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341 | return result;
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342 | }
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343 |
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344 | #endregion
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345 | }
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346 | }
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