1 | #region License Information
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2 |
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3 | /* HeuristicLab
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4 | * Copyright (C) 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.Encodings.SymbolicExpressionTreeEncoding;
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29 |
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30 | namespace HeuristicLab.Problems.DataAnalysis.Symbolic {
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31 | /// <summary>
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32 | /// Simplifier for symbolic expressions
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33 | /// </summary>
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34 | public class VectorTreeSimplifier {
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35 | private static readonly Addition addSymbol = new Addition();
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36 | private static readonly Multiplication mulSymbol = new Multiplication();
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37 | private static readonly Division divSymbol = new Division();
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38 | private static readonly Constant constSymbol = new Constant();
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39 | private static readonly Absolute absSymbol = new Absolute();
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40 | private static readonly Logarithm logSymbol = new Logarithm();
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41 | private static readonly Exponential expSymbol = new Exponential();
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42 | private static readonly Root rootSymbol = new Root();
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43 | private static readonly Square sqrSymbol = new Square();
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44 | private static readonly SquareRoot sqrtSymbol = new SquareRoot();
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45 | private static readonly AnalyticQuotient aqSymbol = new AnalyticQuotient();
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46 | private static readonly Cube cubeSymbol = new Cube();
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47 | private static readonly CubeRoot cubeRootSymbol = new CubeRoot();
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48 | private static readonly Power powSymbol = new Power();
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49 | private static readonly Sine sineSymbol = new Sine();
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50 | private static readonly Cosine cosineSymbol = new Cosine();
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51 | private static readonly Tangent tanSymbol = new Tangent();
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52 | private static readonly IfThenElse ifThenElseSymbol = new IfThenElse();
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53 | private static readonly And andSymbol = new And();
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54 | private static readonly Or orSymbol = new Or();
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55 | private static readonly Not notSymbol = new Not();
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56 | private static readonly GreaterThan gtSymbol = new GreaterThan();
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57 | private static readonly LessThan ltSymbol = new LessThan();
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58 | private static readonly Integral integralSymbol = new Integral();
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59 | private static readonly LaggedVariable laggedVariableSymbol = new LaggedVariable();
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60 | private static readonly TimeLag timeLagSymbol = new TimeLag();
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61 | private static readonly Sum sumSymbol = new Sum();
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62 | private static readonly Mean meanSymbol = new Mean();
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63 | private static readonly Length lengthSymbol = new Length();
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64 |
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65 | private readonly SymbolicDataAnalysisExpressionTreeVectorInterpreter interpreter;
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66 | private readonly IDataAnalysisProblemData problemData;
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67 |
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68 | public VectorTreeSimplifier(SymbolicDataAnalysisExpressionTreeVectorInterpreter interpreter, IDataAnalysisProblemData problemData) {
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69 | this.interpreter = interpreter;
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70 | this.problemData = problemData;
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71 | }
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72 |
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73 | public ISymbolicExpressionTree Simplify(ISymbolicExpressionTree originalTree) {
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74 | var clone = (ISymbolicExpressionTreeNode)originalTree.Root.Clone();
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75 | // macro expand (initially no argument trees)
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76 | var macroExpandedTree = MacroExpand(clone, clone.GetSubtree(0), new List<ISymbolicExpressionTreeNode>());
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77 | ISymbolicExpressionTreeNode rootNode = (new ProgramRootSymbol()).CreateTreeNode();
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78 | rootNode.AddSubtree(GetSimplifiedTree(macroExpandedTree));
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79 |
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80 | #if DEBUG
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81 | // check that each node is only referenced once
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82 | var nodes = rootNode.IterateNodesPrefix().ToArray();
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83 | foreach (var n in nodes) if (nodes.Count(ni => ni == n) > 1) throw new InvalidOperationException();
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84 | #endif
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85 | return new SymbolicExpressionTree(rootNode);
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86 | }
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87 |
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88 | // the argumentTrees list contains already expanded trees used as arguments for invocations
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89 | private static ISymbolicExpressionTreeNode MacroExpand(ISymbolicExpressionTreeNode root, ISymbolicExpressionTreeNode node,
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90 | IList<ISymbolicExpressionTreeNode> argumentTrees) {
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91 | List<ISymbolicExpressionTreeNode> subtrees = new List<ISymbolicExpressionTreeNode>(node.Subtrees);
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92 | while (node.SubtreeCount > 0) node.RemoveSubtree(0);
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93 | if (node.Symbol is InvokeFunction) {
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94 | var invokeSym = node.Symbol as InvokeFunction;
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95 | var defunNode = FindFunctionDefinition(root, invokeSym.FunctionName);
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96 | var macroExpandedArguments = new List<ISymbolicExpressionTreeNode>();
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97 | foreach (var subtree in subtrees) {
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98 | macroExpandedArguments.Add(MacroExpand(root, subtree, argumentTrees));
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99 | }
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100 | return MacroExpand(root, defunNode, macroExpandedArguments);
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101 | } else if (node.Symbol is Argument) {
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102 | var argSym = node.Symbol as Argument;
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103 | // return the correct argument sub-tree (already macro-expanded)
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104 | return (SymbolicExpressionTreeNode)argumentTrees[argSym.ArgumentIndex].Clone();
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105 | } else {
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106 | // recursive application
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107 | foreach (var subtree in subtrees) {
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108 | node.AddSubtree(MacroExpand(root, subtree, argumentTrees));
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109 | }
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110 | return node;
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111 | }
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112 | }
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113 |
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114 | private static ISymbolicExpressionTreeNode FindFunctionDefinition(ISymbolicExpressionTreeNode root, string functionName) {
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115 | foreach (var subtree in root.Subtrees.OfType<DefunTreeNode>()) {
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116 | if (subtree.FunctionName == functionName) return subtree.GetSubtree(0);
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117 | }
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118 |
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119 | throw new ArgumentException("Definition of function " + functionName + " not found.");
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120 | }
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121 |
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122 | #region symbol predicates
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123 |
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124 | // arithmetic
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125 | private static bool IsDivision(ISymbolicExpressionTreeNode node) {
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126 | return node.Symbol is Division;
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127 | }
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128 |
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129 | private static bool IsMultiplication(ISymbolicExpressionTreeNode node) {
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130 | return node.Symbol is Multiplication;
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131 | }
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132 |
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133 | private static bool IsSubtraction(ISymbolicExpressionTreeNode node) {
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134 | return node.Symbol is Subtraction;
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135 | }
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136 |
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137 | private static bool IsAddition(ISymbolicExpressionTreeNode node) {
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138 | return node.Symbol is Addition;
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139 | }
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140 |
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141 | private static bool IsAverage(ISymbolicExpressionTreeNode node) {
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142 | return node.Symbol is Average;
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143 | }
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144 |
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145 | private static bool IsAbsolute(ISymbolicExpressionTreeNode node) {
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146 | return node.Symbol is Absolute;
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147 | }
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148 |
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149 | // exponential
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150 | private static bool IsLog(ISymbolicExpressionTreeNode node) {
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151 | return node.Symbol is Logarithm;
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152 | }
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153 |
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154 | private static bool IsExp(ISymbolicExpressionTreeNode node) {
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155 | return node.Symbol is Exponential;
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156 | }
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157 |
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158 | private static bool IsRoot(ISymbolicExpressionTreeNode node) {
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159 | return node.Symbol is Root;
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160 | }
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161 |
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162 | private static bool IsSquare(ISymbolicExpressionTreeNode node) {
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163 | return node.Symbol is Square;
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164 | }
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165 |
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166 | private static bool IsSquareRoot(ISymbolicExpressionTreeNode node) {
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167 | return node.Symbol is SquareRoot;
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168 | }
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169 |
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170 | private static bool IsCube(ISymbolicExpressionTreeNode node) {
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171 | return node.Symbol is Cube;
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172 | }
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173 |
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174 | private static bool IsCubeRoot(ISymbolicExpressionTreeNode node) {
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175 | return node.Symbol is CubeRoot;
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176 | }
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177 |
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178 | private static bool IsPower(ISymbolicExpressionTreeNode node) {
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179 | return node.Symbol is Power;
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180 | }
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181 |
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182 | // trigonometric
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183 | private static bool IsSine(ISymbolicExpressionTreeNode node) {
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184 | return node.Symbol is Sine;
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185 | }
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186 |
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187 | private static bool IsCosine(ISymbolicExpressionTreeNode node) {
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188 | return node.Symbol is Cosine;
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189 | }
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190 |
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191 | private static bool IsTangent(ISymbolicExpressionTreeNode node) {
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192 | return node.Symbol is Tangent;
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193 | }
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194 |
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195 | private static bool IsAnalyticalQuotient(ISymbolicExpressionTreeNode node) {
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196 | return node.Symbol is AnalyticQuotient;
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197 | }
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198 |
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199 | // boolean
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200 | private static bool IsIfThenElse(ISymbolicExpressionTreeNode node) {
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201 | return node.Symbol is IfThenElse;
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202 | }
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203 |
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204 | private static bool IsAnd(ISymbolicExpressionTreeNode node) {
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205 | return node.Symbol is And;
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206 | }
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207 |
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208 | private static bool IsOr(ISymbolicExpressionTreeNode node) {
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209 | return node.Symbol is Or;
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210 | }
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211 |
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212 | private static bool IsNot(ISymbolicExpressionTreeNode node) {
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213 | return node.Symbol is Not;
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214 | }
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215 |
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216 | // comparison
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217 | private static bool IsGreaterThan(ISymbolicExpressionTreeNode node) {
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218 | return node.Symbol is GreaterThan;
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219 | }
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220 |
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221 | private static bool IsLessThan(ISymbolicExpressionTreeNode node) {
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222 | return node.Symbol is LessThan;
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223 | }
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224 |
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225 | private static bool IsBoolean(ISymbolicExpressionTreeNode node) {
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226 | return
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227 | node.Symbol is GreaterThan ||
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228 | node.Symbol is LessThan ||
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229 | node.Symbol is And ||
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230 | node.Symbol is Or;
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231 | }
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232 |
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233 | // terminals
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234 | private static bool IsVariable(ISymbolicExpressionTreeNode node) {
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235 | return node.Symbol is Variable;
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236 | }
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237 |
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238 | private static bool IsVariableBase(ISymbolicExpressionTreeNode node) {
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239 | return node is VariableTreeNodeBase;
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240 | }
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241 |
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242 | private static bool IsFactor(ISymbolicExpressionTreeNode node) {
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243 | return node is FactorVariableTreeNode;
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244 | }
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245 |
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246 | private static bool IsBinFactor(ISymbolicExpressionTreeNode node) {
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247 | return node is BinaryFactorVariableTreeNode;
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248 | }
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249 |
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250 | private static bool IsConstant(ISymbolicExpressionTreeNode node) {
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251 | return node.Symbol is Constant;
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252 | }
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253 |
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254 | // dynamic
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255 | private static bool IsTimeLag(ISymbolicExpressionTreeNode node) {
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256 | return node.Symbol is TimeLag;
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257 | }
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258 |
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259 | private static bool IsIntegral(ISymbolicExpressionTreeNode node) {
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260 | return node.Symbol is Integral;
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261 | }
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262 |
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263 | private static bool IsSum(ISymbolicExpressionTreeNode node) {
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264 | return node.Symbol is Sum;
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265 | }
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266 |
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267 | private static bool IsMean(ISymbolicExpressionTreeNode node) {
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268 | return node.Symbol is Mean;
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269 | }
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270 | #endregion
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271 |
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272 | #region type predicates
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273 | public bool IsScalarNode(ISymbolicExpressionTreeNode node) {
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274 | var results = interpreter.EvaluateNode(node, problemData.Dataset, problemData.TrainingIndices);
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275 | return results.All(r => r.IsScalar);
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276 | }
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277 | public bool IsVectorNode(ISymbolicExpressionTreeNode node) {
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278 | var results = interpreter.EvaluateNode(node, problemData.Dataset, problemData.TrainingIndices);
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279 | return results.All(r => r.IsVector);
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280 | }
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281 | #endregion
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282 |
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283 | /// <summary>
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284 | /// Creates a new simplified tree
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285 | /// </summary>
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286 | /// <param name="original"></param>
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287 | /// <returns></returns>
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288 | public ISymbolicExpressionTreeNode GetSimplifiedTree(ISymbolicExpressionTreeNode original) {
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289 | if (IsConstant(original) || IsVariableBase(original)) {
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290 | return (ISymbolicExpressionTreeNode)original.Clone();
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291 | } else if (IsAbsolute(original)) {
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292 | return SimplifyAbsolute(original);
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293 | } else if (IsAddition(original)) {
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294 | return SimplifyAddition(original);
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295 | } else if (IsSubtraction(original)) {
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296 | return SimplifySubtraction(original);
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297 | } else if (IsMultiplication(original)) {
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298 | return SimplifyMultiplication(original);
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299 | } else if (IsDivision(original)) {
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300 | return SimplifyDivision(original);
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301 | } else if (IsAverage(original)) {
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302 | return SimplifyAverage(original);
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303 | } else if (IsLog(original)) {
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304 | return SimplifyLog(original);
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305 | } else if (IsExp(original)) {
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306 | return SimplifyExp(original);
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307 | } else if (IsSquare(original)) {
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308 | return SimplifySquare(original);
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309 | } else if (IsSquareRoot(original)) {
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310 | return SimplifySquareRoot(original);
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311 | } else if (IsCube(original)) {
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312 | return SimplifyCube(original);
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313 | } else if (IsCubeRoot(original)) {
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314 | return SimplifyCubeRoot(original);
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315 | } else if (IsPower(original)) {
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316 | return SimplifyPower(original);
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317 | } else if (IsRoot(original)) {
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318 | return SimplifyRoot(original);
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319 | } else if (IsSine(original)) {
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320 | return SimplifySine(original);
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321 | } else if (IsCosine(original)) {
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322 | return SimplifyCosine(original);
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323 | } else if (IsTangent(original)) {
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324 | return SimplifyTangent(original);
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325 | } else if (IsAnalyticalQuotient(original)) {
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326 | return SimplifyAnalyticalQuotient(original);
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327 | } else if (IsIfThenElse(original)) {
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328 | return SimplifyIfThenElse(original);
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329 | } else if (IsGreaterThan(original)) {
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330 | return SimplifyGreaterThan(original);
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331 | } else if (IsLessThan(original)) {
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332 | return SimplifyLessThan(original);
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333 | } else if (IsAnd(original)) {
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334 | return SimplifyAnd(original);
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335 | } else if (IsOr(original)) {
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336 | return SimplifyOr(original);
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337 | } else if (IsNot(original)) {
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338 | return SimplifyNot(original);
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339 | } else if (IsTimeLag(original)) {
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340 | return SimplifyTimeLag(original);
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341 | } else if (IsIntegral(original)) {
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342 | return SimplifyIntegral(original);
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343 | } else if (IsSum(original)) {
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344 | return SimplifySumAggregation(original);
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345 | } else if (IsMean(original)) {
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346 | return SimplifyMeanAggregation(original);
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347 | } else {
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348 | return SimplifyAny(original);
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349 | }
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350 | }
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351 |
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352 | #region specific simplification routines
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353 |
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354 | private ISymbolicExpressionTreeNode SimplifyAny(ISymbolicExpressionTreeNode original) {
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355 | // can't simplify this function but simplify all subtrees
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356 | List<ISymbolicExpressionTreeNode> subtrees = new List<ISymbolicExpressionTreeNode>(original.Subtrees);
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357 | while (original.Subtrees.Count() > 0) original.RemoveSubtree(0);
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358 | var clone = (SymbolicExpressionTreeNode)original.Clone();
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359 | List<ISymbolicExpressionTreeNode> simplifiedSubtrees = new List<ISymbolicExpressionTreeNode>();
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360 | foreach (var subtree in subtrees) {
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361 | simplifiedSubtrees.Add(GetSimplifiedTree(subtree));
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362 | original.AddSubtree(subtree);
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363 | }
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364 | foreach (var simplifiedSubtree in simplifiedSubtrees) {
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365 | clone.AddSubtree(simplifiedSubtree);
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366 | }
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367 | if (simplifiedSubtrees.TrueForAll(t => IsConstant(t))) {
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368 | SimplifyConstantExpression(clone);
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369 | }
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370 | return clone;
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371 | }
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372 |
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373 | private ISymbolicExpressionTreeNode SimplifyConstantExpression(ISymbolicExpressionTreeNode original) {
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374 | // not yet implemented
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375 | return original;
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376 | }
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377 |
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378 | private ISymbolicExpressionTreeNode SimplifyAverage(ISymbolicExpressionTreeNode original) {
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379 | if (original.Subtrees.Count() == 1) {
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380 | return GetSimplifiedTree(original.GetSubtree(0));
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381 | } else {
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382 | // simplify expressions x0..xn
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383 | // make sum(x0..xn) / n
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384 | var sum = original.Subtrees
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385 | .Select(GetSimplifiedTree)
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386 | .Aggregate(MakeSum);
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387 | return MakeFraction(sum, MakeConstant(original.Subtrees.Count()));
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388 | }
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389 | }
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390 |
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391 | private ISymbolicExpressionTreeNode SimplifyDivision(ISymbolicExpressionTreeNode original) {
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392 | if (original.Subtrees.Count() == 1) {
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393 | return Invert(GetSimplifiedTree(original.GetSubtree(0)));
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394 | } else {
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395 | // simplify expressions x0..xn
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396 | // make multiplication (x0 * 1/(x1 * x1 * .. * xn))
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397 | var first = original.GetSubtree(0);
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398 | var second = original.GetSubtree(1);
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399 | var remaining = original.Subtrees.Skip(2);
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400 | return
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401 | MakeProduct(GetSimplifiedTree(first),
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402 | Invert(remaining.Aggregate(GetSimplifiedTree(second), (a, b) => MakeProduct(a, GetSimplifiedTree(b)))));
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403 | }
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404 | }
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405 |
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406 | private ISymbolicExpressionTreeNode SimplifyMultiplication(ISymbolicExpressionTreeNode original) {
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407 | if (original.Subtrees.Count() == 1) {
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408 | return GetSimplifiedTree(original.GetSubtree(0));
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409 | } else {
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410 | return original.Subtrees
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411 | .Select(GetSimplifiedTree)
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412 | .Aggregate(MakeProduct);
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413 | }
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414 | }
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415 |
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416 | private ISymbolicExpressionTreeNode SimplifySubtraction(ISymbolicExpressionTreeNode original) {
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417 | if (original.Subtrees.Count() == 1) {
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418 | return Negate(GetSimplifiedTree(original.GetSubtree(0)));
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419 | } else {
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420 | // simplify expressions x0..xn
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421 | // make addition (x0,-x1..-xn)
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422 | var first = original.Subtrees.First();
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423 | var remaining = original.Subtrees.Skip(1);
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424 | return remaining.Aggregate(GetSimplifiedTree(first), (a, b) => MakeSum(a, Negate(GetSimplifiedTree(b))));
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425 | }
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426 | }
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427 |
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428 | private ISymbolicExpressionTreeNode SimplifyAddition(ISymbolicExpressionTreeNode original) {
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429 | if (original.Subtrees.Count() == 1) {
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430 | return GetSimplifiedTree(original.GetSubtree(0));
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431 | } else {
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432 | // simplify expression x0..xn
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433 | // make addition (x0..xn)
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434 | return original.Subtrees
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435 | .Select(GetSimplifiedTree)
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436 | .Aggregate(MakeSum);
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437 | }
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438 | }
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439 |
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440 | private ISymbolicExpressionTreeNode SimplifyAbsolute(ISymbolicExpressionTreeNode original) {
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441 | return MakeAbs(GetSimplifiedTree(original.GetSubtree(0)));
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442 | }
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443 |
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444 | private ISymbolicExpressionTreeNode SimplifyNot(ISymbolicExpressionTreeNode original) {
|
---|
445 | return MakeNot(GetSimplifiedTree(original.GetSubtree(0)));
|
---|
446 | }
|
---|
447 |
|
---|
448 | private ISymbolicExpressionTreeNode SimplifyOr(ISymbolicExpressionTreeNode original) {
|
---|
449 | return original.Subtrees
|
---|
450 | .Select(GetSimplifiedTree)
|
---|
451 | .Aggregate(MakeOr);
|
---|
452 | }
|
---|
453 |
|
---|
454 | private ISymbolicExpressionTreeNode SimplifyAnd(ISymbolicExpressionTreeNode original) {
|
---|
455 | return original.Subtrees
|
---|
456 | .Select(GetSimplifiedTree)
|
---|
457 | .Aggregate(MakeAnd);
|
---|
458 | }
|
---|
459 |
|
---|
460 | private ISymbolicExpressionTreeNode SimplifyLessThan(ISymbolicExpressionTreeNode original) {
|
---|
461 | return MakeLessThan(GetSimplifiedTree(original.GetSubtree(0)), GetSimplifiedTree(original.GetSubtree(1)));
|
---|
462 | }
|
---|
463 |
|
---|
464 | private ISymbolicExpressionTreeNode SimplifyGreaterThan(ISymbolicExpressionTreeNode original) {
|
---|
465 | return MakeGreaterThan(GetSimplifiedTree(original.GetSubtree(0)), GetSimplifiedTree(original.GetSubtree(1)));
|
---|
466 | }
|
---|
467 |
|
---|
468 | private ISymbolicExpressionTreeNode SimplifyIfThenElse(ISymbolicExpressionTreeNode original) {
|
---|
469 | return MakeIfThenElse(GetSimplifiedTree(original.GetSubtree(0)), GetSimplifiedTree(original.GetSubtree(1)),
|
---|
470 | GetSimplifiedTree(original.GetSubtree(2)));
|
---|
471 | }
|
---|
472 |
|
---|
473 | private ISymbolicExpressionTreeNode SimplifyTangent(ISymbolicExpressionTreeNode original) {
|
---|
474 | return MakeTangent(GetSimplifiedTree(original.GetSubtree(0)));
|
---|
475 | }
|
---|
476 |
|
---|
477 | private ISymbolicExpressionTreeNode SimplifyCosine(ISymbolicExpressionTreeNode original) {
|
---|
478 | return MakeCosine(GetSimplifiedTree(original.GetSubtree(0)));
|
---|
479 | }
|
---|
480 |
|
---|
481 | private ISymbolicExpressionTreeNode SimplifySine(ISymbolicExpressionTreeNode original) {
|
---|
482 | return MakeSine(GetSimplifiedTree(original.GetSubtree(0)));
|
---|
483 | }
|
---|
484 |
|
---|
485 | private ISymbolicExpressionTreeNode SimplifyExp(ISymbolicExpressionTreeNode original) {
|
---|
486 | return MakeExp(GetSimplifiedTree(original.GetSubtree(0)));
|
---|
487 | }
|
---|
488 |
|
---|
489 | private ISymbolicExpressionTreeNode SimplifySquare(ISymbolicExpressionTreeNode original) {
|
---|
490 | return MakeSquare(GetSimplifiedTree(original.GetSubtree(0)));
|
---|
491 | }
|
---|
492 |
|
---|
493 | private ISymbolicExpressionTreeNode SimplifySquareRoot(ISymbolicExpressionTreeNode original) {
|
---|
494 | return MakeSquareRoot(GetSimplifiedTree(original.GetSubtree(0)));
|
---|
495 | }
|
---|
496 | private ISymbolicExpressionTreeNode SimplifyCube(ISymbolicExpressionTreeNode original) {
|
---|
497 | return MakeCube(GetSimplifiedTree(original.GetSubtree(0)));
|
---|
498 | }
|
---|
499 |
|
---|
500 | private ISymbolicExpressionTreeNode SimplifyCubeRoot(ISymbolicExpressionTreeNode original) {
|
---|
501 | return MakeCubeRoot(GetSimplifiedTree(original.GetSubtree(0)));
|
---|
502 | }
|
---|
503 |
|
---|
504 | private ISymbolicExpressionTreeNode SimplifyLog(ISymbolicExpressionTreeNode original) {
|
---|
505 | return MakeLog(GetSimplifiedTree(original.GetSubtree(0)));
|
---|
506 | }
|
---|
507 |
|
---|
508 | private ISymbolicExpressionTreeNode SimplifyRoot(ISymbolicExpressionTreeNode original) {
|
---|
509 | return MakeRoot(GetSimplifiedTree(original.GetSubtree(0)), GetSimplifiedTree(original.GetSubtree(1)));
|
---|
510 | }
|
---|
511 |
|
---|
512 | private ISymbolicExpressionTreeNode SimplifyPower(ISymbolicExpressionTreeNode original) {
|
---|
513 | return MakePower(GetSimplifiedTree(original.GetSubtree(0)), GetSimplifiedTree(original.GetSubtree(1)));
|
---|
514 | }
|
---|
515 |
|
---|
516 | private ISymbolicExpressionTreeNode SimplifyAnalyticalQuotient(ISymbolicExpressionTreeNode original) {
|
---|
517 | return MakeAnalyticalQuotient(GetSimplifiedTree(original.GetSubtree(0)), GetSimplifiedTree(original.GetSubtree(1)));
|
---|
518 | }
|
---|
519 |
|
---|
520 | private ISymbolicExpressionTreeNode SimplifyTimeLag(ISymbolicExpressionTreeNode original) {
|
---|
521 | var laggedTreeNode = original as ILaggedTreeNode;
|
---|
522 | var simplifiedSubtree = GetSimplifiedTree(original.GetSubtree(0));
|
---|
523 | if (!ContainsVariableCondition(simplifiedSubtree)) {
|
---|
524 | return AddLagToDynamicNodes(simplifiedSubtree, laggedTreeNode.Lag);
|
---|
525 | } else {
|
---|
526 | return MakeTimeLag(simplifiedSubtree, laggedTreeNode.Lag);
|
---|
527 | }
|
---|
528 | }
|
---|
529 |
|
---|
530 | private ISymbolicExpressionTreeNode SimplifyIntegral(ISymbolicExpressionTreeNode original) {
|
---|
531 | var laggedTreeNode = original as ILaggedTreeNode;
|
---|
532 | var simplifiedSubtree = GetSimplifiedTree(original.GetSubtree(0));
|
---|
533 | if (IsConstant(simplifiedSubtree)) {
|
---|
534 | return GetSimplifiedTree(MakeProduct(simplifiedSubtree, MakeConstant(-laggedTreeNode.Lag)));
|
---|
535 | } else {
|
---|
536 | return MakeIntegral(simplifiedSubtree, laggedTreeNode.Lag);
|
---|
537 | }
|
---|
538 | }
|
---|
539 |
|
---|
540 | private ISymbolicExpressionTreeNode SimplifySumAggregation(ISymbolicExpressionTreeNode original) {
|
---|
541 | return MakeSumAggregation(GetSimplifiedTree(original.GetSubtree(0)));
|
---|
542 | }
|
---|
543 |
|
---|
544 | private ISymbolicExpressionTreeNode SimplifyMeanAggregation(ISymbolicExpressionTreeNode original) {
|
---|
545 | return MakeMeanAggregation(GetSimplifiedTree(original.GetSubtree(0)));
|
---|
546 | }
|
---|
547 |
|
---|
548 | #endregion
|
---|
549 |
|
---|
550 | #region low level tree restructuring
|
---|
551 |
|
---|
552 | private ISymbolicExpressionTreeNode MakeTimeLag(ISymbolicExpressionTreeNode subtree, int lag) {
|
---|
553 | if (lag == 0) return subtree;
|
---|
554 | if (IsConstant(subtree)) return subtree;
|
---|
555 | var lagNode = (LaggedTreeNode)timeLagSymbol.CreateTreeNode();
|
---|
556 | lagNode.Lag = lag;
|
---|
557 | lagNode.AddSubtree(subtree);
|
---|
558 | return lagNode;
|
---|
559 | }
|
---|
560 |
|
---|
561 | private ISymbolicExpressionTreeNode MakeIntegral(ISymbolicExpressionTreeNode subtree, int lag) {
|
---|
562 | if (lag == 0) return subtree;
|
---|
563 | else if (lag == -1 || lag == 1) {
|
---|
564 | return MakeSum(subtree, AddLagToDynamicNodes((ISymbolicExpressionTreeNode)subtree.Clone(), lag));
|
---|
565 | } else {
|
---|
566 | var node = (LaggedTreeNode)integralSymbol.CreateTreeNode();
|
---|
567 | node.Lag = lag;
|
---|
568 | node.AddSubtree(subtree);
|
---|
569 | return node;
|
---|
570 | }
|
---|
571 | }
|
---|
572 |
|
---|
573 | private ISymbolicExpressionTreeNode MakeNot(ISymbolicExpressionTreeNode t) {
|
---|
574 | if (IsConstant(t)) {
|
---|
575 | var constNode = t as ConstantTreeNode;
|
---|
576 | if (constNode.Value > 0) return MakeConstant(-1.0);
|
---|
577 | else return MakeConstant(1.0);
|
---|
578 | } else if (IsNot(t)) {
|
---|
579 | return t.GetSubtree(0);
|
---|
580 | } else if (!IsBoolean(t)) {
|
---|
581 | var gtNode = gtSymbol.CreateTreeNode();
|
---|
582 | gtNode.AddSubtree(t);
|
---|
583 | gtNode.AddSubtree(MakeConstant(0.0));
|
---|
584 | var notNode = notSymbol.CreateTreeNode();
|
---|
585 | notNode.AddSubtree(gtNode);
|
---|
586 | return notNode;
|
---|
587 | } else {
|
---|
588 | var notNode = notSymbol.CreateTreeNode();
|
---|
589 | notNode.AddSubtree(t);
|
---|
590 | return notNode;
|
---|
591 | }
|
---|
592 | }
|
---|
593 |
|
---|
594 | private ISymbolicExpressionTreeNode MakeOr(ISymbolicExpressionTreeNode a, ISymbolicExpressionTreeNode b) {
|
---|
595 | if (IsConstant(a) && IsConstant(b)) {
|
---|
596 | var constA = a as ConstantTreeNode;
|
---|
597 | var constB = b as ConstantTreeNode;
|
---|
598 | if (constA.Value > 0.0 || constB.Value > 0.0) {
|
---|
599 | return MakeConstant(1.0);
|
---|
600 | } else {
|
---|
601 | return MakeConstant(-1.0);
|
---|
602 | }
|
---|
603 | } else if (IsConstant(a)) {
|
---|
604 | return MakeOr(b, a);
|
---|
605 | } else if (IsConstant(b)) {
|
---|
606 | var constT = b as ConstantTreeNode;
|
---|
607 | if (constT.Value > 0.0) {
|
---|
608 | // boolean expression is necessarily true
|
---|
609 | return MakeConstant(1.0);
|
---|
610 | } else {
|
---|
611 | // the constant value has no effect on the result of the boolean condition so we can drop the constant term
|
---|
612 | var orNode = orSymbol.CreateTreeNode();
|
---|
613 | orNode.AddSubtree(a);
|
---|
614 | return orNode;
|
---|
615 | }
|
---|
616 | } else {
|
---|
617 | var orNode = orSymbol.CreateTreeNode();
|
---|
618 | orNode.AddSubtree(a);
|
---|
619 | orNode.AddSubtree(b);
|
---|
620 | return orNode;
|
---|
621 | }
|
---|
622 | }
|
---|
623 |
|
---|
624 | private ISymbolicExpressionTreeNode MakeAnd(ISymbolicExpressionTreeNode a, ISymbolicExpressionTreeNode b) {
|
---|
625 | if (IsConstant(a) && IsConstant(b)) {
|
---|
626 | var constA = a as ConstantTreeNode;
|
---|
627 | var constB = b as ConstantTreeNode;
|
---|
628 | if (constA.Value > 0.0 && constB.Value > 0.0) {
|
---|
629 | return MakeConstant(1.0);
|
---|
630 | } else {
|
---|
631 | return MakeConstant(-1.0);
|
---|
632 | }
|
---|
633 | } else if (IsConstant(a)) {
|
---|
634 | return MakeAnd(b, a);
|
---|
635 | } else if (IsConstant(b)) {
|
---|
636 | var constB = b as ConstantTreeNode;
|
---|
637 | if (constB.Value > 0.0) {
|
---|
638 | // the constant value has no effect on the result of the boolean condition so we can drop the constant term
|
---|
639 | var andNode = andSymbol.CreateTreeNode();
|
---|
640 | andNode.AddSubtree(a);
|
---|
641 | return andNode;
|
---|
642 | } else {
|
---|
643 | // boolean expression is necessarily false
|
---|
644 | return MakeConstant(-1.0);
|
---|
645 | }
|
---|
646 | } else {
|
---|
647 | var andNode = andSymbol.CreateTreeNode();
|
---|
648 | andNode.AddSubtree(a);
|
---|
649 | andNode.AddSubtree(b);
|
---|
650 | return andNode;
|
---|
651 | }
|
---|
652 | }
|
---|
653 |
|
---|
654 | private ISymbolicExpressionTreeNode MakeLessThan(ISymbolicExpressionTreeNode leftSide,
|
---|
655 | ISymbolicExpressionTreeNode rightSide) {
|
---|
656 | if (IsConstant(leftSide) && IsConstant(rightSide)) {
|
---|
657 | var lsConst = leftSide as ConstantTreeNode;
|
---|
658 | var rsConst = rightSide as ConstantTreeNode;
|
---|
659 | if (lsConst.Value < rsConst.Value) return MakeConstant(1.0);
|
---|
660 | else return MakeConstant(-1.0);
|
---|
661 | } else {
|
---|
662 | var ltNode = ltSymbol.CreateTreeNode();
|
---|
663 | ltNode.AddSubtree(leftSide);
|
---|
664 | ltNode.AddSubtree(rightSide);
|
---|
665 | return ltNode;
|
---|
666 | }
|
---|
667 | }
|
---|
668 |
|
---|
669 | private ISymbolicExpressionTreeNode MakeGreaterThan(ISymbolicExpressionTreeNode leftSide,
|
---|
670 | ISymbolicExpressionTreeNode rightSide) {
|
---|
671 | if (IsConstant(leftSide) && IsConstant(rightSide)) {
|
---|
672 | var lsConst = leftSide as ConstantTreeNode;
|
---|
673 | var rsConst = rightSide as ConstantTreeNode;
|
---|
674 | if (lsConst.Value > rsConst.Value) return MakeConstant(1.0);
|
---|
675 | else return MakeConstant(-1.0);
|
---|
676 | } else {
|
---|
677 | var gtNode = gtSymbol.CreateTreeNode();
|
---|
678 | gtNode.AddSubtree(leftSide);
|
---|
679 | gtNode.AddSubtree(rightSide);
|
---|
680 | return gtNode;
|
---|
681 | }
|
---|
682 | }
|
---|
683 |
|
---|
684 | private ISymbolicExpressionTreeNode MakeIfThenElse(ISymbolicExpressionTreeNode condition,
|
---|
685 | ISymbolicExpressionTreeNode trueBranch, ISymbolicExpressionTreeNode falseBranch) {
|
---|
686 | if (IsConstant(condition)) {
|
---|
687 | var constT = condition as ConstantTreeNode;
|
---|
688 | if (constT.Value > 0.0) return trueBranch;
|
---|
689 | else return falseBranch;
|
---|
690 | } else {
|
---|
691 | var ifNode = ifThenElseSymbol.CreateTreeNode();
|
---|
692 | if (IsBoolean(condition)) {
|
---|
693 | ifNode.AddSubtree(condition);
|
---|
694 | } else {
|
---|
695 | var gtNode = gtSymbol.CreateTreeNode();
|
---|
696 | gtNode.AddSubtree(condition);
|
---|
697 | gtNode.AddSubtree(MakeConstant(0.0));
|
---|
698 | ifNode.AddSubtree(gtNode);
|
---|
699 | }
|
---|
700 | ifNode.AddSubtree(trueBranch);
|
---|
701 | ifNode.AddSubtree(falseBranch);
|
---|
702 | return ifNode;
|
---|
703 | }
|
---|
704 | }
|
---|
705 |
|
---|
706 | private ISymbolicExpressionTreeNode MakeSine(ISymbolicExpressionTreeNode node) {
|
---|
707 | if (IsConstant(node)) {
|
---|
708 | var constT = node as ConstantTreeNode;
|
---|
709 | return MakeConstant(Math.Sin(constT.Value));
|
---|
710 | } else if (IsFactor(node)) {
|
---|
711 | var factor = node as FactorVariableTreeNode;
|
---|
712 | return MakeFactor(factor.Symbol, factor.VariableName, factor.Weights.Select(Math.Sin));
|
---|
713 | } else if (IsBinFactor(node)) {
|
---|
714 | var binFactor = node as BinaryFactorVariableTreeNode;
|
---|
715 | return MakeBinFactor(binFactor.Symbol, binFactor.VariableName, binFactor.VariableValue, Math.Sin(binFactor.Weight));
|
---|
716 | } else {
|
---|
717 | var sineNode = sineSymbol.CreateTreeNode();
|
---|
718 | sineNode.AddSubtree(node);
|
---|
719 | return sineNode;
|
---|
720 | }
|
---|
721 | }
|
---|
722 |
|
---|
723 | private ISymbolicExpressionTreeNode MakeTangent(ISymbolicExpressionTreeNode node) {
|
---|
724 | if (IsConstant(node)) {
|
---|
725 | var constT = node as ConstantTreeNode;
|
---|
726 | return MakeConstant(Math.Tan(constT.Value));
|
---|
727 | } else if (IsFactor(node)) {
|
---|
728 | var factor = node as FactorVariableTreeNode;
|
---|
729 | return MakeFactor(factor.Symbol, factor.VariableName, factor.Weights.Select(Math.Tan));
|
---|
730 | } else if (IsBinFactor(node)) {
|
---|
731 | var binFactor = node as BinaryFactorVariableTreeNode;
|
---|
732 | return MakeBinFactor(binFactor.Symbol, binFactor.VariableName, binFactor.VariableValue, Math.Tan(binFactor.Weight));
|
---|
733 | } else {
|
---|
734 | var tanNode = tanSymbol.CreateTreeNode();
|
---|
735 | tanNode.AddSubtree(node);
|
---|
736 | return tanNode;
|
---|
737 | }
|
---|
738 | }
|
---|
739 |
|
---|
740 | private ISymbolicExpressionTreeNode MakeCosine(ISymbolicExpressionTreeNode node) {
|
---|
741 | if (IsConstant(node)) {
|
---|
742 | var constT = node as ConstantTreeNode;
|
---|
743 | return MakeConstant(Math.Cos(constT.Value));
|
---|
744 | } else if (IsFactor(node)) {
|
---|
745 | var factor = node as FactorVariableTreeNode;
|
---|
746 | return MakeFactor(factor.Symbol, factor.VariableName, factor.Weights.Select(Math.Cos));
|
---|
747 | } else if (IsBinFactor(node)) {
|
---|
748 | var binFactor = node as BinaryFactorVariableTreeNode;
|
---|
749 | // cos(0) = 1 see similar case for Exp(binfactor)
|
---|
750 | return MakeSum(MakeBinFactor(binFactor.Symbol, binFactor.VariableName, binFactor.VariableValue, Math.Cos(binFactor.Weight) - 1),
|
---|
751 | MakeConstant(1.0));
|
---|
752 | } else {
|
---|
753 | var cosNode = cosineSymbol.CreateTreeNode();
|
---|
754 | cosNode.AddSubtree(node);
|
---|
755 | return cosNode;
|
---|
756 | }
|
---|
757 | }
|
---|
758 |
|
---|
759 | private ISymbolicExpressionTreeNode MakeExp(ISymbolicExpressionTreeNode node) {
|
---|
760 | if (IsConstant(node)) {
|
---|
761 | var constT = node as ConstantTreeNode;
|
---|
762 | return MakeConstant(Math.Exp(constT.Value));
|
---|
763 | } else if (IsFactor(node)) {
|
---|
764 | var factNode = node as FactorVariableTreeNode;
|
---|
765 | return MakeFactor(factNode.Symbol, factNode.VariableName, factNode.Weights.Select(w => Math.Exp(w)));
|
---|
766 | } else if (IsBinFactor(node)) {
|
---|
767 | // exp( binfactor w val=a) = if(val=a) exp(w) else exp(0) = binfactor( (exp(w) - 1) val a) + 1
|
---|
768 | var binFactor = node as BinaryFactorVariableTreeNode;
|
---|
769 | return
|
---|
770 | MakeSum(MakeBinFactor(binFactor.Symbol, binFactor.VariableName, binFactor.VariableValue, Math.Exp(binFactor.Weight) - 1), MakeConstant(1.0));
|
---|
771 | } else if (IsLog(node)) {
|
---|
772 | return node.GetSubtree(0);
|
---|
773 | } else if (IsAddition(node)) {
|
---|
774 | return node.Subtrees.Select(s => MakeExp(s)).Aggregate((s, t) => MakeProduct(s, t));
|
---|
775 | } else if (IsSubtraction(node)) {
|
---|
776 | return node.Subtrees.Select(s => MakeExp(s)).Aggregate((s, t) => MakeProduct(s, Negate(t)));
|
---|
777 | } else {
|
---|
778 | var expNode = expSymbol.CreateTreeNode();
|
---|
779 | expNode.AddSubtree(node);
|
---|
780 | return expNode;
|
---|
781 | }
|
---|
782 | }
|
---|
783 | private ISymbolicExpressionTreeNode MakeLog(ISymbolicExpressionTreeNode node) {
|
---|
784 | if (IsConstant(node)) {
|
---|
785 | var constT = node as ConstantTreeNode;
|
---|
786 | return MakeConstant(Math.Log(constT.Value));
|
---|
787 | } else if (IsFactor(node)) {
|
---|
788 | var factNode = node as FactorVariableTreeNode;
|
---|
789 | return MakeFactor(factNode.Symbol, factNode.VariableName, factNode.Weights.Select(w => Math.Log(w)));
|
---|
790 | } else if (IsExp(node)) {
|
---|
791 | return node.GetSubtree(0);
|
---|
792 | } else if (IsSquareRoot(node)) {
|
---|
793 | return MakeFraction(MakeLog(node.GetSubtree(0)), MakeConstant(2.0));
|
---|
794 | } else {
|
---|
795 | var logNode = logSymbol.CreateTreeNode();
|
---|
796 | logNode.AddSubtree(node);
|
---|
797 | return logNode;
|
---|
798 | }
|
---|
799 | }
|
---|
800 |
|
---|
801 | private ISymbolicExpressionTreeNode MakeSquare(ISymbolicExpressionTreeNode node) {
|
---|
802 | if (IsConstant(node)) {
|
---|
803 | var constT = node as ConstantTreeNode;
|
---|
804 | return MakeConstant(constT.Value * constT.Value);
|
---|
805 | } else if (IsFactor(node)) {
|
---|
806 | var factNode = node as FactorVariableTreeNode;
|
---|
807 | return MakeFactor(factNode.Symbol, factNode.VariableName, factNode.Weights.Select(w => w * w));
|
---|
808 | } else if (IsBinFactor(node)) {
|
---|
809 | var binFactor = node as BinaryFactorVariableTreeNode;
|
---|
810 | return MakeBinFactor(binFactor.Symbol, binFactor.VariableName, binFactor.VariableValue, binFactor.Weight * binFactor.Weight);
|
---|
811 | } else if (IsSquareRoot(node)) {
|
---|
812 | return node.GetSubtree(0);
|
---|
813 | } else if (IsMultiplication(node)) {
|
---|
814 | // sqr( x * y ) = sqr(x) * sqr(y)
|
---|
815 | var mulNode = mulSymbol.CreateTreeNode();
|
---|
816 | foreach (var subtree in node.Subtrees) {
|
---|
817 | mulNode.AddSubtree(MakeSquare(subtree));
|
---|
818 | }
|
---|
819 | return mulNode;
|
---|
820 | } else if (IsAbsolute(node)) {
|
---|
821 | return MakeSquare(node.GetSubtree(0)); // sqr(abs(x)) = sqr(x)
|
---|
822 | } else if (IsExp(node)) {
|
---|
823 | return MakeExp(MakeProduct(node.GetSubtree(0), MakeConstant(2.0))); // sqr(exp(x)) = exp(2x)
|
---|
824 | } else if (IsCube(node)) {
|
---|
825 | return MakePower(node.GetSubtree(0), MakeConstant(6));
|
---|
826 | } else {
|
---|
827 | var sqrNode = sqrSymbol.CreateTreeNode();
|
---|
828 | sqrNode.AddSubtree(node);
|
---|
829 | return sqrNode;
|
---|
830 | }
|
---|
831 | }
|
---|
832 |
|
---|
833 | private ISymbolicExpressionTreeNode MakeCube(ISymbolicExpressionTreeNode node) {
|
---|
834 | if (IsConstant(node)) {
|
---|
835 | var constT = node as ConstantTreeNode;
|
---|
836 | return MakeConstant(constT.Value * constT.Value * constT.Value);
|
---|
837 | } else if (IsFactor(node)) {
|
---|
838 | var factNode = node as FactorVariableTreeNode;
|
---|
839 | return MakeFactor(factNode.Symbol, factNode.VariableName, factNode.Weights.Select(w => w * w * w));
|
---|
840 | } else if (IsBinFactor(node)) {
|
---|
841 | var binFactor = node as BinaryFactorVariableTreeNode;
|
---|
842 | return MakeBinFactor(binFactor.Symbol, binFactor.VariableName, binFactor.VariableValue, binFactor.Weight * binFactor.Weight * binFactor.Weight);
|
---|
843 | } else if (IsCubeRoot(node)) {
|
---|
844 | return node.GetSubtree(0); // NOTE: not really accurate because cuberoot(x) with negative x is evaluated to NaN and after this simplification we evaluate as x
|
---|
845 | } else if (IsExp(node)) {
|
---|
846 | return MakeExp(MakeProduct(node.GetSubtree(0), MakeConstant(3)));
|
---|
847 | } else if (IsSquare(node)) {
|
---|
848 | return MakePower(node.GetSubtree(0), MakeConstant(6));
|
---|
849 | } else {
|
---|
850 | var cubeNode = cubeSymbol.CreateTreeNode();
|
---|
851 | cubeNode.AddSubtree(node);
|
---|
852 | return cubeNode;
|
---|
853 | }
|
---|
854 | }
|
---|
855 |
|
---|
856 | private ISymbolicExpressionTreeNode MakeAbs(ISymbolicExpressionTreeNode node) {
|
---|
857 | if (IsConstant(node)) {
|
---|
858 | var constT = node as ConstantTreeNode;
|
---|
859 | return MakeConstant(Math.Abs(constT.Value));
|
---|
860 | } else if (IsFactor(node)) {
|
---|
861 | var factNode = node as FactorVariableTreeNode;
|
---|
862 | return MakeFactor(factNode.Symbol, factNode.VariableName, factNode.Weights.Select(w => Math.Abs(w)));
|
---|
863 | } else if (IsBinFactor(node)) {
|
---|
864 | var binFactor = node as BinaryFactorVariableTreeNode;
|
---|
865 | return MakeBinFactor(binFactor.Symbol, binFactor.VariableName, binFactor.VariableValue, Math.Abs(binFactor.Weight));
|
---|
866 | } else if (IsSquare(node) || IsExp(node) || IsSquareRoot(node) || IsCubeRoot(node)) {
|
---|
867 | return node; // abs(sqr(x)) = sqr(x), abs(exp(x)) = exp(x) ...
|
---|
868 | } else if (IsMultiplication(node)) {
|
---|
869 | var mul = mulSymbol.CreateTreeNode();
|
---|
870 | foreach (var st in node.Subtrees) {
|
---|
871 | mul.AddSubtree(MakeAbs(st));
|
---|
872 | }
|
---|
873 | return mul;
|
---|
874 | } else if (IsDivision(node)) {
|
---|
875 | var div = divSymbol.CreateTreeNode();
|
---|
876 | foreach (var st in node.Subtrees) {
|
---|
877 | div.AddSubtree(MakeAbs(st));
|
---|
878 | }
|
---|
879 | return div;
|
---|
880 | } else {
|
---|
881 | var absNode = absSymbol.CreateTreeNode();
|
---|
882 | absNode.AddSubtree(node);
|
---|
883 | return absNode;
|
---|
884 | }
|
---|
885 | }
|
---|
886 |
|
---|
887 | // constant folding only
|
---|
888 | private ISymbolicExpressionTreeNode MakeAnalyticalQuotient(ISymbolicExpressionTreeNode a, ISymbolicExpressionTreeNode b) {
|
---|
889 | if (IsConstant(b)) {
|
---|
890 | var c = b as ConstantTreeNode;
|
---|
891 | return MakeFraction(a, MakeConstant(Math.Sqrt(1.0 + c.Value * c.Value)));
|
---|
892 | } else if (IsFactor(b)) {
|
---|
893 | var factNode = b as FactorVariableTreeNode;
|
---|
894 | return MakeFraction(a, MakeFactor(factNode.Symbol, factNode.VariableName, factNode.Weights.Select(w => Math.Sqrt(1.0 + w * w))));
|
---|
895 | } else if (IsBinFactor(b)) {
|
---|
896 | var binFactor = b as BinaryFactorVariableTreeNode;
|
---|
897 | return MakeFraction(a, MakeBinFactor(binFactor.Symbol, binFactor.VariableName, binFactor.VariableValue, Math.Sqrt(1.0 + binFactor.Weight * binFactor.Weight)));
|
---|
898 | } else {
|
---|
899 | var aqNode = aqSymbol.CreateTreeNode();
|
---|
900 | aqNode.AddSubtree(a);
|
---|
901 | aqNode.AddSubtree(b);
|
---|
902 | return aqNode;
|
---|
903 | }
|
---|
904 | }
|
---|
905 |
|
---|
906 | private ISymbolicExpressionTreeNode MakeSquareRoot(ISymbolicExpressionTreeNode node) {
|
---|
907 | if (IsConstant(node)) {
|
---|
908 | var constT = node as ConstantTreeNode;
|
---|
909 | return MakeConstant(Math.Sqrt(constT.Value));
|
---|
910 | } else if (IsFactor(node)) {
|
---|
911 | var factNode = node as FactorVariableTreeNode;
|
---|
912 | return MakeFactor(factNode.Symbol, factNode.VariableName, factNode.Weights.Select(w => Math.Sqrt(w)));
|
---|
913 | } else if (IsBinFactor(node)) {
|
---|
914 | var binFactor = node as BinaryFactorVariableTreeNode;
|
---|
915 | return MakeBinFactor(binFactor.Symbol, binFactor.VariableName, binFactor.VariableValue, Math.Sqrt(binFactor.Weight));
|
---|
916 | } else if (IsSquare(node)) {
|
---|
917 | return node.GetSubtree(0); // NOTE: not really accurate because sqrt(x) with negative x is evaluated to NaN and after this simplification we evaluate as x
|
---|
918 | } else {
|
---|
919 | var sqrtNode = sqrtSymbol.CreateTreeNode();
|
---|
920 | sqrtNode.AddSubtree(node);
|
---|
921 | return sqrtNode;
|
---|
922 | }
|
---|
923 | }
|
---|
924 |
|
---|
925 | private ISymbolicExpressionTreeNode MakeCubeRoot(ISymbolicExpressionTreeNode node) {
|
---|
926 | if (IsConstant(node)) {
|
---|
927 | var constT = node as ConstantTreeNode;
|
---|
928 | return MakeConstant(Math.Pow(constT.Value, 1.0 / 3.0));
|
---|
929 | } else if (IsFactor(node)) {
|
---|
930 | var factNode = node as FactorVariableTreeNode;
|
---|
931 | return MakeFactor(factNode.Symbol, factNode.VariableName, factNode.Weights.Select(w => Math.Pow(w, 1.0 / 3.0)));
|
---|
932 | } else if (IsBinFactor(node)) {
|
---|
933 | var binFactor = node as BinaryFactorVariableTreeNode;
|
---|
934 | return MakeBinFactor(binFactor.Symbol, binFactor.VariableName, binFactor.VariableValue, Math.Sqrt(Math.Pow(binFactor.Weight, 1.0 / 3.0)));
|
---|
935 | } else if (IsCube(node)) {
|
---|
936 | return node.GetSubtree(0);
|
---|
937 | } else {
|
---|
938 | var cubeRootNode = cubeRootSymbol.CreateTreeNode();
|
---|
939 | cubeRootNode.AddSubtree(node);
|
---|
940 | return cubeRootNode;
|
---|
941 | }
|
---|
942 | }
|
---|
943 |
|
---|
944 | private ISymbolicExpressionTreeNode MakeRoot(ISymbolicExpressionTreeNode a, ISymbolicExpressionTreeNode b) {
|
---|
945 | if (IsConstant(a) && IsConstant(b)) {
|
---|
946 | var constA = a as ConstantTreeNode;
|
---|
947 | var constB = b as ConstantTreeNode;
|
---|
948 | return MakeConstant(Math.Pow(constA.Value, 1.0 / Math.Round(constB.Value)));
|
---|
949 | } else if (IsFactor(a) && IsConstant(b)) {
|
---|
950 | var factNode = a as FactorVariableTreeNode;
|
---|
951 | var constNode = b as ConstantTreeNode;
|
---|
952 | return MakeFactor(factNode.Symbol, factNode.VariableName,
|
---|
953 | factNode.Weights.Select(w => Math.Pow(w, 1.0 / Math.Round(constNode.Value))));
|
---|
954 | } else if (IsBinFactor(a) && IsConstant(b)) {
|
---|
955 | var binFactor = a as BinaryFactorVariableTreeNode;
|
---|
956 | var constNode = b as ConstantTreeNode;
|
---|
957 | return MakeBinFactor(binFactor.Symbol, binFactor.VariableName, binFactor.VariableValue, Math.Pow(binFactor.Weight, 1.0 / Math.Round(constNode.Value)));
|
---|
958 | } else if (IsConstant(a) && IsFactor(b)) {
|
---|
959 | var constNode = a as ConstantTreeNode;
|
---|
960 | var factNode = b as FactorVariableTreeNode;
|
---|
961 | return MakeFactor(factNode.Symbol, factNode.VariableName, factNode.Weights.Select(w => Math.Pow(constNode.Value, 1.0 / Math.Round(w))));
|
---|
962 | } else if (IsConstant(a) && IsBinFactor(b)) {
|
---|
963 | var constNode = a as ConstantTreeNode;
|
---|
964 | var factNode = b as BinaryFactorVariableTreeNode;
|
---|
965 | return MakeBinFactor(factNode.Symbol, factNode.VariableName, factNode.VariableValue, Math.Pow(constNode.Value, 1.0 / Math.Round(factNode.Weight)));
|
---|
966 | } else if (IsFactor(a) && IsFactor(b) && AreSameTypeAndVariable(a, b)) {
|
---|
967 | var node0 = a as FactorVariableTreeNode;
|
---|
968 | var node1 = b as FactorVariableTreeNode;
|
---|
969 | return MakeFactor(node0.Symbol, node0.VariableName, node0.Weights.Zip(node1.Weights, (u, v) => Math.Pow(u, 1.0 / Math.Round(v))));
|
---|
970 | } else if (IsConstant(b)) {
|
---|
971 | var constB = b as ConstantTreeNode;
|
---|
972 | var constBValue = Math.Round(constB.Value);
|
---|
973 | if (constBValue.IsAlmost(1.0)) {
|
---|
974 | return a;
|
---|
975 | } else if (constBValue.IsAlmost(0.0)) {
|
---|
976 | return MakeConstant(1.0);
|
---|
977 | } else if (constBValue.IsAlmost(-1.0)) {
|
---|
978 | return MakeFraction(MakeConstant(1.0), a);
|
---|
979 | } else if (constBValue < 0) {
|
---|
980 | var rootNode = rootSymbol.CreateTreeNode();
|
---|
981 | rootNode.AddSubtree(a);
|
---|
982 | rootNode.AddSubtree(MakeConstant(-1.0 * constBValue));
|
---|
983 | return MakeFraction(MakeConstant(1.0), rootNode);
|
---|
984 | } else {
|
---|
985 | var rootNode = rootSymbol.CreateTreeNode();
|
---|
986 | rootNode.AddSubtree(a);
|
---|
987 | rootNode.AddSubtree(MakeConstant(constBValue));
|
---|
988 | return rootNode;
|
---|
989 | }
|
---|
990 | } else {
|
---|
991 | var rootNode = rootSymbol.CreateTreeNode();
|
---|
992 | rootNode.AddSubtree(a);
|
---|
993 | rootNode.AddSubtree(b);
|
---|
994 | return rootNode;
|
---|
995 | }
|
---|
996 | }
|
---|
997 |
|
---|
998 |
|
---|
999 | private ISymbolicExpressionTreeNode MakePower(ISymbolicExpressionTreeNode a, ISymbolicExpressionTreeNode b) {
|
---|
1000 | if (IsConstant(a) && IsConstant(b)) {
|
---|
1001 | var constA = a as ConstantTreeNode;
|
---|
1002 | var constB = b as ConstantTreeNode;
|
---|
1003 | return MakeConstant(Math.Pow(constA.Value, Math.Round(constB.Value)));
|
---|
1004 | } else if (IsFactor(a) && IsConstant(b)) {
|
---|
1005 | var factNode = a as FactorVariableTreeNode;
|
---|
1006 | var constNode = b as ConstantTreeNode;
|
---|
1007 | return MakeFactor(factNode.Symbol, factNode.VariableName, factNode.Weights.Select(w => Math.Pow(w, Math.Round(constNode.Value))));
|
---|
1008 | } else if (IsBinFactor(a) && IsConstant(b)) {
|
---|
1009 | var binFactor = a as BinaryFactorVariableTreeNode;
|
---|
1010 | var constNode = b as ConstantTreeNode;
|
---|
1011 | return MakeBinFactor(binFactor.Symbol, binFactor.VariableName, binFactor.VariableValue, Math.Pow(binFactor.Weight, Math.Round(constNode.Value)));
|
---|
1012 | } else if (IsConstant(a) && IsFactor(b)) {
|
---|
1013 | var constNode = a as ConstantTreeNode;
|
---|
1014 | var factNode = b as FactorVariableTreeNode;
|
---|
1015 | return MakeFactor(factNode.Symbol, factNode.VariableName, factNode.Weights.Select(w => Math.Pow(constNode.Value, Math.Round(w))));
|
---|
1016 | } else if (IsConstant(a) && IsBinFactor(b)) {
|
---|
1017 | var constNode = a as ConstantTreeNode;
|
---|
1018 | var factNode = b as BinaryFactorVariableTreeNode;
|
---|
1019 | return MakeBinFactor(factNode.Symbol, factNode.VariableName, factNode.VariableValue, Math.Pow(constNode.Value, Math.Round(factNode.Weight)));
|
---|
1020 | } else if (IsFactor(a) && IsFactor(b) && AreSameTypeAndVariable(a, b)) {
|
---|
1021 | var node0 = a as FactorVariableTreeNode;
|
---|
1022 | var node1 = b as FactorVariableTreeNode;
|
---|
1023 | return MakeFactor(node0.Symbol, node0.VariableName, node0.Weights.Zip(node1.Weights, (u, v) => Math.Pow(u, Math.Round(v))));
|
---|
1024 | } else if (IsConstant(b)) {
|
---|
1025 | var constB = b as ConstantTreeNode;
|
---|
1026 | double exponent = Math.Round(constB.Value);
|
---|
1027 | if (exponent.IsAlmost(0.0)) {
|
---|
1028 | return MakeConstant(1.0);
|
---|
1029 | } else if (exponent.IsAlmost(1.0)) {
|
---|
1030 | return a;
|
---|
1031 | } else if (exponent.IsAlmost(-1.0)) {
|
---|
1032 | return MakeFraction(MakeConstant(1.0), a);
|
---|
1033 | } else if (exponent < 0) {
|
---|
1034 | var powNode = powSymbol.CreateTreeNode();
|
---|
1035 | powNode.AddSubtree(a);
|
---|
1036 | powNode.AddSubtree(MakeConstant(-1.0 * exponent));
|
---|
1037 | return MakeFraction(MakeConstant(1.0), powNode);
|
---|
1038 | } else {
|
---|
1039 | var powNode = powSymbol.CreateTreeNode();
|
---|
1040 | powNode.AddSubtree(a);
|
---|
1041 | powNode.AddSubtree(MakeConstant(exponent));
|
---|
1042 | return powNode;
|
---|
1043 | }
|
---|
1044 | } else {
|
---|
1045 | var powNode = powSymbol.CreateTreeNode();
|
---|
1046 | powNode.AddSubtree(a);
|
---|
1047 | powNode.AddSubtree(b);
|
---|
1048 | return powNode;
|
---|
1049 | }
|
---|
1050 | }
|
---|
1051 |
|
---|
1052 |
|
---|
1053 | // MakeFraction, MakeProduct and MakeSum take two already simplified trees and create a new simplified tree
|
---|
1054 | private ISymbolicExpressionTreeNode MakeFraction(ISymbolicExpressionTreeNode a, ISymbolicExpressionTreeNode b) {
|
---|
1055 | if (IsConstant(a) && IsConstant(b)) {
|
---|
1056 | // fold constants
|
---|
1057 | return MakeConstant(((ConstantTreeNode)a).Value / ((ConstantTreeNode)b).Value);
|
---|
1058 | } else if ((IsConstant(a) && !((ConstantTreeNode)a).Value.IsAlmost(1.0))) {
|
---|
1059 | return MakeFraction(MakeConstant(1.0), MakeProduct(b, Invert(a)));
|
---|
1060 | } else if (IsVariableBase(a) && IsConstant(b)) {
|
---|
1061 | // merge constant values into variable weights
|
---|
1062 | var constB = ((ConstantTreeNode)b).Value;
|
---|
1063 | ((VariableTreeNodeBase)a).Weight /= constB;
|
---|
1064 | return a;
|
---|
1065 | } else if (IsFactor(a) && IsConstant(b)) {
|
---|
1066 | var factNode = a as FactorVariableTreeNode;
|
---|
1067 | var constNode = b as ConstantTreeNode;
|
---|
1068 | return MakeFactor(factNode.Symbol, factNode.VariableName, factNode.Weights.Select(w => w / constNode.Value));
|
---|
1069 | } else if (IsBinFactor(a) && IsConstant(b)) {
|
---|
1070 | var factNode = a as BinaryFactorVariableTreeNode;
|
---|
1071 | var constNode = b as ConstantTreeNode;
|
---|
1072 | return MakeBinFactor(factNode.Symbol, factNode.VariableName, factNode.VariableValue, factNode.Weight / constNode.Value);
|
---|
1073 | } else if (IsFactor(a) && IsFactor(b) && AreSameTypeAndVariable(a, b)) {
|
---|
1074 | var node0 = a as FactorVariableTreeNode;
|
---|
1075 | var node1 = b as FactorVariableTreeNode;
|
---|
1076 | return MakeFactor(node0.Symbol, node0.VariableName, node0.Weights.Zip(node1.Weights, (u, v) => u / v));
|
---|
1077 | } else if (IsFactor(a) && IsBinFactor(b) && ((IVariableTreeNode)a).VariableName == ((IVariableTreeNode)b).VariableName) {
|
---|
1078 | var node0 = a as FactorVariableTreeNode;
|
---|
1079 | var node1 = b as BinaryFactorVariableTreeNode;
|
---|
1080 | var varValues = node0.Symbol.GetVariableValues(node0.VariableName).ToArray();
|
---|
1081 | var wi = Array.IndexOf(varValues, node1.VariableValue);
|
---|
1082 | if (wi < 0) throw new ArgumentException();
|
---|
1083 | var newWeighs = new double[varValues.Length];
|
---|
1084 | node0.Weights.CopyTo(newWeighs, 0);
|
---|
1085 | for (int i = 0; i < newWeighs.Length; i++)
|
---|
1086 | if (wi == i) newWeighs[i] /= node1.Weight;
|
---|
1087 | else newWeighs[i] /= 0.0;
|
---|
1088 | return MakeFactor(node0.Symbol, node0.VariableName, newWeighs);
|
---|
1089 | } else if (IsFactor(a)) {
|
---|
1090 | return MakeFraction(MakeConstant(1.0), MakeProduct(b, Invert(a)));
|
---|
1091 | } else if (IsVariableBase(a) && IsVariableBase(b) && AreSameTypeAndVariable(a, b) && !IsBinFactor(b)) {
|
---|
1092 | // cancel variables (not allowed for bin factors because of division by zero)
|
---|
1093 | var aVar = a as VariableTreeNode;
|
---|
1094 | var bVar = b as VariableTreeNode;
|
---|
1095 | return MakeConstant(aVar.Weight / bVar.Weight);
|
---|
1096 | } else if (IsAddition(a) && IsConstant(b)) {
|
---|
1097 | return a.Subtrees
|
---|
1098 | .Select(x => GetSimplifiedTree(x))
|
---|
1099 | .Select(x => MakeFraction(x, GetSimplifiedTree(b)))
|
---|
1100 | .Aggregate((c, d) => MakeSum(c, d));
|
---|
1101 | } else if (IsMultiplication(a) && IsConstant(b)) {
|
---|
1102 | return MakeProduct(a, Invert(b));
|
---|
1103 | } else if (IsDivision(a) && IsConstant(b)) {
|
---|
1104 | // (a1 / a2) / c => (a1 / (a2 * c))
|
---|
1105 | return MakeFraction(a.GetSubtree(0), MakeProduct(a.GetSubtree(1), b));
|
---|
1106 | } else if (IsDivision(a) && IsDivision(b)) {
|
---|
1107 | // (a1 / a2) / (b1 / b2) =>
|
---|
1108 | return MakeFraction(MakeProduct(a.GetSubtree(0), b.GetSubtree(1)), MakeProduct(a.GetSubtree(1), b.GetSubtree(0)));
|
---|
1109 | } else if (IsDivision(a)) {
|
---|
1110 | // (a1 / a2) / b => (a1 / (a2 * b))
|
---|
1111 | return MakeFraction(a.GetSubtree(0), MakeProduct(a.GetSubtree(1), b));
|
---|
1112 | } else if (IsDivision(b)) {
|
---|
1113 | // a / (b1 / b2) => (a * b2) / b1
|
---|
1114 | return MakeFraction(MakeProduct(a, b.GetSubtree(1)), b.GetSubtree(0));
|
---|
1115 | } else if (IsAnalyticalQuotient(a)) {
|
---|
1116 | return MakeAnalyticalQuotient(a.GetSubtree(0), MakeProduct(a.GetSubtree(1), b));
|
---|
1117 | } else {
|
---|
1118 | var div = divSymbol.CreateTreeNode();
|
---|
1119 | div.AddSubtree(a);
|
---|
1120 | div.AddSubtree(b);
|
---|
1121 | return div;
|
---|
1122 | }
|
---|
1123 | }
|
---|
1124 |
|
---|
1125 | private ISymbolicExpressionTreeNode MakeSum(ISymbolicExpressionTreeNode a, ISymbolicExpressionTreeNode b) {
|
---|
1126 | if (IsConstant(a) && IsConstant(b)) {
|
---|
1127 | // fold constants
|
---|
1128 | ((ConstantTreeNode)a).Value += ((ConstantTreeNode)b).Value;
|
---|
1129 | return a;
|
---|
1130 | } else if (IsConstant(a)) {
|
---|
1131 | // c + x => x + c
|
---|
1132 | // b is not constant => make sure constant is on the right
|
---|
1133 | return MakeSum(b, a);
|
---|
1134 | } else if (IsConstant(b) && ((ConstantTreeNode)b).Value.IsAlmost(0.0)) {
|
---|
1135 | // x + 0 => x
|
---|
1136 | return a;
|
---|
1137 | } else if (IsFactor(a) && IsConstant(b)) {
|
---|
1138 | var factNode = a as FactorVariableTreeNode;
|
---|
1139 | var constNode = b as ConstantTreeNode;
|
---|
1140 | return MakeFactor(factNode.Symbol, factNode.VariableName, factNode.Weights.Select((w) => w + constNode.Value));
|
---|
1141 | } else if (IsFactor(a) && IsFactor(b) && AreSameTypeAndVariable(a, b)) {
|
---|
1142 | var node0 = a as FactorVariableTreeNode;
|
---|
1143 | var node1 = b as FactorVariableTreeNode;
|
---|
1144 | return MakeFactor(node0.Symbol, node0.VariableName, node0.Weights.Zip(node1.Weights, (u, v) => u + v));
|
---|
1145 | } else if (IsBinFactor(a) && IsFactor(b)) {
|
---|
1146 | return MakeSum(b, a);
|
---|
1147 | } else if (IsFactor(a) && IsBinFactor(b) &&
|
---|
1148 | ((IVariableTreeNode)a).VariableName == ((IVariableTreeNode)b).VariableName) {
|
---|
1149 | var node0 = a as FactorVariableTreeNode;
|
---|
1150 | var node1 = b as BinaryFactorVariableTreeNode;
|
---|
1151 | var varValues = node0.Symbol.GetVariableValues(node0.VariableName).ToArray();
|
---|
1152 | var wi = Array.IndexOf(varValues, node1.VariableValue);
|
---|
1153 | if (wi < 0) throw new ArgumentException();
|
---|
1154 | var newWeighs = new double[varValues.Length];
|
---|
1155 | node0.Weights.CopyTo(newWeighs, 0);
|
---|
1156 | newWeighs[wi] += node1.Weight;
|
---|
1157 | return MakeFactor(node0.Symbol, node0.VariableName, newWeighs);
|
---|
1158 | } else if (IsAddition(a) && IsAddition(b)) {
|
---|
1159 | // merge additions
|
---|
1160 | var add = addSymbol.CreateTreeNode();
|
---|
1161 | // add all sub trees except for the last
|
---|
1162 | for (int i = 0; i < a.Subtrees.Count() - 1; i++) add.AddSubtree(a.GetSubtree(i));
|
---|
1163 | for (int i = 0; i < b.Subtrees.Count() - 1; i++) add.AddSubtree(b.GetSubtree(i));
|
---|
1164 | if (IsConstant(a.Subtrees.Last()) && IsConstant(b.Subtrees.Last())) {
|
---|
1165 | add.AddSubtree(MakeSum(a.Subtrees.Last(), b.Subtrees.Last()));
|
---|
1166 | } else if (IsConstant(a.Subtrees.Last())) {
|
---|
1167 | add.AddSubtree(b.Subtrees.Last());
|
---|
1168 | add.AddSubtree(a.Subtrees.Last());
|
---|
1169 | } else {
|
---|
1170 | add.AddSubtree(a.Subtrees.Last());
|
---|
1171 | add.AddSubtree(b.Subtrees.Last());
|
---|
1172 | }
|
---|
1173 | MergeVariablesInSum(add);
|
---|
1174 | if (add.Subtrees.Count() == 1) {
|
---|
1175 | return add.GetSubtree(0);
|
---|
1176 | } else {
|
---|
1177 | return add;
|
---|
1178 | }
|
---|
1179 | } else if (IsAddition(b)) {
|
---|
1180 | return MakeSum(b, a);
|
---|
1181 | } else if (IsAddition(a) && IsConstant(b)) {
|
---|
1182 | // a is an addition and b is a constant => append b to a and make sure the constants are merged
|
---|
1183 | var add = addSymbol.CreateTreeNode();
|
---|
1184 | // add all sub trees except for the last
|
---|
1185 | for (int i = 0; i < a.Subtrees.Count() - 1; i++) add.AddSubtree(a.GetSubtree(i));
|
---|
1186 | if (IsConstant(a.Subtrees.Last()))
|
---|
1187 | add.AddSubtree(MakeSum(a.Subtrees.Last(), b));
|
---|
1188 | else {
|
---|
1189 | add.AddSubtree(a.Subtrees.Last());
|
---|
1190 | add.AddSubtree(b);
|
---|
1191 | }
|
---|
1192 | return add;
|
---|
1193 | } else if (IsAddition(a)) {
|
---|
1194 | // a is already an addition => append b
|
---|
1195 | var add = addSymbol.CreateTreeNode();
|
---|
1196 | add.AddSubtree(b);
|
---|
1197 | foreach (var subtree in a.Subtrees) {
|
---|
1198 | add.AddSubtree(subtree);
|
---|
1199 | }
|
---|
1200 | MergeVariablesInSum(add);
|
---|
1201 | if (add.Subtrees.Count() == 1) {
|
---|
1202 | return add.GetSubtree(0);
|
---|
1203 | } else {
|
---|
1204 | return add;
|
---|
1205 | }
|
---|
1206 | } else {
|
---|
1207 | var add = addSymbol.CreateTreeNode();
|
---|
1208 | add.AddSubtree(a);
|
---|
1209 | add.AddSubtree(b);
|
---|
1210 | MergeVariablesInSum(add);
|
---|
1211 | if (add.Subtrees.Count() == 1) {
|
---|
1212 | return add.GetSubtree(0);
|
---|
1213 | } else {
|
---|
1214 | return add;
|
---|
1215 | }
|
---|
1216 | }
|
---|
1217 | }
|
---|
1218 |
|
---|
1219 | // makes sure variable symbols in sums are combined
|
---|
1220 | private void MergeVariablesInSum(ISymbolicExpressionTreeNode sum) {
|
---|
1221 | var subtrees = new List<ISymbolicExpressionTreeNode>(sum.Subtrees);
|
---|
1222 | while (sum.Subtrees.Any()) sum.RemoveSubtree(0);
|
---|
1223 | var groupedVarNodes = from node in subtrees.OfType<IVariableTreeNode>()
|
---|
1224 | where node.SubtreeCount == 0
|
---|
1225 | group node by GroupId(node) into g
|
---|
1226 | select g;
|
---|
1227 | var constant = (from node in subtrees.OfType<ConstantTreeNode>()
|
---|
1228 | select node.Value).DefaultIfEmpty(0.0).Sum();
|
---|
1229 | var unchangedSubtrees = subtrees.Where(t => t.SubtreeCount > 0 || !(t is IVariableTreeNode) && !(t is ConstantTreeNode));
|
---|
1230 |
|
---|
1231 | foreach (var variableNodeGroup in groupedVarNodes) {
|
---|
1232 | var firstNode = variableNodeGroup.First();
|
---|
1233 | if (firstNode is VariableTreeNodeBase) {
|
---|
1234 | var representative = firstNode as VariableTreeNodeBase;
|
---|
1235 | var weightSum = variableNodeGroup.Cast<VariableTreeNodeBase>().Select(t => t.Weight).Sum();
|
---|
1236 | representative.Weight = weightSum;
|
---|
1237 | sum.AddSubtree(representative);
|
---|
1238 | } else if (firstNode is FactorVariableTreeNode) {
|
---|
1239 | var representative = firstNode as FactorVariableTreeNode;
|
---|
1240 | foreach (var node in variableNodeGroup.Skip(1).Cast<FactorVariableTreeNode>()) {
|
---|
1241 | for (int j = 0; j < representative.Weights.Length; j++) {
|
---|
1242 | representative.Weights[j] += node.Weights[j];
|
---|
1243 | }
|
---|
1244 | }
|
---|
1245 | sum.AddSubtree(representative);
|
---|
1246 | }
|
---|
1247 | }
|
---|
1248 | foreach (var unchangedSubtree in unchangedSubtrees)
|
---|
1249 | sum.AddSubtree(unchangedSubtree);
|
---|
1250 | if (!constant.IsAlmost(0.0)) {
|
---|
1251 | sum.AddSubtree(MakeConstant(constant));
|
---|
1252 | }
|
---|
1253 | }
|
---|
1254 |
|
---|
1255 | // nodes referencing variables can be grouped if they have
|
---|
1256 | private string GroupId(IVariableTreeNode node) {
|
---|
1257 | var binaryFactorNode = node as BinaryFactorVariableTreeNode;
|
---|
1258 | var factorNode = node as FactorVariableTreeNode;
|
---|
1259 | var variableNode = node as VariableTreeNode;
|
---|
1260 | var laggedVarNode = node as LaggedVariableTreeNode;
|
---|
1261 | if (variableNode != null) {
|
---|
1262 | return "var " + variableNode.VariableName;
|
---|
1263 | } else if (binaryFactorNode != null) {
|
---|
1264 | return "binfactor " + binaryFactorNode.VariableName + " " + binaryFactorNode.VariableValue;
|
---|
1265 | } else if (factorNode != null) {
|
---|
1266 | return "factor " + factorNode.VariableName;
|
---|
1267 | } else if (laggedVarNode != null) {
|
---|
1268 | return "lagged " + laggedVarNode.VariableName + " " + laggedVarNode.Lag;
|
---|
1269 | } else {
|
---|
1270 | throw new NotSupportedException();
|
---|
1271 | }
|
---|
1272 | }
|
---|
1273 |
|
---|
1274 |
|
---|
1275 | private ISymbolicExpressionTreeNode MakeProduct(ISymbolicExpressionTreeNode a, ISymbolicExpressionTreeNode b) {
|
---|
1276 | if (IsConstant(a) && IsConstant(b)) {
|
---|
1277 | // fold constants
|
---|
1278 | return MakeConstant(((ConstantTreeNode)a).Value * ((ConstantTreeNode)b).Value);
|
---|
1279 | } else if (IsConstant(a)) {
|
---|
1280 | // a * $ => $ * a
|
---|
1281 | return MakeProduct(b, a);
|
---|
1282 | } else if (IsFactor(a) && IsFactor(b) && AreSameTypeAndVariable(a, b)) {
|
---|
1283 | var node0 = a as FactorVariableTreeNode;
|
---|
1284 | var node1 = b as FactorVariableTreeNode;
|
---|
1285 | return MakeFactor(node0.Symbol, node0.VariableName, node0.Weights.Zip(node1.Weights, (u, v) => u * v));
|
---|
1286 | } else if (IsBinFactor(a) && IsBinFactor(b) && AreSameTypeAndVariable(a, b)) {
|
---|
1287 | var node0 = a as BinaryFactorVariableTreeNode;
|
---|
1288 | var node1 = b as BinaryFactorVariableTreeNode;
|
---|
1289 | return MakeBinFactor(node0.Symbol, node0.VariableName, node0.VariableValue, node0.Weight * node1.Weight);
|
---|
1290 | } else if (IsFactor(a) && IsConstant(b)) {
|
---|
1291 | var node0 = a as FactorVariableTreeNode;
|
---|
1292 | var node1 = b as ConstantTreeNode;
|
---|
1293 | return MakeFactor(node0.Symbol, node0.VariableName, node0.Weights.Select(w => w * node1.Value));
|
---|
1294 | } else if (IsBinFactor(a) && IsConstant(b)) {
|
---|
1295 | var node0 = a as BinaryFactorVariableTreeNode;
|
---|
1296 | var node1 = b as ConstantTreeNode;
|
---|
1297 | return MakeBinFactor(node0.Symbol, node0.VariableName, node0.VariableValue, node0.Weight * node1.Value);
|
---|
1298 | } else if (IsBinFactor(a) && IsFactor(b)) {
|
---|
1299 | return MakeProduct(b, a);
|
---|
1300 | } else if (IsFactor(a) && IsBinFactor(b) &&
|
---|
1301 | ((IVariableTreeNode)a).VariableName == ((IVariableTreeNode)b).VariableName) {
|
---|
1302 | var node0 = a as FactorVariableTreeNode;
|
---|
1303 | var node1 = b as BinaryFactorVariableTreeNode;
|
---|
1304 | var varValues = node0.Symbol.GetVariableValues(node0.VariableName).ToArray();
|
---|
1305 | var wi = Array.IndexOf(varValues, node1.VariableValue);
|
---|
1306 | if (wi < 0) throw new ArgumentException();
|
---|
1307 | return MakeBinFactor(node1.Symbol, node1.VariableName, node1.VariableValue, node1.Weight * node0.Weights[wi]);
|
---|
1308 | } else if (IsConstant(b) && ((ConstantTreeNode)b).Value.IsAlmost(1.0)) {
|
---|
1309 | // $ * 1.0 => $
|
---|
1310 | return a;
|
---|
1311 | } else if (IsConstant(b) && ((ConstantTreeNode)b).Value.IsAlmost(0.0)) {
|
---|
1312 | return MakeConstant(0);
|
---|
1313 | } else if (IsConstant(b) && IsVariableBase(a)) {
|
---|
1314 | // multiply constants into variables weights
|
---|
1315 | ((VariableTreeNodeBase)a).Weight *= ((ConstantTreeNode)b).Value;
|
---|
1316 | return a;
|
---|
1317 | } else if (IsConstant(b) && IsAddition(a) ||
|
---|
1318 | IsFactor(b) && IsAddition(a) ||
|
---|
1319 | IsBinFactor(b) && IsAddition(a)) {
|
---|
1320 | // multiply constants into additions
|
---|
1321 | return a.Subtrees.Select(x => MakeProduct(GetSimplifiedTree(x), GetSimplifiedTree(b))).Aggregate((c, d) => MakeSum(c, d));
|
---|
1322 | } else if (IsDivision(a) && IsDivision(b)) {
|
---|
1323 | // (a1 / a2) * (b1 / b2) => (a1 * b1) / (a2 * b2)
|
---|
1324 | return MakeFraction(MakeProduct(a.GetSubtree(0), b.GetSubtree(0)), MakeProduct(a.GetSubtree(1), b.GetSubtree(1)));
|
---|
1325 | } else if (IsDivision(a)) {
|
---|
1326 | // (a1 / a2) * b => (a1 * b) / a2
|
---|
1327 | return MakeFraction(MakeProduct(a.GetSubtree(0), b), a.GetSubtree(1));
|
---|
1328 | } else if (IsDivision(b)) {
|
---|
1329 | // a * (b1 / b2) => (b1 * a) / b2
|
---|
1330 | return MakeFraction(MakeProduct(b.GetSubtree(0), a), b.GetSubtree(1));
|
---|
1331 | } else if (IsMultiplication(a) && IsMultiplication(b)) {
|
---|
1332 | // merge multiplications (make sure constants are merged)
|
---|
1333 | var mul = mulSymbol.CreateTreeNode();
|
---|
1334 | for (int i = 0; i < a.Subtrees.Count(); i++) mul.AddSubtree(a.GetSubtree(i));
|
---|
1335 | for (int i = 0; i < b.Subtrees.Count(); i++) mul.AddSubtree(b.GetSubtree(i));
|
---|
1336 | MergeVariablesAndConstantsInProduct(mul);
|
---|
1337 | return mul;
|
---|
1338 | } else if (IsMultiplication(b)) {
|
---|
1339 | return MakeProduct(b, a);
|
---|
1340 | } else if (IsMultiplication(a)) {
|
---|
1341 | // a is already an multiplication => append b
|
---|
1342 | a.AddSubtree(GetSimplifiedTree(b));
|
---|
1343 | MergeVariablesAndConstantsInProduct(a);
|
---|
1344 | return a;
|
---|
1345 | } else if (IsAbsolute(a) && IsAbsolute(b)) {
|
---|
1346 | return MakeAbs(MakeProduct(a.GetSubtree(0), b.GetSubtree(0)));
|
---|
1347 | } else if (IsAbsolute(a) && IsConstant(b)) {
|
---|
1348 | var constNode = b as ConstantTreeNode;
|
---|
1349 | var posF = Math.Abs(constNode.Value);
|
---|
1350 | if (constNode.Value > 0) {
|
---|
1351 | return MakeAbs(MakeProduct(a.GetSubtree(0), MakeConstant(posF)));
|
---|
1352 | } else {
|
---|
1353 | var mul = mulSymbol.CreateTreeNode();
|
---|
1354 | mul.AddSubtree(MakeAbs(MakeProduct(a.GetSubtree(0), MakeConstant(posF))));
|
---|
1355 | mul.AddSubtree(MakeConstant(-1.0));
|
---|
1356 | return mul;
|
---|
1357 | }
|
---|
1358 | } else if (IsAnalyticalQuotient(a)) {
|
---|
1359 | return MakeAnalyticalQuotient(MakeProduct(a.GetSubtree(0), b), a.GetSubtree(1));
|
---|
1360 | } else {
|
---|
1361 | var mul = mulSymbol.CreateTreeNode();
|
---|
1362 | mul.AddSubtree(a);
|
---|
1363 | mul.AddSubtree(b);
|
---|
1364 | MergeVariablesAndConstantsInProduct(mul);
|
---|
1365 | return mul;
|
---|
1366 | }
|
---|
1367 | }
|
---|
1368 |
|
---|
1369 | ISymbolicExpressionTreeNode MakeSumAggregation(ISymbolicExpressionTreeNode node) {
|
---|
1370 | if (IsConstant(node)) { // assumes scalar constant
|
---|
1371 | return node;
|
---|
1372 | } else if (IsAddition(node) || IsSubtraction(node)) {
|
---|
1373 | var terms = node.Subtrees;
|
---|
1374 | if (IsSubtraction(node)) {
|
---|
1375 | if (terms.Count() == 1) {
|
---|
1376 | terms = terms.Select(Negate);
|
---|
1377 | } else {
|
---|
1378 | var first = terms.First().ToEnumerable();
|
---|
1379 | var remaining = terms.Skip(1).Select(Negate);
|
---|
1380 | terms = first.Concat(remaining).ToList();
|
---|
1381 | }
|
---|
1382 | }
|
---|
1383 |
|
---|
1384 | var scalarTerms = terms.Where(IsScalarNode).ToList();
|
---|
1385 | var remainingTerms = terms.Except(scalarTerms).ToList();
|
---|
1386 |
|
---|
1387 | if (scalarTerms.Any() && remainingTerms.Any()) {
|
---|
1388 | var scalarNode = scalarTerms.Aggregate(MakeSum);
|
---|
1389 | var vectorNode = remainingTerms.Aggregate(MakeSum);
|
---|
1390 |
|
---|
1391 | var lengthNode = lengthSymbol.CreateTreeNode();
|
---|
1392 | lengthNode.AddSubtree((ISymbolicExpressionTreeNode)vectorNode.Clone());
|
---|
1393 | var scalarMulNode = mulSymbol.CreateTreeNode();
|
---|
1394 | scalarMulNode.AddSubtree(scalarNode);
|
---|
1395 | scalarMulNode.AddSubtree(lengthNode);
|
---|
1396 |
|
---|
1397 | var sumNode = sumSymbol.CreateTreeNode();
|
---|
1398 | sumNode.AddSubtree(vectorNode);
|
---|
1399 |
|
---|
1400 | return MakeSum(scalarMulNode, sumNode);
|
---|
1401 | } else if (scalarTerms.Any()) {
|
---|
1402 | var scalarNode = scalarTerms.Aggregate(MakeSum);
|
---|
1403 | return scalarNode;
|
---|
1404 | } else if (remainingTerms.Any()) {
|
---|
1405 | var vectorNode = remainingTerms.Aggregate(MakeSum);
|
---|
1406 | var sumNode = sumSymbol.CreateTreeNode();
|
---|
1407 | sumNode.AddSubtree(vectorNode);
|
---|
1408 | return sumNode;
|
---|
1409 | } else
|
---|
1410 | throw new InvalidOperationException("Addition does not contain any terms to simplify.");
|
---|
1411 | } else if (IsMultiplication(node) || IsDivision(node)) {
|
---|
1412 | var factors = node.Subtrees;
|
---|
1413 | if (IsDivision(node)) {
|
---|
1414 | if (factors.Count() == 1) {
|
---|
1415 | factors = factors.Select(Invert);
|
---|
1416 | } else {
|
---|
1417 | var first = factors.First().ToEnumerable();
|
---|
1418 | var remaining = factors.Skip(1).Select(Invert);
|
---|
1419 | factors = first.Concat(remaining).ToList();
|
---|
1420 | }
|
---|
1421 | }
|
---|
1422 |
|
---|
1423 | var scalarFactors = factors.Where(IsScalarNode).ToList();
|
---|
1424 | var remainingFactors = factors.Except(scalarFactors).ToList();
|
---|
1425 |
|
---|
1426 | if (scalarFactors.Any() && remainingFactors.Any()) {
|
---|
1427 | var scalarNode = scalarFactors.Aggregate(MakeProduct);
|
---|
1428 | var vectorNode = remainingFactors.Aggregate(MakeProduct);
|
---|
1429 |
|
---|
1430 | var sumNode = sumSymbol.CreateTreeNode();
|
---|
1431 | sumNode.AddSubtree(vectorNode);
|
---|
1432 |
|
---|
1433 | return MakeProduct(scalarNode, sumNode);
|
---|
1434 | } else if (scalarFactors.Any()) {
|
---|
1435 | var scalarNode = scalarFactors.Aggregate(MakeProduct);
|
---|
1436 | return scalarNode;
|
---|
1437 | } else if (remainingFactors.Any()) {
|
---|
1438 | var vectorNode = remainingFactors.Aggregate(MakeProduct);
|
---|
1439 | var sumNode = sumSymbol.CreateTreeNode();
|
---|
1440 | sumNode.AddSubtree(vectorNode);
|
---|
1441 | return sumNode;
|
---|
1442 | } else
|
---|
1443 | throw new InvalidOperationException("Multiplication does not contain any terms to simplify.");
|
---|
1444 | } else {
|
---|
1445 | var sumNode = sumSymbol.CreateTreeNode();
|
---|
1446 | sumNode.AddSubtree(node);
|
---|
1447 | return sumNode;
|
---|
1448 | }
|
---|
1449 | }
|
---|
1450 |
|
---|
1451 | ISymbolicExpressionTreeNode MakeMeanAggregation(ISymbolicExpressionTreeNode node) {
|
---|
1452 | if (IsConstant(node)) { // assumes scalar constant
|
---|
1453 | return node;
|
---|
1454 | } else if (IsAddition(node) || IsSubtraction(node)) {
|
---|
1455 | var terms = node.Subtrees;
|
---|
1456 | if (IsSubtraction(node)) {
|
---|
1457 | if (terms.Count() == 1) {
|
---|
1458 | terms = terms.Select(Negate);
|
---|
1459 | } else {
|
---|
1460 | var first = terms.First().ToEnumerable();
|
---|
1461 | var remaining = terms.Skip(1).Select(Negate);
|
---|
1462 | terms = first.Concat(remaining).ToList();
|
---|
1463 | }
|
---|
1464 | }
|
---|
1465 |
|
---|
1466 | var scalarTerms = terms.Where(IsScalarNode).ToList();
|
---|
1467 | var remainingTerms = terms.Except(scalarTerms).ToList();
|
---|
1468 |
|
---|
1469 | if (scalarTerms.Any() && remainingTerms.Any()) {
|
---|
1470 | var scalarNode = scalarTerms.Aggregate(MakeSum);
|
---|
1471 | var vectorNode = remainingTerms.Aggregate(MakeSum);
|
---|
1472 |
|
---|
1473 | var meanNode = meanSymbol.CreateTreeNode();
|
---|
1474 | meanNode.AddSubtree(vectorNode);
|
---|
1475 |
|
---|
1476 | return MakeSum(scalarNode, meanNode);
|
---|
1477 | } else if (scalarTerms.Any()) {
|
---|
1478 | var scalarNode = scalarTerms.Aggregate(MakeSum);
|
---|
1479 | return scalarNode;
|
---|
1480 | } else if (remainingTerms.Any()) {
|
---|
1481 | var vectorNode = remainingTerms.Aggregate(MakeSum);
|
---|
1482 | var meanNode = meanSymbol.CreateTreeNode();
|
---|
1483 | meanNode.AddSubtree(vectorNode);
|
---|
1484 | return meanNode;
|
---|
1485 | } else
|
---|
1486 | throw new InvalidOperationException("Addition does not contain any terms to simplify.");
|
---|
1487 | } else if (IsMultiplication(node) || IsDivision(node)) {
|
---|
1488 | var factors = node.Subtrees;
|
---|
1489 | if (IsDivision(node)) {
|
---|
1490 | if (factors.Count() == 1) {
|
---|
1491 | factors = factors.Select(Invert);
|
---|
1492 | } else {
|
---|
1493 | var first = factors.First().ToEnumerable();
|
---|
1494 | var remaining = factors.Skip(1).Select(Invert);
|
---|
1495 | factors = first.Concat(remaining).ToList();
|
---|
1496 | }
|
---|
1497 | }
|
---|
1498 |
|
---|
1499 | var scalarFactors = factors.Where(IsScalarNode).ToList();
|
---|
1500 | var remainingFactors = factors.Except(scalarFactors).ToList();
|
---|
1501 |
|
---|
1502 | if (scalarFactors.Any() && remainingFactors.Any()) {
|
---|
1503 | var scalarNode = scalarFactors.Aggregate(MakeProduct);
|
---|
1504 | var vectorNode = remainingFactors.Aggregate(MakeProduct);
|
---|
1505 |
|
---|
1506 | var meanNode = meanSymbol.CreateTreeNode();
|
---|
1507 | meanNode.AddSubtree(vectorNode);
|
---|
1508 |
|
---|
1509 | return MakeProduct(scalarNode, meanNode);
|
---|
1510 | } else if (scalarFactors.Any()) {
|
---|
1511 | var scalarNode = scalarFactors.Aggregate(MakeProduct);
|
---|
1512 | return scalarNode;
|
---|
1513 | } else if (remainingFactors.Any()) {
|
---|
1514 | var vectorNode = remainingFactors.Aggregate(MakeProduct);
|
---|
1515 | var meanNode = meanSymbol.CreateTreeNode();
|
---|
1516 | meanNode.AddSubtree(vectorNode);
|
---|
1517 | return meanNode;
|
---|
1518 | } else
|
---|
1519 | throw new InvalidOperationException("Multiplication does not contain any terms to simplify.");
|
---|
1520 | } else {
|
---|
1521 | var meanNode = meanSymbol.CreateTreeNode();
|
---|
1522 | meanNode.AddSubtree(node);
|
---|
1523 | return meanNode;
|
---|
1524 | }
|
---|
1525 | }
|
---|
1526 |
|
---|
1527 | #endregion
|
---|
1528 |
|
---|
1529 | #region helper functions
|
---|
1530 |
|
---|
1531 | private bool ContainsVariableCondition(ISymbolicExpressionTreeNode node) {
|
---|
1532 | if (node.Symbol is VariableCondition) return true;
|
---|
1533 | foreach (var subtree in node.Subtrees)
|
---|
1534 | if (ContainsVariableCondition(subtree)) return true;
|
---|
1535 | return false;
|
---|
1536 | }
|
---|
1537 |
|
---|
1538 | private ISymbolicExpressionTreeNode AddLagToDynamicNodes(ISymbolicExpressionTreeNode node, int lag) {
|
---|
1539 | var laggedTreeNode = node as ILaggedTreeNode;
|
---|
1540 | var variableNode = node as VariableTreeNode;
|
---|
1541 | var variableConditionNode = node as VariableConditionTreeNode;
|
---|
1542 | if (laggedTreeNode != null)
|
---|
1543 | laggedTreeNode.Lag += lag;
|
---|
1544 | else if (variableNode != null) {
|
---|
1545 | var laggedVariableNode = (LaggedVariableTreeNode)laggedVariableSymbol.CreateTreeNode();
|
---|
1546 | laggedVariableNode.Lag = lag;
|
---|
1547 | laggedVariableNode.VariableName = variableNode.VariableName;
|
---|
1548 | return laggedVariableNode;
|
---|
1549 | } else if (variableConditionNode != null) {
|
---|
1550 | throw new NotSupportedException("Removal of time lags around variable condition symbols is not allowed.");
|
---|
1551 | }
|
---|
1552 | var subtrees = new List<ISymbolicExpressionTreeNode>(node.Subtrees);
|
---|
1553 | while (node.SubtreeCount > 0) node.RemoveSubtree(0);
|
---|
1554 | foreach (var subtree in subtrees) {
|
---|
1555 | node.AddSubtree(AddLagToDynamicNodes(subtree, lag));
|
---|
1556 | }
|
---|
1557 | return node;
|
---|
1558 | }
|
---|
1559 |
|
---|
1560 | private bool AreSameTypeAndVariable(ISymbolicExpressionTreeNode a, ISymbolicExpressionTreeNode b) {
|
---|
1561 | return GroupId((IVariableTreeNode)a) == GroupId((IVariableTreeNode)b);
|
---|
1562 | }
|
---|
1563 |
|
---|
1564 | // helper to combine the constant factors in products and to combine variables (powers of 2, 3...)
|
---|
1565 | private void MergeVariablesAndConstantsInProduct(ISymbolicExpressionTreeNode prod) {
|
---|
1566 | var subtrees = new List<ISymbolicExpressionTreeNode>(prod.Subtrees);
|
---|
1567 | while (prod.Subtrees.Any()) prod.RemoveSubtree(0);
|
---|
1568 | var groupedVarNodes = from node in subtrees.OfType<IVariableTreeNode>()
|
---|
1569 | where node.SubtreeCount == 0
|
---|
1570 | group node by GroupId(node) into g
|
---|
1571 | orderby g.Count()
|
---|
1572 | select g;
|
---|
1573 | var constantProduct = (from node in subtrees.OfType<VariableTreeNodeBase>()
|
---|
1574 | select node.Weight)
|
---|
1575 | .Concat(from node in subtrees.OfType<ConstantTreeNode>()
|
---|
1576 | select node.Value)
|
---|
1577 | .DefaultIfEmpty(1.0)
|
---|
1578 | .Aggregate((c1, c2) => c1 * c2);
|
---|
1579 |
|
---|
1580 | var unchangedSubtrees = from tree in subtrees
|
---|
1581 | where tree.SubtreeCount > 0 || !(tree is IVariableTreeNode) && !(tree is ConstantTreeNode)
|
---|
1582 | select tree;
|
---|
1583 |
|
---|
1584 | foreach (var variableNodeGroup in groupedVarNodes) {
|
---|
1585 | var firstNode = variableNodeGroup.First();
|
---|
1586 | if (firstNode is VariableTreeNodeBase) {
|
---|
1587 | var representative = (VariableTreeNodeBase)firstNode;
|
---|
1588 | representative.Weight = 1.0;
|
---|
1589 | if (variableNodeGroup.Count() > 1) {
|
---|
1590 | var poly = mulSymbol.CreateTreeNode();
|
---|
1591 | for (int p = 0; p < variableNodeGroup.Count(); p++) {
|
---|
1592 | poly.AddSubtree((ISymbolicExpressionTreeNode)representative.Clone());
|
---|
1593 | }
|
---|
1594 | prod.AddSubtree(poly);
|
---|
1595 | } else {
|
---|
1596 | prod.AddSubtree(representative);
|
---|
1597 | }
|
---|
1598 | } else if (firstNode is FactorVariableTreeNode) {
|
---|
1599 | var representative = (FactorVariableTreeNode)firstNode;
|
---|
1600 | foreach (var node in variableNodeGroup.Skip(1).Cast<FactorVariableTreeNode>()) {
|
---|
1601 | for (int j = 0; j < representative.Weights.Length; j++) {
|
---|
1602 | representative.Weights[j] *= node.Weights[j];
|
---|
1603 | }
|
---|
1604 | }
|
---|
1605 | for (int j = 0; j < representative.Weights.Length; j++) {
|
---|
1606 | representative.Weights[j] *= constantProduct;
|
---|
1607 | }
|
---|
1608 | constantProduct = 1.0;
|
---|
1609 | // if the product already contains a factor it is not necessary to multiply a constant below
|
---|
1610 | prod.AddSubtree(representative);
|
---|
1611 | }
|
---|
1612 | }
|
---|
1613 |
|
---|
1614 | foreach (var unchangedSubtree in unchangedSubtrees)
|
---|
1615 | prod.AddSubtree(unchangedSubtree);
|
---|
1616 |
|
---|
1617 | if (!constantProduct.IsAlmost(1.0)) {
|
---|
1618 | prod.AddSubtree(MakeConstant(constantProduct));
|
---|
1619 | }
|
---|
1620 | }
|
---|
1621 |
|
---|
1622 |
|
---|
1623 | /// <summary>
|
---|
1624 | /// x => x * -1
|
---|
1625 | /// Is only used in cases where it is not necessary to create new tree nodes. Manipulates x directly.
|
---|
1626 | /// </summary>
|
---|
1627 | /// <param name="x"></param>
|
---|
1628 | /// <returns>-x</returns>
|
---|
1629 | private ISymbolicExpressionTreeNode Negate(ISymbolicExpressionTreeNode x) {
|
---|
1630 | if (IsConstant(x)) {
|
---|
1631 | ((ConstantTreeNode)x).Value *= -1;
|
---|
1632 | } else if (IsVariableBase(x)) {
|
---|
1633 | var variableTree = (VariableTreeNodeBase)x;
|
---|
1634 | variableTree.Weight *= -1.0;
|
---|
1635 | } else if (IsFactor(x)) {
|
---|
1636 | var factorNode = (FactorVariableTreeNode)x;
|
---|
1637 | for (int i = 0; i < factorNode.Weights.Length; i++) factorNode.Weights[i] *= -1;
|
---|
1638 | } else if (IsBinFactor(x)) {
|
---|
1639 | var factorNode = (BinaryFactorVariableTreeNode)x;
|
---|
1640 | factorNode.Weight *= -1;
|
---|
1641 | } else if (IsAddition(x)) {
|
---|
1642 | // (x0 + x1 + .. + xn) * -1 => (-x0 + -x1 + .. + -xn)
|
---|
1643 | var subtrees = new List<ISymbolicExpressionTreeNode>(x.Subtrees);
|
---|
1644 | while (x.Subtrees.Any()) x.RemoveSubtree(0);
|
---|
1645 | foreach (var subtree in subtrees) {
|
---|
1646 | x.AddSubtree(Negate(subtree));
|
---|
1647 | }
|
---|
1648 | } else if (IsMultiplication(x) || IsDivision(x)) {
|
---|
1649 | // x0 * x1 * .. * xn * -1 => x0 * x1 * .. * -xn
|
---|
1650 | var lastSubTree = x.Subtrees.Last();
|
---|
1651 | x.RemoveSubtree(x.SubtreeCount - 1);
|
---|
1652 | x.AddSubtree(Negate(lastSubTree)); // last is maybe a constant, prefer to negate the constant
|
---|
1653 | } else {
|
---|
1654 | // any other function
|
---|
1655 | return MakeProduct(x, MakeConstant(-1));
|
---|
1656 | }
|
---|
1657 | return x;
|
---|
1658 | }
|
---|
1659 |
|
---|
1660 | /// <summary>
|
---|
1661 | /// x => 1/x
|
---|
1662 | /// Must create new tree nodes
|
---|
1663 | /// </summary>
|
---|
1664 | /// <param name="x"></param>
|
---|
1665 | /// <returns></returns>
|
---|
1666 | private ISymbolicExpressionTreeNode Invert(ISymbolicExpressionTreeNode x) {
|
---|
1667 | if (IsConstant(x)) {
|
---|
1668 | return MakeConstant(1.0 / ((ConstantTreeNode)x).Value);
|
---|
1669 | } else if (IsFactor(x)) {
|
---|
1670 | var factorNode = (FactorVariableTreeNode)x;
|
---|
1671 | return MakeFactor(factorNode.Symbol, factorNode.VariableName, factorNode.Weights.Select(w => 1.0 / w));
|
---|
1672 | } else if (IsDivision(x)) {
|
---|
1673 | return MakeFraction(x.GetSubtree(1), x.GetSubtree(0));
|
---|
1674 | } else {
|
---|
1675 | // any other function
|
---|
1676 | return MakeFraction(MakeConstant(1), x);
|
---|
1677 | }
|
---|
1678 | }
|
---|
1679 |
|
---|
1680 | private ISymbolicExpressionTreeNode MakeConstant(double value) {
|
---|
1681 | ConstantTreeNode constantTreeNode = (ConstantTreeNode)(constSymbol.CreateTreeNode());
|
---|
1682 | constantTreeNode.Value = value;
|
---|
1683 | return constantTreeNode;
|
---|
1684 | }
|
---|
1685 |
|
---|
1686 | private ISymbolicExpressionTreeNode MakeFactor(FactorVariable sy, string variableName, IEnumerable<double> weights) {
|
---|
1687 | var tree = (FactorVariableTreeNode)sy.CreateTreeNode();
|
---|
1688 | tree.VariableName = variableName;
|
---|
1689 | tree.Weights = weights.ToArray();
|
---|
1690 | return tree;
|
---|
1691 | }
|
---|
1692 | private ISymbolicExpressionTreeNode MakeBinFactor(BinaryFactorVariable sy, string variableName, string variableValue, double weight) {
|
---|
1693 | var tree = (BinaryFactorVariableTreeNode)sy.CreateTreeNode();
|
---|
1694 | tree.VariableName = variableName;
|
---|
1695 | tree.VariableValue = variableValue;
|
---|
1696 | tree.Weight = weight;
|
---|
1697 | return tree;
|
---|
1698 | }
|
---|
1699 |
|
---|
1700 |
|
---|
1701 | #endregion
|
---|
1702 | }
|
---|
1703 | }
|
---|