1 | #region License Information
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2 | /* HeuristicLab
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3 | * Copyright (C) 2002-2011 Heuristic and Evolutionary Algorithms Laboratory (HEAL)
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4 | *
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5 | * This file is part of HeuristicLab.
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6 | *
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7 | * HeuristicLab is free software: you can redistribute it and/or modify
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8 | * it under the terms of the GNU General Public License as published by
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9 | * the Free Software Foundation, either version 3 of the License, or
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10 | * (at your option) any later version.
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11 | *
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12 | * HeuristicLab is distributed in the hope that it will be useful,
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13 | * but WITHOUT ANY WARRANTY; without even the implied warranty of
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14 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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15 | * GNU General Public License for more details.
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16 | *
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17 | * You should have received a copy of the GNU General Public License
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18 | * along with HeuristicLab. If not, see <http://www.gnu.org/licenses/>.
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19 | */
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20 | #endregion
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21 |
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22 | using System;
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23 | using System.Collections.Generic;
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24 | using System.Diagnostics;
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25 | using System.Linq;
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26 | using HeuristicLab.Common;
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27 | using HeuristicLab.Encodings.SymbolicExpressionTreeEncoding;
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28 |
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29 | namespace HeuristicLab.Problems.DataAnalysis.Symbolic {
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30 | /// <summary>
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31 | /// Simplifier for symbolic expressions
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32 | /// </summary>
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33 | public class SymbolicDataAnalysisExpressionTreeSimplifier {
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34 | private Addition addSymbol = new Addition();
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35 | private Subtraction subSymbol = new Subtraction();
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36 | private Multiplication mulSymbol = new Multiplication();
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37 | private Division divSymbol = new Division();
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38 | private Constant constSymbol = new Constant();
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39 | private Variable varSymbol = new Variable();
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40 | private Logarithm logSymbol = new Logarithm();
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41 | private Exponential expSymbol = new Exponential();
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42 | private Root rootSymbol = new Root();
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43 | private Power powSymbol = new Power();
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44 | private Sine sineSymbol = new Sine();
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45 | private Cosine cosineSymbol = new Cosine();
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46 | private Tangent tanSymbol = new Tangent();
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47 | private IfThenElse ifThenElseSymbol = new IfThenElse();
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48 | private And andSymbol = new And();
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49 | private Or orSymbol = new Or();
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50 | private Not notSymbol = new Not();
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51 | private GreaterThan gtSymbol = new GreaterThan();
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52 | private LessThan ltSymbol = new LessThan();
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53 |
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54 | public ISymbolicExpressionTree Simplify(ISymbolicExpressionTree originalTree) {
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55 | var clone = (ISymbolicExpressionTreeNode)originalTree.Root.Clone();
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56 | // macro expand (initially no argument trees)
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57 | var macroExpandedTree = MacroExpand(clone, clone.GetSubtree(0), new List<ISymbolicExpressionTreeNode>());
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58 | ISymbolicExpressionTreeNode rootNode = (new ProgramRootSymbol()).CreateTreeNode();
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59 | rootNode.AddSubtree(GetSimplifiedTree(macroExpandedTree));
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60 | return new SymbolicExpressionTree(rootNode);
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61 | }
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62 |
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63 | // the argumentTrees list contains already expanded trees used as arguments for invocations
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64 | private ISymbolicExpressionTreeNode MacroExpand(ISymbolicExpressionTreeNode root, ISymbolicExpressionTreeNode node, IList<ISymbolicExpressionTreeNode> argumentTrees) {
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65 | List<ISymbolicExpressionTreeNode> subtrees = new List<ISymbolicExpressionTreeNode>(node.Subtrees);
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66 | while (node.SubtreesCount > 0) node.RemoveSubtree(0);
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67 | if (node.Symbol is InvokeFunction) {
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68 | var invokeSym = node.Symbol as InvokeFunction;
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69 | var defunNode = FindFunctionDefinition(root, invokeSym.FunctionName);
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70 | var macroExpandedArguments = new List<ISymbolicExpressionTreeNode>();
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71 | foreach (var subtree in subtrees) {
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72 | macroExpandedArguments.Add(MacroExpand(root, subtree, argumentTrees));
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73 | }
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74 | return MacroExpand(root, defunNode, macroExpandedArguments);
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75 | } else if (node.Symbol is Argument) {
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76 | var argSym = node.Symbol as Argument;
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77 | // return the correct argument sub-tree (already macro-expanded)
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78 | return (SymbolicExpressionTreeNode)argumentTrees[argSym.ArgumentIndex].Clone();
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79 | } else {
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80 | // recursive application
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81 | foreach (var subtree in subtrees) {
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82 | node.AddSubtree(MacroExpand(root, subtree, argumentTrees));
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83 | }
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84 | return node;
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85 | }
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86 | }
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87 |
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88 | private ISymbolicExpressionTreeNode FindFunctionDefinition(ISymbolicExpressionTreeNode root, string functionName) {
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89 | foreach (var subtree in root.Subtrees.OfType<DefunTreeNode>()) {
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90 | if (subtree.FunctionName == functionName) return subtree.GetSubtree(0);
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91 | }
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92 |
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93 | throw new ArgumentException("Definition of function " + functionName + " not found.");
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94 | }
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95 |
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96 |
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97 | #region symbol predicates
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98 | // arithmetic
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99 | private bool IsDivision(ISymbolicExpressionTreeNode node) {
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100 | return node.Symbol is Division;
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101 | }
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102 |
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103 | private bool IsMultiplication(ISymbolicExpressionTreeNode node) {
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104 | return node.Symbol is Multiplication;
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105 | }
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106 |
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107 | private bool IsSubtraction(ISymbolicExpressionTreeNode node) {
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108 | return node.Symbol is Subtraction;
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109 | }
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110 |
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111 | private bool IsAddition(ISymbolicExpressionTreeNode node) {
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112 | return node.Symbol is Addition;
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113 | }
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114 |
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115 | private bool IsAverage(ISymbolicExpressionTreeNode node) {
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116 | return node.Symbol is Average;
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117 | }
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118 | // exponential
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119 | private bool IsLog(ISymbolicExpressionTreeNode node) {
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120 | return node.Symbol is Logarithm;
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121 | }
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122 | private bool IsExp(ISymbolicExpressionTreeNode node) {
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123 | return node.Symbol is Exponential;
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124 | }
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125 | private bool IsRoot(ISymbolicExpressionTreeNode node) {
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126 | return node.Symbol is Root;
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127 | }
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128 | private bool IsPower(ISymbolicExpressionTreeNode node) {
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129 | return node.Symbol is Power;
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130 | }
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131 | // trigonometric
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132 | private bool IsSine(ISymbolicExpressionTreeNode node) {
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133 | return node.Symbol is Sine;
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134 | }
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135 | private bool IsCosine(ISymbolicExpressionTreeNode node) {
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136 | return node.Symbol is Cosine;
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137 | }
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138 | private bool IsTangent(ISymbolicExpressionTreeNode node) {
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139 | return node.Symbol is Tangent;
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140 | }
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141 | // boolean
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142 | private bool IsIfThenElse(ISymbolicExpressionTreeNode node) {
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143 | return node.Symbol is IfThenElse;
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144 | }
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145 | private bool IsAnd(ISymbolicExpressionTreeNode node) {
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146 | return node.Symbol is And;
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147 | }
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148 | private bool IsOr(ISymbolicExpressionTreeNode node) {
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149 | return node.Symbol is Or;
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150 | }
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151 | private bool IsNot(ISymbolicExpressionTreeNode node) {
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152 | return node.Symbol is Not;
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153 | }
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154 | // comparison
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155 | private bool IsGreaterThan(ISymbolicExpressionTreeNode node) {
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156 | return node.Symbol is GreaterThan;
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157 | }
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158 | private bool IsLessThan(ISymbolicExpressionTreeNode node) {
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159 | return node.Symbol is LessThan;
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160 | }
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161 |
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162 | private bool IsBoolean(ISymbolicExpressionTreeNode node) {
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163 | return
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164 | node.Symbol is GreaterThan ||
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165 | node.Symbol is LessThan ||
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166 | node.Symbol is And ||
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167 | node.Symbol is Or;
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168 | }
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169 |
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170 | // terminals
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171 | private bool IsVariable(ISymbolicExpressionTreeNode node) {
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172 | return node.Symbol is Variable;
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173 | }
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174 |
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175 | private bool IsConstant(ISymbolicExpressionTreeNode node) {
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176 | return node.Symbol is Constant;
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177 | }
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178 |
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179 | #endregion
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180 |
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181 | /// <summary>
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182 | /// Creates a new simplified tree
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183 | /// </summary>
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184 | /// <param name="original"></param>
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185 | /// <returns></returns>
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186 | public ISymbolicExpressionTreeNode GetSimplifiedTree(ISymbolicExpressionTreeNode original) {
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187 | if (IsConstant(original) || IsVariable(original)) {
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188 | return (ISymbolicExpressionTreeNode)original.Clone();
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189 | } else if (IsAddition(original)) {
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190 | return SimplifyAddition(original);
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191 | } else if (IsSubtraction(original)) {
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192 | return SimplifySubtraction(original);
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193 | } else if (IsMultiplication(original)) {
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194 | return SimplifyMultiplication(original);
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195 | } else if (IsDivision(original)) {
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196 | return SimplifyDivision(original);
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197 | } else if (IsAverage(original)) {
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198 | return SimplifyAverage(original);
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199 | } else if (IsLog(original)) {
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200 | return SimplifyLog(original);
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201 | } else if (IsExp(original)) {
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202 | return SimplifyExp(original);
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203 | } else if (IsRoot(original)) {
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204 | return SimplifyRoot(original);
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205 | } else if (IsPower(original)) {
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206 | return SimplifyPower(original);
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207 | } else if (IsSine(original)) {
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208 | return SimplifySine(original);
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209 | } else if (IsCosine(original)) {
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210 | return SimplifyCosine(original);
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211 | } else if (IsTangent(original)) {
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212 | return SimplifyTangent(original);
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213 | } else if (IsIfThenElse(original)) {
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214 | return SimplifyIfThenElse(original);
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215 | } else if (IsGreaterThan(original)) {
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216 | return SimplifyGreaterThan(original);
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217 | } else if (IsLessThan(original)) {
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218 | return SimplifyLessThan(original);
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219 | } else if (IsAnd(original)) {
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220 | return SimplifyAnd(original);
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221 | } else if (IsOr(original)) {
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222 | return SimplifyOr(original);
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223 | } else if (IsNot(original)) {
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224 | return SimplifyNot(original);
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225 | } else {
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226 | return SimplifyAny(original);
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227 | }
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228 | }
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229 |
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230 |
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231 | #region specific simplification routines
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232 | private ISymbolicExpressionTreeNode SimplifyAny(ISymbolicExpressionTreeNode original) {
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233 | // can't simplify this function but simplify all subtrees
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234 | List<ISymbolicExpressionTreeNode> subtrees = new List<ISymbolicExpressionTreeNode>(original.Subtrees);
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235 | while (original.Subtrees.Count() > 0) original.RemoveSubtree(0);
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236 | var clone = (SymbolicExpressionTreeNode)original.Clone();
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237 | List<ISymbolicExpressionTreeNode> simplifiedSubtrees = new List<ISymbolicExpressionTreeNode>();
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238 | foreach (var subtree in subtrees) {
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239 | simplifiedSubtrees.Add(GetSimplifiedTree(subtree));
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240 | original.AddSubtree(subtree);
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241 | }
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242 | foreach (var simplifiedSubtree in simplifiedSubtrees) {
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243 | clone.AddSubtree(simplifiedSubtree);
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244 | }
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245 | if (simplifiedSubtrees.TrueForAll(t => IsConstant(t))) {
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246 | SimplifyConstantExpression(clone);
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247 | }
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248 | return clone;
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249 | }
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250 |
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251 | private ISymbolicExpressionTreeNode SimplifyConstantExpression(ISymbolicExpressionTreeNode original) {
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252 | // not yet implemented
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253 | return original;
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254 | }
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255 |
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256 | private ISymbolicExpressionTreeNode SimplifyAverage(ISymbolicExpressionTreeNode original) {
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257 | if (original.Subtrees.Count() == 1) {
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258 | return GetSimplifiedTree(original.GetSubtree(0));
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259 | } else {
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260 | // simplify expressions x0..xn
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261 | // make sum(x0..xn) / n
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262 | var sum = original.Subtrees
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263 | .Select(x => GetSimplifiedTree(x))
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264 | .Aggregate((a, b) => MakeSum(a, b));
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265 | return MakeFraction(sum, MakeConstant(original.Subtrees.Count()));
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266 | }
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267 | }
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268 |
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269 | private ISymbolicExpressionTreeNode SimplifyDivision(ISymbolicExpressionTreeNode original) {
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270 | if (original.Subtrees.Count() == 1) {
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271 | return Invert(GetSimplifiedTree(original.GetSubtree(0)));
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272 | } else {
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273 | // simplify expressions x0..xn
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274 | // make multiplication (x0 * 1/(x1 * x1 * .. * xn))
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275 | var simplifiedTrees = original.Subtrees.Select(x => GetSimplifiedTree(x));
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276 | return
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277 | MakeProduct(simplifiedTrees.First(), Invert(simplifiedTrees.Skip(1).Aggregate((a, b) => MakeProduct(a, b))));
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278 | }
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279 | }
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280 |
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281 | private ISymbolicExpressionTreeNode SimplifyMultiplication(ISymbolicExpressionTreeNode original) {
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282 | if (original.Subtrees.Count() == 1) {
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283 | return GetSimplifiedTree(original.GetSubtree(0));
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284 | } else {
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285 | return original.Subtrees
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286 | .Select(x => GetSimplifiedTree(x))
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287 | .Aggregate((a, b) => MakeProduct(a, b));
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288 | }
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289 | }
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290 |
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291 | private ISymbolicExpressionTreeNode SimplifySubtraction(ISymbolicExpressionTreeNode original) {
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292 | if (original.Subtrees.Count() == 1) {
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293 | return Negate(GetSimplifiedTree(original.GetSubtree(0)));
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294 | } else {
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295 | // simplify expressions x0..xn
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296 | // make addition (x0,-x1..-xn)
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297 | var simplifiedTrees = original.Subtrees.Select(x => GetSimplifiedTree(x));
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298 | return simplifiedTrees.Take(1)
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299 | .Concat(simplifiedTrees.Skip(1).Select(x => Negate(x)))
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300 | .Aggregate((a, b) => MakeSum(a, b));
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301 | }
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302 | }
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303 |
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304 | private ISymbolicExpressionTreeNode SimplifyAddition(ISymbolicExpressionTreeNode original) {
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305 | if (original.Subtrees.Count() == 1) {
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306 | return GetSimplifiedTree(original.GetSubtree(0));
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307 | } else {
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308 | // simplify expression x0..xn
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309 | // make addition (x0..xn)
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310 | return original.Subtrees
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311 | .Select(x => GetSimplifiedTree(x))
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312 | .Aggregate((a, b) => MakeSum(a, b));
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313 | }
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314 | }
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315 |
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316 | private ISymbolicExpressionTreeNode SimplifyNot(ISymbolicExpressionTreeNode original) {
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317 | return MakeNot(GetSimplifiedTree(original.GetSubtree(0)));
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318 | }
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319 | private ISymbolicExpressionTreeNode SimplifyOr(ISymbolicExpressionTreeNode original) {
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320 | return original.Subtrees
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321 | .Select(x => GetSimplifiedTree(x))
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322 | .Aggregate((a, b) => MakeOr(a, b));
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323 | }
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324 | private ISymbolicExpressionTreeNode SimplifyAnd(ISymbolicExpressionTreeNode original) {
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325 | return original.Subtrees
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326 | .Select(x => GetSimplifiedTree(x))
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327 | .Aggregate((a, b) => MakeAnd(a, b));
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328 | }
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329 | private ISymbolicExpressionTreeNode SimplifyLessThan(ISymbolicExpressionTreeNode original) {
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330 | return MakeLessThan(GetSimplifiedTree(original.GetSubtree(0)), GetSimplifiedTree(original.GetSubtree(1)));
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331 | }
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332 | private ISymbolicExpressionTreeNode SimplifyGreaterThan(ISymbolicExpressionTreeNode original) {
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333 | return MakeGreaterThan(GetSimplifiedTree(original.GetSubtree(0)), GetSimplifiedTree(original.GetSubtree(1)));
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334 | }
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335 | private ISymbolicExpressionTreeNode SimplifyIfThenElse(ISymbolicExpressionTreeNode original) {
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336 | return MakeIfThenElse(GetSimplifiedTree(original.GetSubtree(0)), GetSimplifiedTree(original.GetSubtree(1)), GetSimplifiedTree(original.GetSubtree(2)));
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337 | }
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338 | private ISymbolicExpressionTreeNode SimplifyTangent(ISymbolicExpressionTreeNode original) {
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339 | return MakeTangent(GetSimplifiedTree(original.GetSubtree(0)));
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340 | }
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341 | private ISymbolicExpressionTreeNode SimplifyCosine(ISymbolicExpressionTreeNode original) {
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342 | return MakeCosine(GetSimplifiedTree(original.GetSubtree(0)));
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343 | }
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344 | private ISymbolicExpressionTreeNode SimplifySine(ISymbolicExpressionTreeNode original) {
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345 | return MakeSine(GetSimplifiedTree(original.GetSubtree(0)));
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346 | }
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347 | private ISymbolicExpressionTreeNode SimplifyExp(ISymbolicExpressionTreeNode original) {
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348 | return MakeExp(GetSimplifiedTree(original.GetSubtree(0)));
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349 | }
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350 |
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351 | private ISymbolicExpressionTreeNode SimplifyLog(ISymbolicExpressionTreeNode original) {
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352 | return MakeLog(GetSimplifiedTree(original.GetSubtree(0)));
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353 | }
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354 | private ISymbolicExpressionTreeNode SimplifyRoot(ISymbolicExpressionTreeNode original) {
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355 | return MakeRoot(GetSimplifiedTree(original.GetSubtree(0)), GetSimplifiedTree(original.GetSubtree(1)));
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356 | }
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357 |
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358 | private ISymbolicExpressionTreeNode SimplifyPower(ISymbolicExpressionTreeNode original) {
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359 | return MakePower(GetSimplifiedTree(original.GetSubtree(0)), GetSimplifiedTree(original.GetSubtree(1)));
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360 | }
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361 | #endregion
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362 |
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363 | #region low level tree restructuring
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364 | private ISymbolicExpressionTreeNode MakeNot(ISymbolicExpressionTreeNode t) {
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365 | if (IsConstant(t)) {
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366 | var constNode = t as ConstantTreeNode;
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367 | if (constNode.Value > 0) return MakeConstant(-1.0);
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368 | else return MakeConstant(1.0);
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369 | } else if (IsNot(t)) {
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370 | return t.GetSubtree(0);
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371 | } else if (!IsBoolean(t)) {
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372 | var gtNode = gtSymbol.CreateTreeNode();
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373 | gtNode.AddSubtree(t); gtNode.AddSubtree(MakeConstant(0.0));
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374 | var notNode = notSymbol.CreateTreeNode();
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375 | notNode.AddSubtree(gtNode);
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376 | return notNode;
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377 | } else {
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378 | var notNode = notSymbol.CreateTreeNode();
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379 | notNode.AddSubtree(t);
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380 | return notNode;
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381 | }
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382 | }
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383 |
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384 | private ISymbolicExpressionTreeNode MakeOr(ISymbolicExpressionTreeNode a, ISymbolicExpressionTreeNode b) {
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385 | if (IsConstant(a) && IsConstant(b)) {
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386 | var constA = a as ConstantTreeNode;
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387 | var constB = b as ConstantTreeNode;
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388 | if (constA.Value > 0.0 || constB.Value > 0.0) {
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389 | return MakeConstant(1.0);
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390 | } else {
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391 | return MakeConstant(-1.0);
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392 | }
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393 | } else if (IsConstant(a)) {
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394 | return MakeOr(b, a);
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395 | } else if (IsConstant(b)) {
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396 | var constT = b as ConstantTreeNode;
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397 | if (constT.Value > 0.0) {
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398 | // boolean expression is necessarily true
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399 | return MakeConstant(1.0);
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400 | } else {
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401 | // the constant value has no effect on the result of the boolean condition so we can drop the constant term
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402 | var orNode = orSymbol.CreateTreeNode();
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403 | orNode.AddSubtree(a);
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404 | return orNode;
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405 | }
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406 | } else {
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407 | var orNode = orSymbol.CreateTreeNode();
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408 | orNode.AddSubtree(a);
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409 | orNode.AddSubtree(b);
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410 | return orNode;
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411 | }
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412 | }
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413 | private ISymbolicExpressionTreeNode MakeAnd(ISymbolicExpressionTreeNode a, ISymbolicExpressionTreeNode b) {
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414 | if (IsConstant(a) && IsConstant(b)) {
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415 | var constA = a as ConstantTreeNode;
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416 | var constB = b as ConstantTreeNode;
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417 | if (constA.Value > 0.0 && constB.Value > 0.0) {
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418 | return MakeConstant(1.0);
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419 | } else {
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420 | return MakeConstant(-1.0);
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421 | }
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422 | } else if (IsConstant(a)) {
|
---|
423 | return MakeAnd(b, a);
|
---|
424 | } else if (IsConstant(b)) {
|
---|
425 | var constB = b as ConstantTreeNode;
|
---|
426 | if (constB.Value > 0.0) {
|
---|
427 | // the constant value has no effect on the result of the boolean condition so we can drop the constant term
|
---|
428 | var andNode = andSymbol.CreateTreeNode();
|
---|
429 | andNode.AddSubtree(a);
|
---|
430 | return andNode;
|
---|
431 | } else {
|
---|
432 | // boolean expression is necessarily false
|
---|
433 | return MakeConstant(-1.0);
|
---|
434 | }
|
---|
435 | } else {
|
---|
436 | var andNode = andSymbol.CreateTreeNode();
|
---|
437 | andNode.AddSubtree(a);
|
---|
438 | andNode.AddSubtree(b);
|
---|
439 | return andNode;
|
---|
440 | }
|
---|
441 | }
|
---|
442 | private ISymbolicExpressionTreeNode MakeLessThan(ISymbolicExpressionTreeNode leftSide, ISymbolicExpressionTreeNode rightSide) {
|
---|
443 | if (IsConstant(leftSide) && IsConstant(rightSide)) {
|
---|
444 | var lsConst = leftSide as ConstantTreeNode;
|
---|
445 | var rsConst = rightSide as ConstantTreeNode;
|
---|
446 | if (lsConst.Value < rsConst.Value) return MakeConstant(1.0);
|
---|
447 | else return MakeConstant(-1.0);
|
---|
448 | } else {
|
---|
449 | var ltNode = ltSymbol.CreateTreeNode();
|
---|
450 | ltNode.AddSubtree(leftSide);
|
---|
451 | ltNode.AddSubtree(rightSide);
|
---|
452 | return ltNode;
|
---|
453 | }
|
---|
454 | }
|
---|
455 | private ISymbolicExpressionTreeNode MakeGreaterThan(ISymbolicExpressionTreeNode leftSide, ISymbolicExpressionTreeNode rightSide) {
|
---|
456 | if (IsConstant(leftSide) && IsConstant(rightSide)) {
|
---|
457 | var lsConst = leftSide as ConstantTreeNode;
|
---|
458 | var rsConst = rightSide as ConstantTreeNode;
|
---|
459 | if (lsConst.Value > rsConst.Value) return MakeConstant(1.0);
|
---|
460 | else return MakeConstant(-1.0);
|
---|
461 | } else {
|
---|
462 | var gtNode = gtSymbol.CreateTreeNode();
|
---|
463 | gtNode.AddSubtree(leftSide);
|
---|
464 | gtNode.AddSubtree(rightSide);
|
---|
465 | return gtNode;
|
---|
466 | }
|
---|
467 | }
|
---|
468 | private ISymbolicExpressionTreeNode MakeIfThenElse(ISymbolicExpressionTreeNode condition, ISymbolicExpressionTreeNode trueBranch, ISymbolicExpressionTreeNode falseBranch) {
|
---|
469 | if (IsConstant(condition)) {
|
---|
470 | var constT = condition as ConstantTreeNode;
|
---|
471 | if (constT.Value > 0.0) return trueBranch;
|
---|
472 | else return falseBranch;
|
---|
473 | } else {
|
---|
474 | var ifNode = ifThenElseSymbol.CreateTreeNode();
|
---|
475 | if (IsBoolean(condition)) {
|
---|
476 | ifNode.AddSubtree(condition);
|
---|
477 | } else {
|
---|
478 | var gtNode = gtSymbol.CreateTreeNode();
|
---|
479 | gtNode.AddSubtree(condition); gtNode.AddSubtree(MakeConstant(0.0));
|
---|
480 | ifNode.AddSubtree(gtNode);
|
---|
481 | }
|
---|
482 | ifNode.AddSubtree(trueBranch);
|
---|
483 | ifNode.AddSubtree(falseBranch);
|
---|
484 | return ifNode;
|
---|
485 | }
|
---|
486 | }
|
---|
487 |
|
---|
488 | private ISymbolicExpressionTreeNode MakeSine(ISymbolicExpressionTreeNode node) {
|
---|
489 | if (IsConstant(node)) {
|
---|
490 | var constT = node as ConstantTreeNode;
|
---|
491 | return MakeConstant(Math.Sin(constT.Value));
|
---|
492 | } else {
|
---|
493 | var sineNode = sineSymbol.CreateTreeNode();
|
---|
494 | sineNode.AddSubtree(node);
|
---|
495 | return sineNode;
|
---|
496 | }
|
---|
497 | }
|
---|
498 | private ISymbolicExpressionTreeNode MakeTangent(ISymbolicExpressionTreeNode node) {
|
---|
499 | if (IsConstant(node)) {
|
---|
500 | var constT = node as ConstantTreeNode;
|
---|
501 | return MakeConstant(Math.Tan(constT.Value));
|
---|
502 | } else {
|
---|
503 | var tanNode = tanSymbol.CreateTreeNode();
|
---|
504 | tanNode.AddSubtree(node);
|
---|
505 | return tanNode;
|
---|
506 | }
|
---|
507 | }
|
---|
508 | private ISymbolicExpressionTreeNode MakeCosine(ISymbolicExpressionTreeNode node) {
|
---|
509 | if (IsConstant(node)) {
|
---|
510 | var constT = node as ConstantTreeNode;
|
---|
511 | return MakeConstant(Math.Cos(constT.Value));
|
---|
512 | } else {
|
---|
513 | var cosNode = cosineSymbol.CreateTreeNode();
|
---|
514 | cosNode.AddSubtree(node);
|
---|
515 | return cosNode;
|
---|
516 | }
|
---|
517 | }
|
---|
518 | private ISymbolicExpressionTreeNode MakeExp(ISymbolicExpressionTreeNode node) {
|
---|
519 | if (IsConstant(node)) {
|
---|
520 | var constT = node as ConstantTreeNode;
|
---|
521 | return MakeConstant(Math.Exp(constT.Value));
|
---|
522 | } else if (IsLog(node)) {
|
---|
523 | return node.GetSubtree(0);
|
---|
524 | } else if (IsAddition(node)) {
|
---|
525 | return node.Subtrees.Select(s => MakeExp(s)).Aggregate((s, t) => MakeProduct(s, t));
|
---|
526 | } else if (IsSubtraction(node)) {
|
---|
527 | return node.Subtrees.Select(s => MakeExp(s)).Aggregate((s, t) => MakeProduct(s, Negate(t)));
|
---|
528 | } else {
|
---|
529 | var expNode = expSymbol.CreateTreeNode();
|
---|
530 | expNode.AddSubtree(node);
|
---|
531 | return expNode;
|
---|
532 | }
|
---|
533 | }
|
---|
534 | private ISymbolicExpressionTreeNode MakeLog(ISymbolicExpressionTreeNode node) {
|
---|
535 | if (IsConstant(node)) {
|
---|
536 | var constT = node as ConstantTreeNode;
|
---|
537 | return MakeConstant(Math.Log(constT.Value));
|
---|
538 | } else if (IsExp(node)) {
|
---|
539 | return node.GetSubtree(0);
|
---|
540 | } else {
|
---|
541 | var logNode = logSymbol.CreateTreeNode();
|
---|
542 | logNode.AddSubtree(node);
|
---|
543 | return logNode;
|
---|
544 | }
|
---|
545 | }
|
---|
546 | private ISymbolicExpressionTreeNode MakeRoot(ISymbolicExpressionTreeNode a, ISymbolicExpressionTreeNode b) {
|
---|
547 | if (IsConstant(a) && IsConstant(b)) {
|
---|
548 | var constA = a as ConstantTreeNode;
|
---|
549 | var constB = b as ConstantTreeNode;
|
---|
550 | return MakeConstant(Math.Pow(constA.Value, 1.0 / Math.Round(constB.Value)));
|
---|
551 | } else if (IsConstant(b)) {
|
---|
552 | var constB = b as ConstantTreeNode;
|
---|
553 | var constBValue = Math.Round(constB.Value);
|
---|
554 | if (constBValue.IsAlmost(1.0)) {
|
---|
555 | return a;
|
---|
556 | } else if (constBValue.IsAlmost(0.0)) {
|
---|
557 | return MakeConstant(1.0);
|
---|
558 | } else if (constBValue.IsAlmost(-1.0)) {
|
---|
559 | return MakeFraction(MakeConstant(1.0), a);
|
---|
560 | } else if (constBValue < 0) {
|
---|
561 | var rootNode = rootSymbol.CreateTreeNode();
|
---|
562 | rootNode.AddSubtree(a);
|
---|
563 | rootNode.AddSubtree(MakeConstant(-1.0 * constBValue));
|
---|
564 | return MakeFraction(MakeConstant(1.0), rootNode);
|
---|
565 | } else {
|
---|
566 | var rootNode = rootSymbol.CreateTreeNode();
|
---|
567 | rootNode.AddSubtree(a);
|
---|
568 | rootNode.AddSubtree(MakeConstant(constBValue));
|
---|
569 | return rootNode;
|
---|
570 | }
|
---|
571 | } else {
|
---|
572 | var rootNode = rootSymbol.CreateTreeNode();
|
---|
573 | rootNode.AddSubtree(a);
|
---|
574 | rootNode.AddSubtree(b);
|
---|
575 | return rootNode;
|
---|
576 | }
|
---|
577 | }
|
---|
578 | private ISymbolicExpressionTreeNode MakePower(ISymbolicExpressionTreeNode a, ISymbolicExpressionTreeNode b) {
|
---|
579 | if (IsConstant(a) && IsConstant(b)) {
|
---|
580 | var constA = a as ConstantTreeNode;
|
---|
581 | var constB = b as ConstantTreeNode;
|
---|
582 | return MakeConstant(Math.Pow(constA.Value, Math.Round(constB.Value)));
|
---|
583 | } else if (IsConstant(b)) {
|
---|
584 | var constB = b as ConstantTreeNode;
|
---|
585 | double exponent = Math.Round(constB.Value);
|
---|
586 | if (exponent.IsAlmost(0.0)) {
|
---|
587 | return MakeConstant(1.0);
|
---|
588 | } else if (exponent.IsAlmost(1.0)) {
|
---|
589 | return a;
|
---|
590 | } else if (exponent.IsAlmost(-1.0)) {
|
---|
591 | return MakeFraction(MakeConstant(1.0), a);
|
---|
592 | } else if (exponent < 0) {
|
---|
593 | var powNode = powSymbol.CreateTreeNode();
|
---|
594 | powNode.AddSubtree(a);
|
---|
595 | powNode.AddSubtree(MakeConstant(-1.0 * exponent));
|
---|
596 | return MakeFraction(MakeConstant(1.0), powNode);
|
---|
597 | } else {
|
---|
598 | var powNode = powSymbol.CreateTreeNode();
|
---|
599 | powNode.AddSubtree(a);
|
---|
600 | powNode.AddSubtree(MakeConstant(exponent));
|
---|
601 | return powNode;
|
---|
602 | }
|
---|
603 | } else {
|
---|
604 | var powNode = powSymbol.CreateTreeNode();
|
---|
605 | powNode.AddSubtree(a);
|
---|
606 | powNode.AddSubtree(b);
|
---|
607 | return powNode;
|
---|
608 | }
|
---|
609 | }
|
---|
610 |
|
---|
611 |
|
---|
612 | // MakeFraction, MakeProduct and MakeSum take two already simplified trees and create a new simplified tree
|
---|
613 | private ISymbolicExpressionTreeNode MakeFraction(ISymbolicExpressionTreeNode a, ISymbolicExpressionTreeNode b) {
|
---|
614 | if (IsConstant(a) && IsConstant(b)) {
|
---|
615 | // fold constants
|
---|
616 | return MakeConstant(((ConstantTreeNode)a).Value / ((ConstantTreeNode)b).Value);
|
---|
617 | } if (IsConstant(a) && !((ConstantTreeNode)a).Value.IsAlmost(1.0)) {
|
---|
618 | return MakeFraction(MakeConstant(1.0), MakeProduct(b, Invert(a)));
|
---|
619 | } else if (IsVariable(a) && IsConstant(b)) {
|
---|
620 | // merge constant values into variable weights
|
---|
621 | var constB = ((ConstantTreeNode)b).Value;
|
---|
622 | ((VariableTreeNode)a).Weight /= constB;
|
---|
623 | return a;
|
---|
624 | } else if (IsVariable(a) && IsVariable(b) && AreSameVariable(a, b)) {
|
---|
625 | // cancel variables
|
---|
626 | var aVar = a as VariableTreeNode;
|
---|
627 | var bVar = b as VariableTreeNode;
|
---|
628 | return MakeConstant(aVar.Weight / bVar.Weight);
|
---|
629 | } else if (IsAddition(a) && IsConstant(b)) {
|
---|
630 | return a.Subtrees
|
---|
631 | .Select(x => GetSimplifiedTree(x))
|
---|
632 | .Select(x => MakeFraction(x, b))
|
---|
633 | .Aggregate((c, d) => MakeSum(c, d));
|
---|
634 | } else if (IsMultiplication(a) && IsConstant(b)) {
|
---|
635 | return MakeProduct(a, Invert(b));
|
---|
636 | } else if (IsDivision(a) && IsConstant(b)) {
|
---|
637 | // (a1 / a2) / c => (a1 / (a2 * c))
|
---|
638 | Trace.Assert(a.Subtrees.Count() == 2);
|
---|
639 | return MakeFraction(a.GetSubtree(0), MakeProduct(a.GetSubtree(1), b));
|
---|
640 | } else if (IsDivision(a) && IsDivision(b)) {
|
---|
641 | // (a1 / a2) / (b1 / b2) =>
|
---|
642 | Trace.Assert(a.Subtrees.Count() == 2);
|
---|
643 | Trace.Assert(b.Subtrees.Count() == 2);
|
---|
644 | return MakeFraction(MakeProduct(a.GetSubtree(0), b.GetSubtree(1)), MakeProduct(a.GetSubtree(1), b.GetSubtree(0)));
|
---|
645 | } else if (IsDivision(a)) {
|
---|
646 | // (a1 / a2) / b => (a1 / (a2 * b))
|
---|
647 | Trace.Assert(a.Subtrees.Count() == 2);
|
---|
648 | return MakeFraction(a.GetSubtree(0), MakeProduct(a.GetSubtree(1), b));
|
---|
649 | } else if (IsDivision(b)) {
|
---|
650 | // a / (b1 / b2) => (a * b2) / b1
|
---|
651 | Trace.Assert(b.Subtrees.Count() == 2);
|
---|
652 | return MakeFraction(MakeProduct(a, b.GetSubtree(1)), b.GetSubtree(0));
|
---|
653 | } else {
|
---|
654 | var div = divSymbol.CreateTreeNode();
|
---|
655 | div.AddSubtree(a);
|
---|
656 | div.AddSubtree(b);
|
---|
657 | return div;
|
---|
658 | }
|
---|
659 | }
|
---|
660 |
|
---|
661 | private ISymbolicExpressionTreeNode MakeSum(ISymbolicExpressionTreeNode a, ISymbolicExpressionTreeNode b) {
|
---|
662 | if (IsConstant(a) && IsConstant(b)) {
|
---|
663 | // fold constants
|
---|
664 | ((ConstantTreeNode)a).Value += ((ConstantTreeNode)b).Value;
|
---|
665 | return a;
|
---|
666 | } else if (IsConstant(a)) {
|
---|
667 | // c + x => x + c
|
---|
668 | // b is not constant => make sure constant is on the right
|
---|
669 | return MakeSum(b, a);
|
---|
670 | } else if (IsConstant(b) && ((ConstantTreeNode)b).Value.IsAlmost(0.0)) {
|
---|
671 | // x + 0 => x
|
---|
672 | return a;
|
---|
673 | } else if (IsAddition(a) && IsAddition(b)) {
|
---|
674 | // merge additions
|
---|
675 | var add = addSymbol.CreateTreeNode();
|
---|
676 | // add all sub trees except for the last
|
---|
677 | for (int i = 0; i < a.Subtrees.Count() - 1; i++) add.AddSubtree(a.GetSubtree(i));
|
---|
678 | for (int i = 0; i < b.Subtrees.Count() - 1; i++) add.AddSubtree(b.GetSubtree(i));
|
---|
679 | if (IsConstant(a.Subtrees.Last()) && IsConstant(b.Subtrees.Last())) {
|
---|
680 | add.AddSubtree(MakeSum(a.Subtrees.Last(), b.Subtrees.Last()));
|
---|
681 | } else if (IsConstant(a.Subtrees.Last())) {
|
---|
682 | add.AddSubtree(b.Subtrees.Last());
|
---|
683 | add.AddSubtree(a.Subtrees.Last());
|
---|
684 | } else {
|
---|
685 | add.AddSubtree(a.Subtrees.Last());
|
---|
686 | add.AddSubtree(b.Subtrees.Last());
|
---|
687 | }
|
---|
688 | MergeVariablesInSum(add);
|
---|
689 | if (add.Subtrees.Count() == 1) {
|
---|
690 | return add.GetSubtree(0);
|
---|
691 | } else {
|
---|
692 | return add;
|
---|
693 | }
|
---|
694 | } else if (IsAddition(b)) {
|
---|
695 | return MakeSum(b, a);
|
---|
696 | } else if (IsAddition(a) && IsConstant(b)) {
|
---|
697 | // a is an addition and b is a constant => append b to a and make sure the constants are merged
|
---|
698 | var add = addSymbol.CreateTreeNode();
|
---|
699 | // add all sub trees except for the last
|
---|
700 | for (int i = 0; i < a.Subtrees.Count() - 1; i++) add.AddSubtree(a.GetSubtree(i));
|
---|
701 | if (IsConstant(a.Subtrees.Last()))
|
---|
702 | add.AddSubtree(MakeSum(a.Subtrees.Last(), b));
|
---|
703 | else {
|
---|
704 | add.AddSubtree(a.Subtrees.Last());
|
---|
705 | add.AddSubtree(b);
|
---|
706 | }
|
---|
707 | return add;
|
---|
708 | } else if (IsAddition(a)) {
|
---|
709 | // a is already an addition => append b
|
---|
710 | var add = addSymbol.CreateTreeNode();
|
---|
711 | add.AddSubtree(b);
|
---|
712 | foreach (var subtree in a.Subtrees) {
|
---|
713 | add.AddSubtree(subtree);
|
---|
714 | }
|
---|
715 | MergeVariablesInSum(add);
|
---|
716 | if (add.Subtrees.Count() == 1) {
|
---|
717 | return add.GetSubtree(0);
|
---|
718 | } else {
|
---|
719 | return add;
|
---|
720 | }
|
---|
721 | } else {
|
---|
722 | var add = addSymbol.CreateTreeNode();
|
---|
723 | add.AddSubtree(a);
|
---|
724 | add.AddSubtree(b);
|
---|
725 | MergeVariablesInSum(add);
|
---|
726 | if (add.Subtrees.Count() == 1) {
|
---|
727 | return add.GetSubtree(0);
|
---|
728 | } else {
|
---|
729 | return add;
|
---|
730 | }
|
---|
731 | }
|
---|
732 | }
|
---|
733 |
|
---|
734 | // makes sure variable symbols in sums are combined
|
---|
735 | // possible improvement: combine sums of products where the products only reference the same variable
|
---|
736 | private void MergeVariablesInSum(ISymbolicExpressionTreeNode sum) {
|
---|
737 | var subtrees = new List<ISymbolicExpressionTreeNode>(sum.Subtrees);
|
---|
738 | while (sum.Subtrees.Count() > 0) sum.RemoveSubtree(0);
|
---|
739 | var groupedVarNodes = from node in subtrees.OfType<VariableTreeNode>()
|
---|
740 | let lag = (node is LaggedVariableTreeNode) ? ((LaggedVariableTreeNode)node).Lag : 0
|
---|
741 | group node by node.VariableName + lag into g
|
---|
742 | select g;
|
---|
743 | var unchangedSubtrees = subtrees.Where(t => !(t is VariableTreeNode));
|
---|
744 |
|
---|
745 | foreach (var variableNodeGroup in groupedVarNodes) {
|
---|
746 | var weightSum = variableNodeGroup.Select(t => t.Weight).Sum();
|
---|
747 | var representative = variableNodeGroup.First();
|
---|
748 | representative.Weight = weightSum;
|
---|
749 | sum.AddSubtree(representative);
|
---|
750 | }
|
---|
751 | foreach (var unchangedSubtree in unchangedSubtrees)
|
---|
752 | sum.AddSubtree(unchangedSubtree);
|
---|
753 | }
|
---|
754 |
|
---|
755 |
|
---|
756 | private ISymbolicExpressionTreeNode MakeProduct(ISymbolicExpressionTreeNode a, ISymbolicExpressionTreeNode b) {
|
---|
757 | if (IsConstant(a) && IsConstant(b)) {
|
---|
758 | // fold constants
|
---|
759 | ((ConstantTreeNode)a).Value *= ((ConstantTreeNode)b).Value;
|
---|
760 | return a;
|
---|
761 | } else if (IsConstant(a)) {
|
---|
762 | // a * $ => $ * a
|
---|
763 | return MakeProduct(b, a);
|
---|
764 | } else if (IsConstant(b) && ((ConstantTreeNode)b).Value.IsAlmost(1.0)) {
|
---|
765 | // $ * 1.0 => $
|
---|
766 | return a;
|
---|
767 | } else if (IsConstant(b) && IsVariable(a)) {
|
---|
768 | // multiply constants into variables weights
|
---|
769 | ((VariableTreeNode)a).Weight *= ((ConstantTreeNode)b).Value;
|
---|
770 | return a;
|
---|
771 | } else if (IsConstant(b) && IsAddition(a)) {
|
---|
772 | // multiply constants into additions
|
---|
773 | return a.Subtrees.Select(x => MakeProduct(x, b)).Aggregate((c, d) => MakeSum(c, d));
|
---|
774 | } else if (IsDivision(a) && IsDivision(b)) {
|
---|
775 | // (a1 / a2) * (b1 / b2) => (a1 * b1) / (a2 * b2)
|
---|
776 | Trace.Assert(a.Subtrees.Count() == 2);
|
---|
777 | Trace.Assert(b.Subtrees.Count() == 2);
|
---|
778 | return MakeFraction(MakeProduct(a.GetSubtree(0), b.GetSubtree(0)), MakeProduct(a.GetSubtree(1), b.GetSubtree(1)));
|
---|
779 | } else if (IsDivision(a)) {
|
---|
780 | // (a1 / a2) * b => (a1 * b) / a2
|
---|
781 | Trace.Assert(a.Subtrees.Count() == 2);
|
---|
782 | return MakeFraction(MakeProduct(a.GetSubtree(0), b), a.GetSubtree(1));
|
---|
783 | } else if (IsDivision(b)) {
|
---|
784 | // a * (b1 / b2) => (b1 * a) / b2
|
---|
785 | Trace.Assert(b.Subtrees.Count() == 2);
|
---|
786 | return MakeFraction(MakeProduct(b.GetSubtree(0), a), b.GetSubtree(1));
|
---|
787 | } else if (IsMultiplication(a) && IsMultiplication(b)) {
|
---|
788 | // merge multiplications (make sure constants are merged)
|
---|
789 | var mul = mulSymbol.CreateTreeNode();
|
---|
790 | for (int i = 0; i < a.Subtrees.Count(); i++) mul.AddSubtree(a.GetSubtree(i));
|
---|
791 | for (int i = 0; i < b.Subtrees.Count(); i++) mul.AddSubtree(b.GetSubtree(i));
|
---|
792 | MergeVariablesAndConstantsInProduct(mul);
|
---|
793 | return mul;
|
---|
794 | } else if (IsMultiplication(b)) {
|
---|
795 | return MakeProduct(b, a);
|
---|
796 | } else if (IsMultiplication(a)) {
|
---|
797 | // a is already an multiplication => append b
|
---|
798 | a.AddSubtree(b);
|
---|
799 | MergeVariablesAndConstantsInProduct(a);
|
---|
800 | return a;
|
---|
801 | } else {
|
---|
802 | var mul = mulSymbol.CreateTreeNode();
|
---|
803 | mul.AddSubtree(a);
|
---|
804 | mul.AddSubtree(b);
|
---|
805 | MergeVariablesAndConstantsInProduct(mul);
|
---|
806 | return mul;
|
---|
807 | }
|
---|
808 | }
|
---|
809 | #endregion
|
---|
810 |
|
---|
811 |
|
---|
812 | #region helper functions
|
---|
813 |
|
---|
814 | private bool AreSameVariable(ISymbolicExpressionTreeNode a, ISymbolicExpressionTreeNode b) {
|
---|
815 | var aLaggedVar = a as LaggedVariableTreeNode;
|
---|
816 | var bLaggedVar = b as LaggedVariableTreeNode;
|
---|
817 | if (aLaggedVar != null && bLaggedVar != null) {
|
---|
818 | return aLaggedVar.VariableName == bLaggedVar.VariableName &&
|
---|
819 | aLaggedVar.Lag == bLaggedVar.Lag;
|
---|
820 | }
|
---|
821 | var aVar = a as VariableTreeNode;
|
---|
822 | var bVar = b as VariableTreeNode;
|
---|
823 | if (aVar != null && bVar != null) {
|
---|
824 | return aVar.VariableName == bVar.VariableName;
|
---|
825 | }
|
---|
826 | return false;
|
---|
827 | }
|
---|
828 |
|
---|
829 | // helper to combine the constant factors in products and to combine variables (powers of 2, 3...)
|
---|
830 | private void MergeVariablesAndConstantsInProduct(ISymbolicExpressionTreeNode prod) {
|
---|
831 | var subtrees = new List<ISymbolicExpressionTreeNode>(prod.Subtrees);
|
---|
832 | while (prod.Subtrees.Count() > 0) prod.RemoveSubtree(0);
|
---|
833 | var groupedVarNodes = from node in subtrees.OfType<VariableTreeNode>()
|
---|
834 | let lag = (node is LaggedVariableTreeNode) ? ((LaggedVariableTreeNode)node).Lag : 0
|
---|
835 | group node by node.VariableName + lag into g
|
---|
836 | orderby g.Count()
|
---|
837 | select g;
|
---|
838 | var constantProduct = (from node in subtrees.OfType<VariableTreeNode>()
|
---|
839 | select node.Weight)
|
---|
840 | .Concat(from node in subtrees.OfType<ConstantTreeNode>()
|
---|
841 | select node.Value)
|
---|
842 | .DefaultIfEmpty(1.0)
|
---|
843 | .Aggregate((c1, c2) => c1 * c2);
|
---|
844 |
|
---|
845 | var unchangedSubtrees = from tree in subtrees
|
---|
846 | where !(tree is VariableTreeNode)
|
---|
847 | where !(tree is ConstantTreeNode)
|
---|
848 | select tree;
|
---|
849 |
|
---|
850 | foreach (var variableNodeGroup in groupedVarNodes) {
|
---|
851 | var representative = variableNodeGroup.First();
|
---|
852 | representative.Weight = 1.0;
|
---|
853 | if (variableNodeGroup.Count() > 1) {
|
---|
854 | var poly = mulSymbol.CreateTreeNode();
|
---|
855 | for (int p = 0; p < variableNodeGroup.Count(); p++) {
|
---|
856 | poly.AddSubtree((ISymbolicExpressionTreeNode)representative.Clone());
|
---|
857 | }
|
---|
858 | prod.AddSubtree(poly);
|
---|
859 | } else {
|
---|
860 | prod.AddSubtree(representative);
|
---|
861 | }
|
---|
862 | }
|
---|
863 |
|
---|
864 | foreach (var unchangedSubtree in unchangedSubtrees)
|
---|
865 | prod.AddSubtree(unchangedSubtree);
|
---|
866 |
|
---|
867 | if (!constantProduct.IsAlmost(1.0)) {
|
---|
868 | prod.AddSubtree(MakeConstant(constantProduct));
|
---|
869 | }
|
---|
870 | }
|
---|
871 |
|
---|
872 |
|
---|
873 | /// <summary>
|
---|
874 | /// x => x * -1
|
---|
875 | /// Doesn't create new trees and manipulates x
|
---|
876 | /// </summary>
|
---|
877 | /// <param name="x"></param>
|
---|
878 | /// <returns>-x</returns>
|
---|
879 | private ISymbolicExpressionTreeNode Negate(ISymbolicExpressionTreeNode x) {
|
---|
880 | if (IsConstant(x)) {
|
---|
881 | ((ConstantTreeNode)x).Value *= -1;
|
---|
882 | } else if (IsVariable(x)) {
|
---|
883 | var variableTree = (VariableTreeNode)x;
|
---|
884 | variableTree.Weight *= -1.0;
|
---|
885 | } else if (IsAddition(x)) {
|
---|
886 | // (x0 + x1 + .. + xn) * -1 => (-x0 + -x1 + .. + -xn)
|
---|
887 | List<ISymbolicExpressionTreeNode> subtrees = new List<ISymbolicExpressionTreeNode>(x.Subtrees);
|
---|
888 | while (x.Subtrees.Count() > 0) x.RemoveSubtree(0);
|
---|
889 | foreach (var subtree in subtrees) {
|
---|
890 | x.AddSubtree(Negate(subtree));
|
---|
891 | }
|
---|
892 | } else if (IsMultiplication(x) || IsDivision(x)) {
|
---|
893 | // x0 * x1 * .. * xn * -1 => x0 * x1 * .. * -xn
|
---|
894 | var lastSubTree = x.Subtrees.Last();
|
---|
895 | x.RemoveSubtree(x.SubtreesCount - 1);
|
---|
896 | x.AddSubtree(Negate(lastSubTree)); // last is maybe a constant, prefer to negate the constant
|
---|
897 | } else {
|
---|
898 | // any other function
|
---|
899 | return MakeProduct(x, MakeConstant(-1));
|
---|
900 | }
|
---|
901 | return x;
|
---|
902 | }
|
---|
903 |
|
---|
904 | /// <summary>
|
---|
905 | /// x => 1/x
|
---|
906 | /// Doesn't create new trees and manipulates x
|
---|
907 | /// </summary>
|
---|
908 | /// <param name="x"></param>
|
---|
909 | /// <returns></returns>
|
---|
910 | private ISymbolicExpressionTreeNode Invert(ISymbolicExpressionTreeNode x) {
|
---|
911 | if (IsConstant(x)) {
|
---|
912 | return MakeConstant(1.0 / ((ConstantTreeNode)x).Value);
|
---|
913 | } else if (IsDivision(x)) {
|
---|
914 | Trace.Assert(x.Subtrees.Count() == 2);
|
---|
915 | return MakeFraction(x.GetSubtree(1), x.GetSubtree(0));
|
---|
916 | } else {
|
---|
917 | // any other function
|
---|
918 | return MakeFraction(MakeConstant(1), x);
|
---|
919 | }
|
---|
920 | }
|
---|
921 |
|
---|
922 | private ISymbolicExpressionTreeNode MakeConstant(double value) {
|
---|
923 | ConstantTreeNode constantTreeNode = (ConstantTreeNode)(constSymbol.CreateTreeNode());
|
---|
924 | constantTreeNode.Value = value;
|
---|
925 | return constantTreeNode;
|
---|
926 | }
|
---|
927 |
|
---|
928 | private ISymbolicExpressionTreeNode MakeVariable(double weight, string name) {
|
---|
929 | var tree = (VariableTreeNode)varSymbol.CreateTreeNode();
|
---|
930 | tree.Weight = weight;
|
---|
931 | tree.VariableName = name;
|
---|
932 | return tree;
|
---|
933 | }
|
---|
934 | #endregion
|
---|
935 | }
|
---|
936 | }
|
---|