[3442] | 1 | #region License Information
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| 2 | /* HeuristicLab
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[5445] | 3 | * Copyright (C) 2002-2011 Heuristic and Evolutionary Algorithms Laboratory (HEAL)
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[3442] | 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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[4068] | 24 | using System.Diagnostics;
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[3442] | 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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[3462] | 28 | using HeuristicLab.Encodings.SymbolicExpressionTreeEncoding.Symbols;
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[3442] | 29 | using HeuristicLab.Problems.DataAnalysis.Symbolic.Symbols;
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| 30 |
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| 31 | namespace HeuristicLab.Problems.DataAnalysis.Symbolic {
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| 32 | /// <summary>
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| 33 | /// Simplistic simplifier for arithmetic expressions
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| 34 | /// </summary>
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| 35 | public class SymbolicSimplifier {
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[3462] | 36 | private Addition addSymbol = new Addition();
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[5461] | 37 | private Subtraction subSymbol = new Subtraction();
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[3462] | 38 | private Multiplication mulSymbol = new Multiplication();
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| 39 | private Division divSymbol = new Division();
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| 40 | private Constant constSymbol = new Constant();
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| 41 | private Variable varSymbol = new Variable();
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[5455] | 42 | private Logarithm logSymbol = new Logarithm();
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| 43 | private Exponential expSymbol = new Exponential();
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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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[3462] | 53 |
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[3442] | 54 | public SymbolicExpressionTree Simplify(SymbolicExpressionTree originalTree) {
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| 55 | var clone = (SymbolicExpressionTreeNode)originalTree.Root.Clone();
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| 56 | // macro expand (initially no argument trees)
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| 57 | var macroExpandedTree = MacroExpand(clone, clone.SubTrees[0], new List<SymbolicExpressionTreeNode>());
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[4477] | 58 | SymbolicExpressionTreeNode 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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[3442] | 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 SymbolicExpressionTreeNode MacroExpand(SymbolicExpressionTreeNode root, SymbolicExpressionTreeNode node, IList<SymbolicExpressionTreeNode> argumentTrees) {
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| 65 | List<SymbolicExpressionTreeNode> subtrees = new List<SymbolicExpressionTreeNode>(node.SubTrees);
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[3985] | 66 | while (node.SubTrees.Count > 0) node.RemoveSubTree(0);
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[3442] | 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<SymbolicExpressionTreeNode>();
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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 SymbolicExpressionTreeNode FindFunctionDefinition(SymbolicExpressionTreeNode 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.SubTrees[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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[4239] | 96 |
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| 97 | #region symbol predicates
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[5455] | 98 | // arithmetic
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| 99 | private bool IsDivision(SymbolicExpressionTreeNode node) {
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| 100 | return node.Symbol is Division;
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[4239] | 101 | }
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| 102 |
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[5455] | 103 | private bool IsMultiplication(SymbolicExpressionTreeNode node) {
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| 104 | return node.Symbol is Multiplication;
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[4239] | 105 | }
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| 106 |
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[5455] | 107 | private bool IsSubtraction(SymbolicExpressionTreeNode node) {
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| 108 | return node.Symbol is Subtraction;
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[4239] | 109 | }
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| 110 |
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[5455] | 111 | private bool IsAddition(SymbolicExpressionTreeNode node) {
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| 112 | return node.Symbol is Addition;
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[4239] | 113 | }
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| 114 |
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[5455] | 115 | private bool IsAverage(SymbolicExpressionTreeNode node) {
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| 116 | return node.Symbol is Average;
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[4239] | 117 | }
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[5455] | 118 | // exponential
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| 119 | private bool IsLog(SymbolicExpressionTreeNode node) {
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| 120 | return node.Symbol is Logarithm;
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| 121 | }
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| 122 | private bool IsExp(SymbolicExpressionTreeNode node) {
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| 123 | return node.Symbol is Exponential;
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| 124 | }
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| 125 | // trigonometric
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| 126 | private bool IsSine(SymbolicExpressionTreeNode node) {
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| 127 | return node.Symbol is Sine;
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| 128 | }
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| 129 | private bool IsCosine(SymbolicExpressionTreeNode node) {
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| 130 | return node.Symbol is Cosine;
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| 131 | }
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| 132 | private bool IsTangent(SymbolicExpressionTreeNode node) {
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| 133 | return node.Symbol is Tangent;
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| 134 | }
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| 135 | // boolean
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| 136 | private bool IsIfThenElse(SymbolicExpressionTreeNode node) {
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| 137 | return node.Symbol is IfThenElse;
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| 138 | }
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| 139 | private bool IsAnd(SymbolicExpressionTreeNode node) {
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| 140 | return node.Symbol is And;
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| 141 | }
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| 142 | private bool IsOr(SymbolicExpressionTreeNode node) {
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| 143 | return node.Symbol is Or;
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| 144 | }
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| 145 | private bool IsNot(SymbolicExpressionTreeNode node) {
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| 146 | return node.Symbol is Not;
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| 147 | }
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| 148 | // comparison
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| 149 | private bool IsGreaterThan(SymbolicExpressionTreeNode node) {
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| 150 | return node.Symbol is GreaterThan;
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| 151 | }
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| 152 | private bool IsLessThan(SymbolicExpressionTreeNode node) {
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| 153 | return node.Symbol is LessThan;
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| 154 | }
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[4239] | 155 |
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[5461] | 156 | private bool IsBoolean(SymbolicExpressionTreeNode node) {
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| 157 | return
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| 158 | node.Symbol is GreaterThan ||
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| 159 | node.Symbol is LessThan ||
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| 160 | node.Symbol is And ||
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| 161 | node.Symbol is Or;
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| 162 | }
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| 163 |
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[5455] | 164 | // terminals
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| 165 | private bool IsVariable(SymbolicExpressionTreeNode node) {
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| 166 | return node.Symbol is Variable;
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[4239] | 167 | }
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| 168 |
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[5455] | 169 | private bool IsConstant(SymbolicExpressionTreeNode node) {
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| 170 | return node.Symbol is Constant;
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[4239] | 171 | }
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[5455] | 172 |
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[4239] | 173 | #endregion
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| 174 |
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[3442] | 175 | /// <summary>
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| 176 | /// Creates a new simplified tree
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| 177 | /// </summary>
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| 178 | /// <param name="original"></param>
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| 179 | /// <returns></returns>
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| 180 | public SymbolicExpressionTreeNode GetSimplifiedTree(SymbolicExpressionTreeNode original) {
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| 181 | if (IsConstant(original) || IsVariable(original)) {
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| 182 | return (SymbolicExpressionTreeNode)original.Clone();
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| 183 | } else if (IsAddition(original)) {
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[4239] | 184 | return SimplifyAddition(original);
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[3442] | 185 | } else if (IsSubtraction(original)) {
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[4239] | 186 | return SimplifySubtraction(original);
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[3442] | 187 | } else if (IsMultiplication(original)) {
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[4239] | 188 | return SimplifyMultiplication(original);
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[3442] | 189 | } else if (IsDivision(original)) {
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[4239] | 190 | return SimplifyDivision(original);
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[3876] | 191 | } else if (IsAverage(original)) {
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[4239] | 192 | return SimplifyAverage(original);
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| 193 | } else if (IsLog(original)) {
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[5455] | 194 | return SimplifyLog(original);
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| 195 | } else if (IsExp(original)) {
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| 196 | return SimplifyExp(original);
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| 197 | } else if (IsSine(original)) {
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| 198 | return SimplifySine(original);
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| 199 | } else if (IsCosine(original)) {
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| 200 | return SimplifyCosine(original);
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| 201 | } else if (IsTangent(original)) {
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| 202 | return SimplifyTangent(original);
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[4239] | 203 | } else if (IsIfThenElse(original)) {
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[5455] | 204 | return SimplifyIfThenElse(original);
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| 205 | } else if (IsGreaterThan(original)) {
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| 206 | return SimplifyGreaterThan(original);
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| 207 | } else if (IsLessThan(original)) {
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| 208 | return SimplifyLessThan(original);
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| 209 | } else if (IsAnd(original)) {
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| 210 | return SimplifyAnd(original);
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| 211 | } else if (IsOr(original)) {
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| 212 | return SimplifyOr(original);
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| 213 | } else if (IsNot(original)) {
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| 214 | return SimplifyNot(original);
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[3442] | 215 | } else {
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[4239] | 216 | return SimplifyAny(original);
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[3442] | 217 | }
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| 218 | }
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| 219 |
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[5455] | 220 |
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[4239] | 221 | #region specific simplification routines
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| 222 | private SymbolicExpressionTreeNode SimplifyAny(SymbolicExpressionTreeNode original) {
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| 223 | // can't simplify this function but simplify all subtrees
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| 224 | List<SymbolicExpressionTreeNode> subTrees = new List<SymbolicExpressionTreeNode>(original.SubTrees);
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| 225 | while (original.SubTrees.Count > 0) original.RemoveSubTree(0);
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| 226 | var clone = (SymbolicExpressionTreeNode)original.Clone();
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| 227 | List<SymbolicExpressionTreeNode> simplifiedSubTrees = new List<SymbolicExpressionTreeNode>();
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| 228 | foreach (var subTree in subTrees) {
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| 229 | simplifiedSubTrees.Add(GetSimplifiedTree(subTree));
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| 230 | original.AddSubTree(subTree);
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| 231 | }
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| 232 | foreach (var simplifiedSubtree in simplifiedSubTrees) {
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| 233 | clone.AddSubTree(simplifiedSubtree);
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| 234 | }
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| 235 | if (simplifiedSubTrees.TrueForAll(t => IsConstant(t))) {
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| 236 | SimplifyConstantExpression(clone);
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| 237 | }
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| 238 | return clone;
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| 239 | }
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| 240 |
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| 241 | private SymbolicExpressionTreeNode SimplifyConstantExpression(SymbolicExpressionTreeNode original) {
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| 242 | // not yet implemented
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| 243 | return original;
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| 244 | }
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| 245 |
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| 246 | private SymbolicExpressionTreeNode SimplifyAverage(SymbolicExpressionTreeNode original) {
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| 247 | if (original.SubTrees.Count == 1) {
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| 248 | return GetSimplifiedTree(original.SubTrees[0]);
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[3442] | 249 | } else {
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[4239] | 250 | // simplify expressions x0..xn
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| 251 | // make sum(x0..xn) / n
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| 252 | Trace.Assert(original.SubTrees.Count > 1);
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| 253 | var sum = original.SubTrees
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| 254 | .Select(x => GetSimplifiedTree(x))
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| 255 | .Aggregate((a, b) => MakeSum(a, b));
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| 256 | return MakeFraction(sum, MakeConstant(original.SubTrees.Count));
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[3442] | 257 | }
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| 258 | }
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| 259 |
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[4239] | 260 | private SymbolicExpressionTreeNode SimplifyDivision(SymbolicExpressionTreeNode original) {
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| 261 | if (original.SubTrees.Count == 1) {
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| 262 | return Invert(GetSimplifiedTree(original.SubTrees[0]));
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[3442] | 263 | } else {
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[4239] | 264 | // simplify expressions x0..xn
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| 265 | // make multiplication (x0 * 1/(x1 * x1 * .. * xn))
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| 266 | Trace.Assert(original.SubTrees.Count > 1);
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| 267 | var simplifiedTrees = original.SubTrees.Select(x => GetSimplifiedTree(x));
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| 268 | return
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| 269 | MakeProduct(simplifiedTrees.First(), Invert(simplifiedTrees.Skip(1).Aggregate((a, b) => MakeProduct(a, b))));
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[3442] | 270 | }
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| 271 | }
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| 272 |
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[4239] | 273 | private SymbolicExpressionTreeNode SimplifyMultiplication(SymbolicExpressionTreeNode original) {
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| 274 | if (original.SubTrees.Count == 1) {
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| 275 | return GetSimplifiedTree(original.SubTrees[0]);
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| 276 | } else {
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| 277 | Trace.Assert(original.SubTrees.Count > 1);
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| 278 | return original.SubTrees
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| 279 | .Select(x => GetSimplifiedTree(x))
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| 280 | .Aggregate((a, b) => MakeProduct(a, b));
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| 281 | }
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| 282 | }
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| 283 |
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| 284 | private SymbolicExpressionTreeNode SimplifySubtraction(SymbolicExpressionTreeNode original) {
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| 285 | if (original.SubTrees.Count == 1) {
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| 286 | return Negate(GetSimplifiedTree(original.SubTrees[0]));
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| 287 | } else {
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| 288 | // simplify expressions x0..xn
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| 289 | // make addition (x0,-x1..-xn)
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| 290 | Trace.Assert(original.SubTrees.Count > 1);
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| 291 | var simplifiedTrees = original.SubTrees.Select(x => GetSimplifiedTree(x));
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| 292 | return simplifiedTrees.Take(1)
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| 293 | .Concat(simplifiedTrees.Skip(1).Select(x => Negate(x)))
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| 294 | .Aggregate((a, b) => MakeSum(a, b));
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| 295 | }
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| 296 | }
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| 297 |
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| 298 | private SymbolicExpressionTreeNode SimplifyAddition(SymbolicExpressionTreeNode original) {
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| 299 | if (original.SubTrees.Count == 1) {
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| 300 | return GetSimplifiedTree(original.SubTrees[0]);
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| 301 | } else {
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| 302 | // simplify expression x0..xn
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| 303 | // make addition (x0..xn)
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| 304 | Trace.Assert(original.SubTrees.Count > 1);
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| 305 | return original.SubTrees
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| 306 | .Select(x => GetSimplifiedTree(x))
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| 307 | .Aggregate((a, b) => MakeSum(a, b));
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| 308 | }
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| 309 | }
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[5455] | 310 |
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| 311 | private SymbolicExpressionTreeNode SimplifyNot(SymbolicExpressionTreeNode original) {
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| 312 | return MakeNot(GetSimplifiedTree(original.SubTrees[0]));
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| 313 | }
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| 314 | private SymbolicExpressionTreeNode SimplifyOr(SymbolicExpressionTreeNode original) {
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| 315 | return original.SubTrees
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| 316 | .Select(x => GetSimplifiedTree(x))
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| 317 | .Aggregate((a, b) => MakeOr(a, b));
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| 318 | }
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| 319 | private SymbolicExpressionTreeNode SimplifyAnd(SymbolicExpressionTreeNode 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) => MakeAnd(a, b));
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| 323 | }
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| 324 | private SymbolicExpressionTreeNode SimplifyLessThan(SymbolicExpressionTreeNode original) {
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| 325 | return MakeLessThan(GetSimplifiedTree(original.SubTrees[0]), GetSimplifiedTree(original.SubTrees[1]));
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| 326 | }
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| 327 | private SymbolicExpressionTreeNode SimplifyGreaterThan(SymbolicExpressionTreeNode original) {
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| 328 | return MakeGreaterThan(GetSimplifiedTree(original.SubTrees[0]), GetSimplifiedTree(original.SubTrees[1]));
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| 329 | }
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| 330 | private SymbolicExpressionTreeNode SimplifyIfThenElse(SymbolicExpressionTreeNode original) {
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| 331 | return MakeIfThenElse(GetSimplifiedTree(original.SubTrees[0]), GetSimplifiedTree(original.SubTrees[1]), GetSimplifiedTree(original.SubTrees[2]));
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| 332 | }
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| 333 | private SymbolicExpressionTreeNode SimplifyTangent(SymbolicExpressionTreeNode original) {
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| 334 | return MakeTangent(GetSimplifiedTree(original.SubTrees[0]));
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| 335 | }
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| 336 | private SymbolicExpressionTreeNode SimplifyCosine(SymbolicExpressionTreeNode original) {
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| 337 | return MakeCosine(GetSimplifiedTree(original.SubTrees[0]));
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| 338 | }
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| 339 | private SymbolicExpressionTreeNode SimplifySine(SymbolicExpressionTreeNode original) {
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| 340 | return MakeSine(GetSimplifiedTree(original.SubTrees[0]));
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| 341 | }
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| 342 | private SymbolicExpressionTreeNode SimplifyExp(SymbolicExpressionTreeNode original) {
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| 343 | return MakeExp(GetSimplifiedTree(original.SubTrees[0]));
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| 344 | }
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| 345 |
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| 346 | private SymbolicExpressionTreeNode SimplifyLog(SymbolicExpressionTreeNode original) {
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| 347 | return MakeLog(GetSimplifiedTree(original.SubTrees[0]));
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| 348 | }
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| 349 |
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[4239] | 350 | #endregion
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| 351 |
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| 352 |
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| 353 |
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| 354 | #region low level tree restructuring
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[5455] | 355 | private SymbolicExpressionTreeNode MakeNot(SymbolicExpressionTreeNode t) {
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| 356 | return MakeProduct(t, MakeConstant(-1.0));
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| 357 | }
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| 358 |
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| 359 | private SymbolicExpressionTreeNode MakeOr(SymbolicExpressionTreeNode a, SymbolicExpressionTreeNode b) {
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| 360 | if (IsConstant(a) && IsConstant(b)) {
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| 361 | var constA = a as ConstantTreeNode;
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| 362 | var constB = b as ConstantTreeNode;
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| 363 | if (constA.Value > 0.0 || constB.Value > 0.0) {
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| 364 | return MakeConstant(1.0);
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| 365 | } else {
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| 366 | return MakeConstant(-1.0);
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| 367 | }
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| 368 | } else if (IsConstant(a)) {
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| 369 | return MakeOr(b, a);
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| 370 | } else if (IsConstant(b)) {
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| 371 | var constT = b as ConstantTreeNode;
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| 372 | if (constT.Value > 0.0) {
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| 373 | // boolean expression is necessarily true
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| 374 | return MakeConstant(1.0);
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| 375 | } else {
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| 376 | // the constant value has no effect on the result of the boolean condition so we can drop the constant term
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| 377 | var orNode = orSymbol.CreateTreeNode();
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| 378 | orNode.AddSubTree(a);
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| 379 | return orNode;
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| 380 | }
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| 381 | } else {
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| 382 | var orNode = orSymbol.CreateTreeNode();
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| 383 | orNode.AddSubTree(a);
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| 384 | orNode.AddSubTree(b);
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| 385 | return orNode;
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| 386 | }
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| 387 | }
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| 388 | private SymbolicExpressionTreeNode MakeAnd(SymbolicExpressionTreeNode a, SymbolicExpressionTreeNode b) {
|
---|
| 389 | if (IsConstant(a) && IsConstant(b)) {
|
---|
| 390 | var constA = a as ConstantTreeNode;
|
---|
| 391 | var constB = b as ConstantTreeNode;
|
---|
| 392 | if (constA.Value > 0.0 && constB.Value > 0.0) {
|
---|
| 393 | return MakeConstant(1.0);
|
---|
| 394 | } else {
|
---|
| 395 | return MakeConstant(-1.0);
|
---|
| 396 | }
|
---|
| 397 | } else if (IsConstant(a)) {
|
---|
| 398 | return MakeAnd(b, a);
|
---|
| 399 | } else if (IsConstant(b)) {
|
---|
| 400 | var constB = b as ConstantTreeNode;
|
---|
| 401 | if (constB.Value > 0.0) {
|
---|
| 402 | // the constant value has no effect on the result of the boolean condition so we can drop the constant term
|
---|
| 403 | var andNode = andSymbol.CreateTreeNode();
|
---|
| 404 | andNode.AddSubTree(a);
|
---|
| 405 | return andNode;
|
---|
| 406 | } else {
|
---|
| 407 | // boolean expression is necessarily false
|
---|
| 408 | return MakeConstant(-1.0);
|
---|
| 409 | }
|
---|
| 410 | } else {
|
---|
| 411 | var andNode = andSymbol.CreateTreeNode();
|
---|
| 412 | andNode.AddSubTree(a);
|
---|
| 413 | andNode.AddSubTree(b);
|
---|
| 414 | return andNode;
|
---|
| 415 | }
|
---|
| 416 | }
|
---|
| 417 | private SymbolicExpressionTreeNode MakeLessThan(SymbolicExpressionTreeNode leftSide, SymbolicExpressionTreeNode rightSide) {
|
---|
| 418 | if (IsConstant(leftSide) && IsConstant(rightSide)) {
|
---|
| 419 | var lsConst = leftSide as ConstantTreeNode;
|
---|
| 420 | var rsConst = rightSide as ConstantTreeNode;
|
---|
| 421 | if (lsConst.Value < rsConst.Value) return MakeConstant(1.0);
|
---|
| 422 | else return MakeConstant(-1.0);
|
---|
| 423 | } else {
|
---|
| 424 | var ltNode = ltSymbol.CreateTreeNode();
|
---|
| 425 | ltNode.AddSubTree(leftSide);
|
---|
| 426 | ltNode.AddSubTree(rightSide);
|
---|
| 427 | return ltNode;
|
---|
| 428 | }
|
---|
| 429 | }
|
---|
| 430 | private SymbolicExpressionTreeNode MakeGreaterThan(SymbolicExpressionTreeNode leftSide, SymbolicExpressionTreeNode rightSide) {
|
---|
| 431 | if (IsConstant(leftSide) && IsConstant(rightSide)) {
|
---|
| 432 | var lsConst = leftSide as ConstantTreeNode;
|
---|
| 433 | var rsConst = rightSide as ConstantTreeNode;
|
---|
| 434 | if (lsConst.Value > rsConst.Value) return MakeConstant(1.0);
|
---|
| 435 | else return MakeConstant(-1.0);
|
---|
| 436 | } else {
|
---|
| 437 | var gtNode = gtSymbol.CreateTreeNode();
|
---|
| 438 | gtNode.AddSubTree(leftSide);
|
---|
| 439 | gtNode.AddSubTree(rightSide);
|
---|
| 440 | return gtNode;
|
---|
| 441 | }
|
---|
| 442 | }
|
---|
| 443 | private SymbolicExpressionTreeNode MakeIfThenElse(SymbolicExpressionTreeNode condition, SymbolicExpressionTreeNode trueBranch, SymbolicExpressionTreeNode falseBranch) {
|
---|
| 444 | if (IsConstant(condition)) {
|
---|
| 445 | var constT = condition as ConstantTreeNode;
|
---|
| 446 | if (constT.Value > 0.0) return trueBranch;
|
---|
| 447 | else return falseBranch;
|
---|
| 448 | } else {
|
---|
| 449 | var ifNode = ifThenElseSymbol.CreateTreeNode();
|
---|
[5461] | 450 | if (IsBoolean(condition)) {
|
---|
| 451 | ifNode.AddSubTree(condition);
|
---|
| 452 | } else {
|
---|
| 453 | var gtNode = gtSymbol.CreateTreeNode();
|
---|
| 454 | gtNode.AddSubTree(condition); gtNode.AddSubTree(MakeConstant(0.0));
|
---|
| 455 | ifNode.AddSubTree(gtNode);
|
---|
| 456 | }
|
---|
[5455] | 457 | ifNode.AddSubTree(trueBranch);
|
---|
| 458 | ifNode.AddSubTree(falseBranch);
|
---|
| 459 | return ifNode;
|
---|
| 460 | }
|
---|
| 461 | }
|
---|
[5461] | 462 |
|
---|
[5455] | 463 | private SymbolicExpressionTreeNode MakeSine(SymbolicExpressionTreeNode node) {
|
---|
| 464 | // todo implement more transformation rules
|
---|
| 465 | if (IsConstant(node)) {
|
---|
| 466 | var constT = node as ConstantTreeNode;
|
---|
| 467 | return MakeConstant(Math.Sin(constT.Value));
|
---|
| 468 | } else {
|
---|
| 469 | var sineNode = sineSymbol.CreateTreeNode();
|
---|
| 470 | sineNode.AddSubTree(node);
|
---|
| 471 | return sineNode;
|
---|
| 472 | }
|
---|
| 473 | }
|
---|
| 474 | private SymbolicExpressionTreeNode MakeTangent(SymbolicExpressionTreeNode node) {
|
---|
| 475 | // todo implement more transformation rules
|
---|
| 476 | if (IsConstant(node)) {
|
---|
| 477 | var constT = node as ConstantTreeNode;
|
---|
| 478 | return MakeConstant(Math.Tan(constT.Value));
|
---|
| 479 | } else {
|
---|
| 480 | var tanNode = tanSymbol.CreateTreeNode();
|
---|
| 481 | tanNode.AddSubTree(node);
|
---|
| 482 | return tanNode;
|
---|
| 483 | }
|
---|
| 484 | }
|
---|
| 485 | private SymbolicExpressionTreeNode MakeCosine(SymbolicExpressionTreeNode node) {
|
---|
| 486 | // todo implement more transformation rules
|
---|
| 487 | if (IsConstant(node)) {
|
---|
| 488 | var constT = node as ConstantTreeNode;
|
---|
| 489 | return MakeConstant(Math.Cos(constT.Value));
|
---|
| 490 | } else {
|
---|
| 491 | var cosNode = cosineSymbol.CreateTreeNode();
|
---|
| 492 | cosNode.AddSubTree(node);
|
---|
| 493 | return cosNode;
|
---|
| 494 | }
|
---|
| 495 | }
|
---|
| 496 | private SymbolicExpressionTreeNode MakeExp(SymbolicExpressionTreeNode node) {
|
---|
| 497 | // todo implement more transformation rules
|
---|
| 498 | if (IsConstant(node)) {
|
---|
| 499 | var constT = node as ConstantTreeNode;
|
---|
| 500 | return MakeConstant(Math.Exp(constT.Value));
|
---|
[5461] | 501 | } else if (IsLog(node)) {
|
---|
| 502 | return node.SubTrees[0];
|
---|
[5455] | 503 | } else {
|
---|
| 504 | var expNode = expSymbol.CreateTreeNode();
|
---|
| 505 | expNode.AddSubTree(node);
|
---|
| 506 | return expNode;
|
---|
| 507 | }
|
---|
| 508 | }
|
---|
| 509 | private SymbolicExpressionTreeNode MakeLog(SymbolicExpressionTreeNode node) {
|
---|
| 510 | // todo implement more transformation rules
|
---|
| 511 | if (IsConstant(node)) {
|
---|
| 512 | var constT = node as ConstantTreeNode;
|
---|
| 513 | return MakeConstant(Math.Log(constT.Value));
|
---|
[5461] | 514 | } else if (IsExp(node)) {
|
---|
| 515 | return node.SubTrees[0];
|
---|
| 516 | } else if (IsMultiplication(node)) {
|
---|
| 517 | return node.SubTrees.Select(s => MakeLog(s)).Aggregate((x, y) => MakeSum(x, y));
|
---|
| 518 | } else if (IsDivision(node)) {
|
---|
| 519 | var subtractionNode = subSymbol.CreateTreeNode();
|
---|
| 520 | foreach (var subTree in node.SubTrees) {
|
---|
| 521 | subtractionNode.AddSubTree(MakeLog(subTree));
|
---|
| 522 | }
|
---|
| 523 | return subtractionNode;
|
---|
[5455] | 524 | } else {
|
---|
| 525 | var logNode = logSymbol.CreateTreeNode();
|
---|
| 526 | logNode.AddSubTree(node);
|
---|
| 527 | return logNode;
|
---|
| 528 | }
|
---|
| 529 | }
|
---|
| 530 |
|
---|
| 531 |
|
---|
[4239] | 532 | // MakeFraction, MakeProduct and MakeSum take two already simplified trees and create a new simplified tree
|
---|
| 533 | private SymbolicExpressionTreeNode MakeFraction(SymbolicExpressionTreeNode a, SymbolicExpressionTreeNode b) {
|
---|
[3442] | 534 | if (IsConstant(a) && IsConstant(b)) {
|
---|
[4239] | 535 | // fold constants
|
---|
[3442] | 536 | return MakeConstant(((ConstantTreeNode)a).Value / ((ConstantTreeNode)b).Value);
|
---|
[4239] | 537 | } if (IsConstant(a) && !((ConstantTreeNode)a).Value.IsAlmost(1.0)) {
|
---|
| 538 | return MakeFraction(MakeConstant(1.0), MakeProduct(b, Invert(a)));
|
---|
[3442] | 539 | } else if (IsVariable(a) && IsConstant(b)) {
|
---|
[4239] | 540 | // merge constant values into variable weights
|
---|
[3442] | 541 | var constB = ((ConstantTreeNode)b).Value;
|
---|
| 542 | ((VariableTreeNode)a).Weight /= constB;
|
---|
| 543 | return a;
|
---|
[5461] | 544 | } else if (IsVariable(a) && IsVariable(b) && AreSameVariable(a, b)) {
|
---|
| 545 | // cancel variables
|
---|
| 546 | var aVar = a as VariableTreeNode;
|
---|
| 547 | var bVar = b as VariableTreeNode;
|
---|
| 548 | return MakeConstant(aVar.Weight / bVar.Weight);
|
---|
[4239] | 549 | } else if (IsAddition(a) && IsConstant(b)) {
|
---|
| 550 | return a.SubTrees
|
---|
[4398] | 551 | .Select(x => GetSimplifiedTree(x))
|
---|
[4239] | 552 | .Select(x => MakeFraction(x, b))
|
---|
| 553 | .Aggregate((c, d) => MakeSum(c, d));
|
---|
| 554 | } else if (IsMultiplication(a) && IsConstant(b)) {
|
---|
| 555 | return MakeProduct(a, Invert(b));
|
---|
| 556 | } else if (IsDivision(a) && IsConstant(b)) {
|
---|
| 557 | // (a1 / a2) / c => (a1 / (a2 * c))
|
---|
| 558 | Trace.Assert(a.SubTrees.Count == 2);
|
---|
| 559 | return MakeFraction(a.SubTrees[0], MakeProduct(a.SubTrees[1], b));
|
---|
| 560 | } else if (IsDivision(a) && IsDivision(b)) {
|
---|
| 561 | // (a1 / a2) / (b1 / b2) =>
|
---|
| 562 | Trace.Assert(a.SubTrees.Count == 2);
|
---|
| 563 | Trace.Assert(b.SubTrees.Count == 2);
|
---|
| 564 | return MakeFraction(MakeProduct(a.SubTrees[0], b.SubTrees[1]), MakeProduct(a.SubTrees[1], b.SubTrees[0]));
|
---|
| 565 | } else if (IsDivision(a)) {
|
---|
| 566 | // (a1 / a2) / b => (a1 / (a2 * b))
|
---|
| 567 | Trace.Assert(a.SubTrees.Count == 2);
|
---|
| 568 | return MakeFraction(a.SubTrees[0], MakeProduct(a.SubTrees[1], b));
|
---|
| 569 | } else if (IsDivision(b)) {
|
---|
| 570 | // a / (b1 / b2) => (a * b2) / b1
|
---|
| 571 | Trace.Assert(b.SubTrees.Count == 2);
|
---|
| 572 | return MakeFraction(MakeProduct(a, b.SubTrees[1]), b.SubTrees[0]);
|
---|
[3442] | 573 | } else {
|
---|
[3462] | 574 | var div = divSymbol.CreateTreeNode();
|
---|
[3985] | 575 | div.AddSubTree(a);
|
---|
| 576 | div.AddSubTree(b);
|
---|
[3442] | 577 | return div;
|
---|
| 578 | }
|
---|
| 579 | }
|
---|
| 580 |
|
---|
[4239] | 581 | private SymbolicExpressionTreeNode MakeSum(SymbolicExpressionTreeNode a, SymbolicExpressionTreeNode b) {
|
---|
[3442] | 582 | if (IsConstant(a) && IsConstant(b)) {
|
---|
[4239] | 583 | // fold constants
|
---|
[3442] | 584 | ((ConstantTreeNode)a).Value += ((ConstantTreeNode)b).Value;
|
---|
| 585 | return a;
|
---|
| 586 | } else if (IsConstant(a)) {
|
---|
| 587 | // c + x => x + c
|
---|
| 588 | // b is not constant => make sure constant is on the right
|
---|
[4239] | 589 | return MakeSum(b, a);
|
---|
[3442] | 590 | } else if (IsConstant(b) && ((ConstantTreeNode)b).Value.IsAlmost(0.0)) {
|
---|
| 591 | // x + 0 => x
|
---|
| 592 | return a;
|
---|
| 593 | } else if (IsAddition(a) && IsAddition(b)) {
|
---|
| 594 | // merge additions
|
---|
[3462] | 595 | var add = addSymbol.CreateTreeNode();
|
---|
[3442] | 596 | for (int i = 0; i < a.SubTrees.Count - 1; i++) add.AddSubTree(a.SubTrees[i]);
|
---|
| 597 | for (int i = 0; i < b.SubTrees.Count - 1; i++) add.AddSubTree(b.SubTrees[i]);
|
---|
| 598 | if (IsConstant(a.SubTrees.Last()) && IsConstant(b.SubTrees.Last())) {
|
---|
[4239] | 599 | add.AddSubTree(MakeSum(a.SubTrees.Last(), b.SubTrees.Last()));
|
---|
[3442] | 600 | } else if (IsConstant(a.SubTrees.Last())) {
|
---|
| 601 | add.AddSubTree(b.SubTrees.Last());
|
---|
| 602 | add.AddSubTree(a.SubTrees.Last());
|
---|
| 603 | } else {
|
---|
| 604 | add.AddSubTree(a.SubTrees.Last());
|
---|
| 605 | add.AddSubTree(b.SubTrees.Last());
|
---|
| 606 | }
|
---|
[4239] | 607 | MergeVariablesInSum(add);
|
---|
[5461] | 608 | if (add.SubTrees.Count == 1) {
|
---|
| 609 | return add.SubTrees[0];
|
---|
| 610 | } else {
|
---|
| 611 | return add;
|
---|
| 612 | }
|
---|
[3442] | 613 | } else if (IsAddition(b)) {
|
---|
[4239] | 614 | return MakeSum(b, a);
|
---|
[3442] | 615 | } else if (IsAddition(a) && IsConstant(b)) {
|
---|
[4239] | 616 | // a is an addition and b is a constant => append b to a and make sure the constants are merged
|
---|
[3462] | 617 | var add = addSymbol.CreateTreeNode();
|
---|
[3442] | 618 | for (int i = 0; i < a.SubTrees.Count - 1; i++) add.AddSubTree(a.SubTrees[i]);
|
---|
| 619 | if (IsConstant(a.SubTrees.Last()))
|
---|
[4239] | 620 | add.AddSubTree(MakeSum(a.SubTrees.Last(), b));
|
---|
[3442] | 621 | else {
|
---|
| 622 | add.AddSubTree(a.SubTrees.Last());
|
---|
| 623 | add.AddSubTree(b);
|
---|
| 624 | }
|
---|
| 625 | return add;
|
---|
| 626 | } else if (IsAddition(a)) {
|
---|
[4239] | 627 | // a is already an addition => append b
|
---|
[3462] | 628 | var add = addSymbol.CreateTreeNode();
|
---|
[3442] | 629 | add.AddSubTree(b);
|
---|
| 630 | foreach (var subTree in a.SubTrees) {
|
---|
| 631 | add.AddSubTree(subTree);
|
---|
| 632 | }
|
---|
[4239] | 633 | MergeVariablesInSum(add);
|
---|
[5461] | 634 | if (add.SubTrees.Count == 1) {
|
---|
| 635 | return add.SubTrees[0];
|
---|
| 636 | } else {
|
---|
| 637 | return add;
|
---|
| 638 | }
|
---|
[3442] | 639 | } else {
|
---|
[3462] | 640 | var add = addSymbol.CreateTreeNode();
|
---|
[3985] | 641 | add.AddSubTree(a);
|
---|
| 642 | add.AddSubTree(b);
|
---|
[4239] | 643 | MergeVariablesInSum(add);
|
---|
[5461] | 644 | if (add.SubTrees.Count == 1) {
|
---|
| 645 | return add.SubTrees[0];
|
---|
| 646 | } else {
|
---|
| 647 | return add;
|
---|
| 648 | }
|
---|
[3442] | 649 | }
|
---|
| 650 | }
|
---|
| 651 |
|
---|
[4239] | 652 | // makes sure variable symbols in sums are combined
|
---|
[5461] | 653 | // possible improvement: combine sums of products where the products only reference the same variable
|
---|
[4239] | 654 | private void MergeVariablesInSum(SymbolicExpressionTreeNode sum) {
|
---|
| 655 | var subtrees = new List<SymbolicExpressionTreeNode>(sum.SubTrees);
|
---|
| 656 | while (sum.SubTrees.Count > 0) sum.RemoveSubTree(0);
|
---|
[3442] | 657 | var groupedVarNodes = from node in subtrees.OfType<VariableTreeNode>()
|
---|
[5377] | 658 | let lag = (node is LaggedVariableTreeNode) ? ((LaggedVariableTreeNode)node).Lag : 0
|
---|
| 659 | group node by node.VariableName + lag into g
|
---|
[3442] | 660 | select g;
|
---|
| 661 | var unchangedSubTrees = subtrees.Where(t => !(t is VariableTreeNode));
|
---|
| 662 |
|
---|
| 663 | foreach (var variableNodeGroup in groupedVarNodes) {
|
---|
| 664 | var weightSum = variableNodeGroup.Select(t => t.Weight).Sum();
|
---|
| 665 | var representative = variableNodeGroup.First();
|
---|
| 666 | representative.Weight = weightSum;
|
---|
[4239] | 667 | sum.AddSubTree(representative);
|
---|
[3442] | 668 | }
|
---|
| 669 | foreach (var unchangedSubtree in unchangedSubTrees)
|
---|
[4239] | 670 | sum.AddSubTree(unchangedSubtree);
|
---|
[3442] | 671 | }
|
---|
| 672 |
|
---|
[4239] | 673 |
|
---|
| 674 | private SymbolicExpressionTreeNode MakeProduct(SymbolicExpressionTreeNode a, SymbolicExpressionTreeNode b) {
|
---|
[3442] | 675 | if (IsConstant(a) && IsConstant(b)) {
|
---|
[4239] | 676 | // fold constants
|
---|
[3442] | 677 | ((ConstantTreeNode)a).Value *= ((ConstantTreeNode)b).Value;
|
---|
| 678 | return a;
|
---|
| 679 | } else if (IsConstant(a)) {
|
---|
[4239] | 680 | // a * $ => $ * a
|
---|
| 681 | return MakeProduct(b, a);
|
---|
[3442] | 682 | } else if (IsConstant(b) && ((ConstantTreeNode)b).Value.IsAlmost(1.0)) {
|
---|
[4239] | 683 | // $ * 1.0 => $
|
---|
[3442] | 684 | return a;
|
---|
| 685 | } else if (IsConstant(b) && IsVariable(a)) {
|
---|
[4239] | 686 | // multiply constants into variables weights
|
---|
[3442] | 687 | ((VariableTreeNode)a).Weight *= ((ConstantTreeNode)b).Value;
|
---|
| 688 | return a;
|
---|
| 689 | } else if (IsConstant(b) && IsAddition(a)) {
|
---|
[4239] | 690 | // multiply constants into additions
|
---|
| 691 | return a.SubTrees.Select(x => MakeProduct(x, b)).Aggregate((c, d) => MakeSum(c, d));
|
---|
[4068] | 692 | } else if (IsDivision(a) && IsDivision(b)) {
|
---|
[4239] | 693 | // (a1 / a2) * (b1 / b2) => (a1 * b1) / (a2 * b2)
|
---|
| 694 | Trace.Assert(a.SubTrees.Count == 2);
|
---|
| 695 | Trace.Assert(b.SubTrees.Count == 2);
|
---|
| 696 | return MakeFraction(MakeProduct(a.SubTrees[0], b.SubTrees[0]), MakeProduct(a.SubTrees[1], b.SubTrees[1]));
|
---|
[3442] | 697 | } else if (IsDivision(a)) {
|
---|
[4239] | 698 | // (a1 / a2) * b => (a1 * b) / a2
|
---|
[3442] | 699 | Trace.Assert(a.SubTrees.Count == 2);
|
---|
[4239] | 700 | return MakeFraction(MakeProduct(a.SubTrees[0], b), a.SubTrees[1]);
|
---|
[3442] | 701 | } else if (IsDivision(b)) {
|
---|
[4239] | 702 | // a * (b1 / b2) => (b1 * a) / b2
|
---|
[3442] | 703 | Trace.Assert(b.SubTrees.Count == 2);
|
---|
[4239] | 704 | return MakeFraction(MakeProduct(b.SubTrees[0], a), b.SubTrees[1]);
|
---|
[3442] | 705 | } else if (IsMultiplication(a) && IsMultiplication(b)) {
|
---|
[4239] | 706 | // merge multiplications (make sure constants are merged)
|
---|
[3462] | 707 | var mul = mulSymbol.CreateTreeNode();
|
---|
[4239] | 708 | for (int i = 0; i < a.SubTrees.Count; i++) mul.AddSubTree(a.SubTrees[i]);
|
---|
| 709 | for (int i = 0; i < b.SubTrees.Count; i++) mul.AddSubTree(b.SubTrees[i]);
|
---|
| 710 | MergeVariablesAndConstantsInProduct(mul);
|
---|
[3442] | 711 | return mul;
|
---|
[4239] | 712 | } else if (IsMultiplication(b)) {
|
---|
| 713 | return MakeProduct(b, a);
|
---|
[3442] | 714 | } else if (IsMultiplication(a)) {
|
---|
[4239] | 715 | // a is already an multiplication => append b
|
---|
| 716 | a.AddSubTree(b);
|
---|
| 717 | MergeVariablesAndConstantsInProduct(a);
|
---|
| 718 | return a;
|
---|
[3442] | 719 | } else {
|
---|
[3462] | 720 | var mul = mulSymbol.CreateTreeNode();
|
---|
[3442] | 721 | mul.SubTrees.Add(a);
|
---|
| 722 | mul.SubTrees.Add(b);
|
---|
[4239] | 723 | MergeVariablesAndConstantsInProduct(mul);
|
---|
[3442] | 724 | return mul;
|
---|
| 725 | }
|
---|
| 726 | }
|
---|
[4239] | 727 | #endregion
|
---|
[3442] | 728 |
|
---|
[5461] | 729 |
|
---|
| 730 | #region helper functions
|
---|
| 731 |
|
---|
| 732 | private bool AreSameVariable(SymbolicExpressionTreeNode a, SymbolicExpressionTreeNode b) {
|
---|
| 733 | var aLaggedVar = a as LaggedVariableTreeNode;
|
---|
| 734 | var bLaggedVar = b as LaggedVariableTreeNode;
|
---|
| 735 | if (aLaggedVar != null && bLaggedVar != null) {
|
---|
| 736 | return aLaggedVar.VariableName == bLaggedVar.VariableName &&
|
---|
| 737 | aLaggedVar.Lag == bLaggedVar.Lag;
|
---|
| 738 | }
|
---|
| 739 | var aVar = a as VariableTreeNode;
|
---|
| 740 | var bVar = b as VariableTreeNode;
|
---|
| 741 | if (aVar != null && bVar != null) {
|
---|
| 742 | return aVar.VariableName == bVar.VariableName;
|
---|
| 743 | }
|
---|
| 744 | return false;
|
---|
| 745 | }
|
---|
| 746 |
|
---|
[4239] | 747 | // helper to combine the constant factors in products and to combine variables (powers of 2, 3...)
|
---|
| 748 | private void MergeVariablesAndConstantsInProduct(SymbolicExpressionTreeNode prod) {
|
---|
| 749 | var subtrees = new List<SymbolicExpressionTreeNode>(prod.SubTrees);
|
---|
| 750 | while (prod.SubTrees.Count > 0) prod.RemoveSubTree(0);
|
---|
| 751 | var groupedVarNodes = from node in subtrees.OfType<VariableTreeNode>()
|
---|
[5377] | 752 | let lag = (node is LaggedVariableTreeNode) ? ((LaggedVariableTreeNode)node).Lag : 0
|
---|
| 753 | group node by node.VariableName + lag into g
|
---|
[4239] | 754 | orderby g.Count()
|
---|
| 755 | select g;
|
---|
| 756 | var constantProduct = (from node in subtrees.OfType<VariableTreeNode>()
|
---|
| 757 | select node.Weight)
|
---|
| 758 | .Concat(from node in subtrees.OfType<ConstantTreeNode>()
|
---|
| 759 | select node.Value)
|
---|
| 760 | .DefaultIfEmpty(1.0)
|
---|
| 761 | .Aggregate((c1, c2) => c1 * c2);
|
---|
[3442] | 762 |
|
---|
[4239] | 763 | var unchangedSubTrees = from tree in subtrees
|
---|
| 764 | where !(tree is VariableTreeNode)
|
---|
| 765 | where !(tree is ConstantTreeNode)
|
---|
| 766 | select tree;
|
---|
[3442] | 767 |
|
---|
[4239] | 768 | foreach (var variableNodeGroup in groupedVarNodes) {
|
---|
| 769 | var representative = variableNodeGroup.First();
|
---|
| 770 | representative.Weight = 1.0;
|
---|
| 771 | if (variableNodeGroup.Count() > 1) {
|
---|
| 772 | var poly = mulSymbol.CreateTreeNode();
|
---|
| 773 | for (int p = 0; p < variableNodeGroup.Count(); p++) {
|
---|
| 774 | poly.AddSubTree((SymbolicExpressionTreeNode)representative.Clone());
|
---|
| 775 | }
|
---|
| 776 | prod.AddSubTree(poly);
|
---|
| 777 | } else {
|
---|
| 778 | prod.AddSubTree(representative);
|
---|
| 779 | }
|
---|
| 780 | }
|
---|
[3442] | 781 |
|
---|
[4239] | 782 | foreach (var unchangedSubtree in unchangedSubTrees)
|
---|
| 783 | prod.AddSubTree(unchangedSubtree);
|
---|
[3442] | 784 |
|
---|
[4239] | 785 | if (!constantProduct.IsAlmost(1.0)) {
|
---|
| 786 | prod.AddSubTree(MakeConstant(constantProduct));
|
---|
| 787 | }
|
---|
[3442] | 788 | }
|
---|
| 789 |
|
---|
[4239] | 790 |
|
---|
| 791 | /// <summary>
|
---|
| 792 | /// x => x * -1
|
---|
| 793 | /// Doesn't create new trees and manipulates x
|
---|
| 794 | /// </summary>
|
---|
| 795 | /// <param name="x"></param>
|
---|
| 796 | /// <returns>-x</returns>
|
---|
| 797 | private SymbolicExpressionTreeNode Negate(SymbolicExpressionTreeNode x) {
|
---|
| 798 | if (IsConstant(x)) {
|
---|
| 799 | ((ConstantTreeNode)x).Value *= -1;
|
---|
| 800 | } else if (IsVariable(x)) {
|
---|
| 801 | var variableTree = (VariableTreeNode)x;
|
---|
| 802 | variableTree.Weight *= -1.0;
|
---|
| 803 | } else if (IsAddition(x)) {
|
---|
| 804 | // (x0 + x1 + .. + xn) * -1 => (-x0 + -x1 + .. + -xn)
|
---|
[5108] | 805 | for (int i = 0; i < x.SubTrees.Count; i++)
|
---|
| 806 | x.SubTrees[i] = Negate(x.SubTrees[i]);
|
---|
[4239] | 807 | } else if (IsMultiplication(x) || IsDivision(x)) {
|
---|
| 808 | // x0 * x1 * .. * xn * -1 => x0 * x1 * .. * -xn
|
---|
[5108] | 809 | x.SubTrees[x.SubTrees.Count - 1] = Negate(x.SubTrees.Last()); // last is maybe a constant, prefer to negate the constant
|
---|
[4239] | 810 | } else {
|
---|
| 811 | // any other function
|
---|
| 812 | return MakeProduct(x, MakeConstant(-1));
|
---|
| 813 | }
|
---|
| 814 | return x;
|
---|
[3442] | 815 | }
|
---|
[3876] | 816 |
|
---|
[4239] | 817 | /// <summary>
|
---|
| 818 | /// x => 1/x
|
---|
| 819 | /// Doesn't create new trees and manipulates x
|
---|
| 820 | /// </summary>
|
---|
| 821 | /// <param name="x"></param>
|
---|
| 822 | /// <returns></returns>
|
---|
| 823 | private SymbolicExpressionTreeNode Invert(SymbolicExpressionTreeNode x) {
|
---|
| 824 | if (IsConstant(x)) {
|
---|
| 825 | return MakeConstant(1.0 / ((ConstantTreeNode)x).Value);
|
---|
| 826 | } else if (IsDivision(x)) {
|
---|
| 827 | Trace.Assert(x.SubTrees.Count == 2);
|
---|
| 828 | return MakeFraction(x.SubTrees[1], x.SubTrees[0]);
|
---|
| 829 | } else {
|
---|
| 830 | // any other function
|
---|
| 831 | return MakeFraction(MakeConstant(1), x);
|
---|
| 832 | }
|
---|
[3876] | 833 | }
|
---|
[3442] | 834 |
|
---|
| 835 | private SymbolicExpressionTreeNode MakeConstant(double value) {
|
---|
[3462] | 836 | ConstantTreeNode constantTreeNode = (ConstantTreeNode)(constSymbol.CreateTreeNode());
|
---|
[3442] | 837 | constantTreeNode.Value = value;
|
---|
| 838 | return (SymbolicExpressionTreeNode)constantTreeNode;
|
---|
| 839 | }
|
---|
| 840 |
|
---|
| 841 | private SymbolicExpressionTreeNode MakeVariable(double weight, string name) {
|
---|
[3462] | 842 | var tree = (VariableTreeNode)varSymbol.CreateTreeNode();
|
---|
[3442] | 843 | tree.Weight = weight;
|
---|
| 844 | tree.VariableName = name;
|
---|
| 845 | return tree;
|
---|
| 846 | }
|
---|
[4239] | 847 | #endregion
|
---|
[3442] | 848 | }
|
---|
| 849 | }
|
---|