[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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| 37 | private Multiplication mulSymbol = new Multiplication();
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| 38 | private Division divSymbol = new Division();
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| 39 | private Constant constSymbol = new Constant();
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| 40 | private Variable varSymbol = new Variable();
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[5455] | 41 | private Logarithm logSymbol = new Logarithm();
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| 42 | private Exponential expSymbol = new Exponential();
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| 43 | private Sine sineSymbol = new Sine();
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| 44 | private Cosine cosineSymbol = new Cosine();
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| 45 | private Tangent tanSymbol = new Tangent();
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| 46 | private IfThenElse ifThenElseSymbol = new IfThenElse();
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| 47 | private And andSymbol = new And();
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| 48 | private Or orSymbol = new Or();
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| 49 | private Not notSymbol = new Not();
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| 50 | private GreaterThan gtSymbol = new GreaterThan();
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| 51 | private LessThan ltSymbol = new LessThan();
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[3462] | 52 |
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[3442] | 53 | public SymbolicExpressionTree Simplify(SymbolicExpressionTree originalTree) {
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| 54 | var clone = (SymbolicExpressionTreeNode)originalTree.Root.Clone();
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| 55 | // macro expand (initially no argument trees)
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| 56 | var macroExpandedTree = MacroExpand(clone, clone.SubTrees[0], new List<SymbolicExpressionTreeNode>());
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[4477] | 57 | SymbolicExpressionTreeNode rootNode = (new ProgramRootSymbol()).CreateTreeNode();
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| 58 | rootNode.AddSubTree(GetSimplifiedTree(macroExpandedTree));
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| 59 | return new SymbolicExpressionTree(rootNode);
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[3442] | 60 | }
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| 61 |
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| 62 | // the argumentTrees list contains already expanded trees used as arguments for invocations
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| 63 | private SymbolicExpressionTreeNode MacroExpand(SymbolicExpressionTreeNode root, SymbolicExpressionTreeNode node, IList<SymbolicExpressionTreeNode> argumentTrees) {
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| 64 | List<SymbolicExpressionTreeNode> subtrees = new List<SymbolicExpressionTreeNode>(node.SubTrees);
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[3985] | 65 | while (node.SubTrees.Count > 0) node.RemoveSubTree(0);
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[3442] | 66 | if (node.Symbol is InvokeFunction) {
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| 67 | var invokeSym = node.Symbol as InvokeFunction;
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| 68 | var defunNode = FindFunctionDefinition(root, invokeSym.FunctionName);
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| 69 | var macroExpandedArguments = new List<SymbolicExpressionTreeNode>();
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| 70 | foreach (var subtree in subtrees) {
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| 71 | macroExpandedArguments.Add(MacroExpand(root, subtree, argumentTrees));
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| 72 | }
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| 73 | return MacroExpand(root, defunNode, macroExpandedArguments);
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| 74 | } else if (node.Symbol is Argument) {
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| 75 | var argSym = node.Symbol as Argument;
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| 76 | // return the correct argument sub-tree (already macro-expanded)
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| 77 | return (SymbolicExpressionTreeNode)argumentTrees[argSym.ArgumentIndex].Clone();
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| 78 | } else {
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| 79 | // recursive application
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| 80 | foreach (var subtree in subtrees) {
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| 81 | node.AddSubTree(MacroExpand(root, subtree, argumentTrees));
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| 82 | }
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| 83 | return node;
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| 84 | }
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| 85 | }
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| 86 |
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| 87 | private SymbolicExpressionTreeNode FindFunctionDefinition(SymbolicExpressionTreeNode root, string functionName) {
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| 88 | foreach (var subtree in root.SubTrees.OfType<DefunTreeNode>()) {
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| 89 | if (subtree.FunctionName == functionName) return subtree.SubTrees[0];
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| 90 | }
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| 91 |
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| 92 | throw new ArgumentException("Definition of function " + functionName + " not found.");
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| 93 | }
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| 94 |
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[4239] | 95 |
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| 96 | #region symbol predicates
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[5455] | 97 | // arithmetic
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| 98 | private bool IsDivision(SymbolicExpressionTreeNode node) {
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| 99 | return node.Symbol is Division;
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[4239] | 100 | }
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| 101 |
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[5455] | 102 | private bool IsMultiplication(SymbolicExpressionTreeNode node) {
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| 103 | return node.Symbol is Multiplication;
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[4239] | 104 | }
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| 105 |
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[5455] | 106 | private bool IsSubtraction(SymbolicExpressionTreeNode node) {
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| 107 | return node.Symbol is Subtraction;
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[4239] | 108 | }
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| 109 |
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[5455] | 110 | private bool IsAddition(SymbolicExpressionTreeNode node) {
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| 111 | return node.Symbol is Addition;
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[4239] | 112 | }
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| 113 |
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[5455] | 114 | private bool IsAverage(SymbolicExpressionTreeNode node) {
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| 115 | return node.Symbol is Average;
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[4239] | 116 | }
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[5455] | 117 | // exponential
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| 118 | private bool IsLog(SymbolicExpressionTreeNode node) {
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| 119 | return node.Symbol is Logarithm;
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| 120 | }
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| 121 | private bool IsExp(SymbolicExpressionTreeNode node) {
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| 122 | return node.Symbol is Exponential;
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| 123 | }
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| 124 | // trigonometric
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| 125 | private bool IsSine(SymbolicExpressionTreeNode node) {
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| 126 | return node.Symbol is Sine;
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| 127 | }
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| 128 | private bool IsCosine(SymbolicExpressionTreeNode node) {
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| 129 | return node.Symbol is Cosine;
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| 130 | }
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| 131 | private bool IsTangent(SymbolicExpressionTreeNode node) {
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| 132 | return node.Symbol is Tangent;
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| 133 | }
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| 134 | // boolean
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| 135 | private bool IsIfThenElse(SymbolicExpressionTreeNode node) {
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| 136 | return node.Symbol is IfThenElse;
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| 137 | }
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| 138 | private bool IsAnd(SymbolicExpressionTreeNode node) {
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| 139 | return node.Symbol is And;
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| 140 | }
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| 141 | private bool IsOr(SymbolicExpressionTreeNode node) {
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| 142 | return node.Symbol is Or;
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| 143 | }
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| 144 | private bool IsNot(SymbolicExpressionTreeNode node) {
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| 145 | return node.Symbol is Not;
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| 146 | }
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| 147 | // comparison
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| 148 | private bool IsGreaterThan(SymbolicExpressionTreeNode node) {
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| 149 | return node.Symbol is GreaterThan;
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| 150 | }
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| 151 | private bool IsLessThan(SymbolicExpressionTreeNode node) {
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| 152 | return node.Symbol is LessThan;
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| 153 | }
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[4239] | 154 |
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[5455] | 155 | // terminals
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| 156 | private bool IsVariable(SymbolicExpressionTreeNode node) {
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| 157 | return node.Symbol is Variable;
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[4239] | 158 | }
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| 159 |
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[5455] | 160 | private bool IsConstant(SymbolicExpressionTreeNode node) {
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| 161 | return node.Symbol is Constant;
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[4239] | 162 | }
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[5455] | 163 |
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[4239] | 164 | #endregion
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| 165 |
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[3442] | 166 | /// <summary>
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| 167 | /// Creates a new simplified tree
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| 168 | /// </summary>
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| 169 | /// <param name="original"></param>
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| 170 | /// <returns></returns>
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| 171 | public SymbolicExpressionTreeNode GetSimplifiedTree(SymbolicExpressionTreeNode original) {
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| 172 | if (IsConstant(original) || IsVariable(original)) {
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| 173 | return (SymbolicExpressionTreeNode)original.Clone();
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| 174 | } else if (IsAddition(original)) {
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[4239] | 175 | return SimplifyAddition(original);
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[3442] | 176 | } else if (IsSubtraction(original)) {
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[4239] | 177 | return SimplifySubtraction(original);
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[3442] | 178 | } else if (IsMultiplication(original)) {
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[4239] | 179 | return SimplifyMultiplication(original);
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[3442] | 180 | } else if (IsDivision(original)) {
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[4239] | 181 | return SimplifyDivision(original);
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[3876] | 182 | } else if (IsAverage(original)) {
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[4239] | 183 | return SimplifyAverage(original);
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| 184 | } else if (IsLog(original)) {
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[5455] | 185 | return SimplifyLog(original);
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| 186 | } else if (IsExp(original)) {
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| 187 | return SimplifyExp(original);
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| 188 | } else if (IsSine(original)) {
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| 189 | return SimplifySine(original);
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| 190 | } else if (IsCosine(original)) {
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| 191 | return SimplifyCosine(original);
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| 192 | } else if (IsTangent(original)) {
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| 193 | return SimplifyTangent(original);
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[4239] | 194 | } else if (IsIfThenElse(original)) {
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[5455] | 195 | return SimplifyIfThenElse(original);
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| 196 | } else if (IsGreaterThan(original)) {
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| 197 | return SimplifyGreaterThan(original);
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| 198 | } else if (IsLessThan(original)) {
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| 199 | return SimplifyLessThan(original);
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| 200 | } else if (IsAnd(original)) {
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| 201 | return SimplifyAnd(original);
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| 202 | } else if (IsOr(original)) {
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| 203 | return SimplifyOr(original);
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| 204 | } else if (IsNot(original)) {
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| 205 | return SimplifyNot(original);
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[3442] | 206 | } else {
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[4239] | 207 | return SimplifyAny(original);
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[3442] | 208 | }
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| 209 | }
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| 210 |
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[5455] | 211 |
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[4239] | 212 | #region specific simplification routines
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| 213 | private SymbolicExpressionTreeNode SimplifyAny(SymbolicExpressionTreeNode original) {
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| 214 | // can't simplify this function but simplify all subtrees
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| 215 | List<SymbolicExpressionTreeNode> subTrees = new List<SymbolicExpressionTreeNode>(original.SubTrees);
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| 216 | while (original.SubTrees.Count > 0) original.RemoveSubTree(0);
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| 217 | var clone = (SymbolicExpressionTreeNode)original.Clone();
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| 218 | List<SymbolicExpressionTreeNode> simplifiedSubTrees = new List<SymbolicExpressionTreeNode>();
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| 219 | foreach (var subTree in subTrees) {
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| 220 | simplifiedSubTrees.Add(GetSimplifiedTree(subTree));
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| 221 | original.AddSubTree(subTree);
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| 222 | }
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| 223 | foreach (var simplifiedSubtree in simplifiedSubTrees) {
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| 224 | clone.AddSubTree(simplifiedSubtree);
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| 225 | }
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| 226 | if (simplifiedSubTrees.TrueForAll(t => IsConstant(t))) {
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| 227 | SimplifyConstantExpression(clone);
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| 228 | }
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| 229 | return clone;
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| 230 | }
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| 231 |
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| 232 | private SymbolicExpressionTreeNode SimplifyConstantExpression(SymbolicExpressionTreeNode original) {
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| 233 | // not yet implemented
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| 234 | return original;
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| 235 | }
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| 236 |
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| 237 | private SymbolicExpressionTreeNode SimplifyAverage(SymbolicExpressionTreeNode original) {
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| 238 | if (original.SubTrees.Count == 1) {
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| 239 | return GetSimplifiedTree(original.SubTrees[0]);
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[3442] | 240 | } else {
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[4239] | 241 | // simplify expressions x0..xn
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| 242 | // make sum(x0..xn) / n
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| 243 | Trace.Assert(original.SubTrees.Count > 1);
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| 244 | var sum = original.SubTrees
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| 245 | .Select(x => GetSimplifiedTree(x))
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| 246 | .Aggregate((a, b) => MakeSum(a, b));
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| 247 | return MakeFraction(sum, MakeConstant(original.SubTrees.Count));
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[3442] | 248 | }
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| 249 | }
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| 250 |
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[4239] | 251 | private SymbolicExpressionTreeNode SimplifyDivision(SymbolicExpressionTreeNode original) {
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| 252 | if (original.SubTrees.Count == 1) {
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| 253 | return Invert(GetSimplifiedTree(original.SubTrees[0]));
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[3442] | 254 | } else {
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[4239] | 255 | // simplify expressions x0..xn
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| 256 | // make multiplication (x0 * 1/(x1 * x1 * .. * xn))
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| 257 | Trace.Assert(original.SubTrees.Count > 1);
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| 258 | var simplifiedTrees = original.SubTrees.Select(x => GetSimplifiedTree(x));
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| 259 | return
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| 260 | MakeProduct(simplifiedTrees.First(), Invert(simplifiedTrees.Skip(1).Aggregate((a, b) => MakeProduct(a, b))));
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[3442] | 261 | }
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| 262 | }
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| 263 |
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[4239] | 264 | private SymbolicExpressionTreeNode SimplifyMultiplication(SymbolicExpressionTreeNode original) {
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| 265 | if (original.SubTrees.Count == 1) {
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| 266 | return GetSimplifiedTree(original.SubTrees[0]);
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| 267 | } else {
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| 268 | Trace.Assert(original.SubTrees.Count > 1);
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| 269 | return original.SubTrees
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| 270 | .Select(x => GetSimplifiedTree(x))
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| 271 | .Aggregate((a, b) => MakeProduct(a, b));
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| 272 | }
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| 273 | }
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| 274 |
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| 275 | private SymbolicExpressionTreeNode SimplifySubtraction(SymbolicExpressionTreeNode original) {
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| 276 | if (original.SubTrees.Count == 1) {
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| 277 | return Negate(GetSimplifiedTree(original.SubTrees[0]));
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| 278 | } else {
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| 279 | // simplify expressions x0..xn
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| 280 | // make addition (x0,-x1..-xn)
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| 281 | Trace.Assert(original.SubTrees.Count > 1);
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| 282 | var simplifiedTrees = original.SubTrees.Select(x => GetSimplifiedTree(x));
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| 283 | return simplifiedTrees.Take(1)
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| 284 | .Concat(simplifiedTrees.Skip(1).Select(x => Negate(x)))
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| 285 | .Aggregate((a, b) => MakeSum(a, b));
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| 286 | }
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| 287 | }
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| 288 |
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| 289 | private SymbolicExpressionTreeNode SimplifyAddition(SymbolicExpressionTreeNode original) {
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| 290 | if (original.SubTrees.Count == 1) {
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| 291 | return GetSimplifiedTree(original.SubTrees[0]);
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| 292 | } else {
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| 293 | // simplify expression x0..xn
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| 294 | // make addition (x0..xn)
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| 295 | Trace.Assert(original.SubTrees.Count > 1);
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| 296 | return original.SubTrees
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| 297 | .Select(x => GetSimplifiedTree(x))
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| 298 | .Aggregate((a, b) => MakeSum(a, b));
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| 299 | }
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| 300 | }
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[5455] | 301 |
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| 302 | private SymbolicExpressionTreeNode SimplifyNot(SymbolicExpressionTreeNode original) {
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| 303 | return MakeNot(GetSimplifiedTree(original.SubTrees[0]));
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| 304 | }
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| 305 | private SymbolicExpressionTreeNode SimplifyOr(SymbolicExpressionTreeNode original) {
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| 306 | return original.SubTrees
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| 307 | .Select(x => GetSimplifiedTree(x))
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| 308 | .Aggregate((a, b) => MakeOr(a, b));
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| 309 | }
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| 310 | private SymbolicExpressionTreeNode SimplifyAnd(SymbolicExpressionTreeNode original) {
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| 311 | return original.SubTrees
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| 312 | .Select(x => GetSimplifiedTree(x))
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| 313 | .Aggregate((a, b) => MakeAnd(a, b));
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| 314 | }
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| 315 | private SymbolicExpressionTreeNode SimplifyLessThan(SymbolicExpressionTreeNode original) {
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| 316 | return MakeLessThan(GetSimplifiedTree(original.SubTrees[0]), GetSimplifiedTree(original.SubTrees[1]));
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| 317 | }
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| 318 | private SymbolicExpressionTreeNode SimplifyGreaterThan(SymbolicExpressionTreeNode original) {
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| 319 | return MakeGreaterThan(GetSimplifiedTree(original.SubTrees[0]), GetSimplifiedTree(original.SubTrees[1]));
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| 320 | }
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| 321 | private SymbolicExpressionTreeNode SimplifyIfThenElse(SymbolicExpressionTreeNode original) {
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| 322 | return MakeIfThenElse(GetSimplifiedTree(original.SubTrees[0]), GetSimplifiedTree(original.SubTrees[1]), GetSimplifiedTree(original.SubTrees[2]));
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| 323 | }
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| 324 | private SymbolicExpressionTreeNode SimplifyTangent(SymbolicExpressionTreeNode original) {
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| 325 | return MakeTangent(GetSimplifiedTree(original.SubTrees[0]));
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| 326 | }
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| 327 | private SymbolicExpressionTreeNode SimplifyCosine(SymbolicExpressionTreeNode original) {
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| 328 | return MakeCosine(GetSimplifiedTree(original.SubTrees[0]));
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| 329 | }
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| 330 | private SymbolicExpressionTreeNode SimplifySine(SymbolicExpressionTreeNode original) {
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| 331 | return MakeSine(GetSimplifiedTree(original.SubTrees[0]));
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| 332 | }
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| 333 | private SymbolicExpressionTreeNode SimplifyExp(SymbolicExpressionTreeNode original) {
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| 334 | return MakeExp(GetSimplifiedTree(original.SubTrees[0]));
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| 335 | }
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| 336 |
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| 337 | private SymbolicExpressionTreeNode SimplifyLog(SymbolicExpressionTreeNode original) {
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| 338 | return MakeLog(GetSimplifiedTree(original.SubTrees[0]));
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| 339 | }
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| 340 |
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[4239] | 341 | #endregion
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| 342 |
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| 343 |
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| 344 |
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| 345 | #region low level tree restructuring
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[5455] | 346 | private SymbolicExpressionTreeNode MakeNot(SymbolicExpressionTreeNode t) {
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| 347 | return MakeProduct(t, MakeConstant(-1.0));
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| 348 | }
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| 349 |
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| 350 | private SymbolicExpressionTreeNode MakeOr(SymbolicExpressionTreeNode a, SymbolicExpressionTreeNode b) {
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| 351 | if (IsConstant(a) && IsConstant(b)) {
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| 352 | var constA = a as ConstantTreeNode;
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| 353 | var constB = b as ConstantTreeNode;
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| 354 | if (constA.Value > 0.0 || constB.Value > 0.0) {
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| 355 | return MakeConstant(1.0);
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| 356 | } else {
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| 357 | return MakeConstant(-1.0);
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| 358 | }
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| 359 | } else if (IsConstant(a)) {
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| 360 | return MakeOr(b, a);
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| 361 | } else if (IsConstant(b)) {
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| 362 | var constT = b as ConstantTreeNode;
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| 363 | if (constT.Value > 0.0) {
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| 364 | // boolean expression is necessarily true
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| 365 | return MakeConstant(1.0);
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| 366 | } else {
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| 367 | // the constant value has no effect on the result of the boolean condition so we can drop the constant term
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| 368 | var orNode = orSymbol.CreateTreeNode();
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| 369 | orNode.AddSubTree(a);
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| 370 | return orNode;
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| 371 | }
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| 372 | } else {
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| 373 | var orNode = orSymbol.CreateTreeNode();
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| 374 | orNode.AddSubTree(a);
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| 375 | orNode.AddSubTree(b);
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| 376 | return orNode;
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| 377 | }
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| 378 | }
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| 379 | private SymbolicExpressionTreeNode MakeAnd(SymbolicExpressionTreeNode a, SymbolicExpressionTreeNode b) {
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| 380 | if (IsConstant(a) && IsConstant(b)) {
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| 381 | var constA = a as ConstantTreeNode;
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| 382 | var constB = b as ConstantTreeNode;
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| 383 | if (constA.Value > 0.0 && constB.Value > 0.0) {
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| 384 | return MakeConstant(1.0);
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| 385 | } else {
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| 386 | return MakeConstant(-1.0);
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| 387 | }
|
---|
| 388 | } else if (IsConstant(a)) {
|
---|
| 389 | return MakeAnd(b, a);
|
---|
| 390 | } else if (IsConstant(b)) {
|
---|
| 391 | var constB = b as ConstantTreeNode;
|
---|
| 392 | if (constB.Value > 0.0) {
|
---|
| 393 | // the constant value has no effect on the result of the boolean condition so we can drop the constant term
|
---|
| 394 | var andNode = andSymbol.CreateTreeNode();
|
---|
| 395 | andNode.AddSubTree(a);
|
---|
| 396 | return andNode;
|
---|
| 397 | } else {
|
---|
| 398 | // boolean expression is necessarily false
|
---|
| 399 | return MakeConstant(-1.0);
|
---|
| 400 | }
|
---|
| 401 | } else {
|
---|
| 402 | var andNode = andSymbol.CreateTreeNode();
|
---|
| 403 | andNode.AddSubTree(a);
|
---|
| 404 | andNode.AddSubTree(b);
|
---|
| 405 | return andNode;
|
---|
| 406 | }
|
---|
| 407 | }
|
---|
| 408 | private SymbolicExpressionTreeNode MakeLessThan(SymbolicExpressionTreeNode leftSide, SymbolicExpressionTreeNode rightSide) {
|
---|
| 409 | if (IsConstant(leftSide) && IsConstant(rightSide)) {
|
---|
| 410 | var lsConst = leftSide as ConstantTreeNode;
|
---|
| 411 | var rsConst = rightSide as ConstantTreeNode;
|
---|
| 412 | if (lsConst.Value < rsConst.Value) return MakeConstant(1.0);
|
---|
| 413 | else return MakeConstant(-1.0);
|
---|
| 414 | } else {
|
---|
| 415 | var ltNode = ltSymbol.CreateTreeNode();
|
---|
| 416 | ltNode.AddSubTree(leftSide);
|
---|
| 417 | ltNode.AddSubTree(rightSide);
|
---|
| 418 | return ltNode;
|
---|
| 419 | }
|
---|
| 420 | }
|
---|
| 421 | private SymbolicExpressionTreeNode MakeGreaterThan(SymbolicExpressionTreeNode leftSide, SymbolicExpressionTreeNode rightSide) {
|
---|
| 422 | if (IsConstant(leftSide) && IsConstant(rightSide)) {
|
---|
| 423 | var lsConst = leftSide as ConstantTreeNode;
|
---|
| 424 | var rsConst = rightSide as ConstantTreeNode;
|
---|
| 425 | if (lsConst.Value > rsConst.Value) return MakeConstant(1.0);
|
---|
| 426 | else return MakeConstant(-1.0);
|
---|
| 427 | } else {
|
---|
| 428 | var gtNode = gtSymbol.CreateTreeNode();
|
---|
| 429 | gtNode.AddSubTree(leftSide);
|
---|
| 430 | gtNode.AddSubTree(rightSide);
|
---|
| 431 | return gtNode;
|
---|
| 432 | }
|
---|
| 433 | }
|
---|
| 434 | private SymbolicExpressionTreeNode MakeIfThenElse(SymbolicExpressionTreeNode condition, SymbolicExpressionTreeNode trueBranch, SymbolicExpressionTreeNode falseBranch) {
|
---|
| 435 | if (IsConstant(condition)) {
|
---|
| 436 | var constT = condition as ConstantTreeNode;
|
---|
| 437 | if (constT.Value > 0.0) return trueBranch;
|
---|
| 438 | else return falseBranch;
|
---|
| 439 | } else {
|
---|
| 440 | var ifNode = ifThenElseSymbol.CreateTreeNode();
|
---|
| 441 | ifNode.AddSubTree(condition);
|
---|
| 442 | ifNode.AddSubTree(trueBranch);
|
---|
| 443 | ifNode.AddSubTree(falseBranch);
|
---|
| 444 | return ifNode;
|
---|
| 445 | }
|
---|
| 446 | }
|
---|
| 447 | private SymbolicExpressionTreeNode MakeSine(SymbolicExpressionTreeNode node) {
|
---|
| 448 | // todo implement more transformation rules
|
---|
| 449 | if (IsConstant(node)) {
|
---|
| 450 | var constT = node as ConstantTreeNode;
|
---|
| 451 | return MakeConstant(Math.Sin(constT.Value));
|
---|
| 452 | } else {
|
---|
| 453 | var sineNode = sineSymbol.CreateTreeNode();
|
---|
| 454 | sineNode.AddSubTree(node);
|
---|
| 455 | return sineNode;
|
---|
| 456 | }
|
---|
| 457 | }
|
---|
| 458 | private SymbolicExpressionTreeNode MakeTangent(SymbolicExpressionTreeNode node) {
|
---|
| 459 | // todo implement more transformation rules
|
---|
| 460 | if (IsConstant(node)) {
|
---|
| 461 | var constT = node as ConstantTreeNode;
|
---|
| 462 | return MakeConstant(Math.Tan(constT.Value));
|
---|
| 463 | } else {
|
---|
| 464 | var tanNode = tanSymbol.CreateTreeNode();
|
---|
| 465 | tanNode.AddSubTree(node);
|
---|
| 466 | return tanNode;
|
---|
| 467 | }
|
---|
| 468 | }
|
---|
| 469 | private SymbolicExpressionTreeNode MakeCosine(SymbolicExpressionTreeNode node) {
|
---|
| 470 | // todo implement more transformation rules
|
---|
| 471 | if (IsConstant(node)) {
|
---|
| 472 | var constT = node as ConstantTreeNode;
|
---|
| 473 | return MakeConstant(Math.Cos(constT.Value));
|
---|
| 474 | } else {
|
---|
| 475 | var cosNode = cosineSymbol.CreateTreeNode();
|
---|
| 476 | cosNode.AddSubTree(node);
|
---|
| 477 | return cosNode;
|
---|
| 478 | }
|
---|
| 479 | }
|
---|
| 480 | private SymbolicExpressionTreeNode MakeExp(SymbolicExpressionTreeNode node) {
|
---|
| 481 | // todo implement more transformation rules
|
---|
| 482 | if (IsConstant(node)) {
|
---|
| 483 | var constT = node as ConstantTreeNode;
|
---|
| 484 | return MakeConstant(Math.Exp(constT.Value));
|
---|
| 485 | } else {
|
---|
| 486 | var expNode = expSymbol.CreateTreeNode();
|
---|
| 487 | expNode.AddSubTree(node);
|
---|
| 488 | return expNode;
|
---|
| 489 | }
|
---|
| 490 | }
|
---|
| 491 | private SymbolicExpressionTreeNode MakeLog(SymbolicExpressionTreeNode node) {
|
---|
| 492 | // todo implement more transformation rules
|
---|
| 493 | if (IsConstant(node)) {
|
---|
| 494 | var constT = node as ConstantTreeNode;
|
---|
| 495 | return MakeConstant(Math.Log(constT.Value));
|
---|
| 496 | } else {
|
---|
| 497 | var logNode = logSymbol.CreateTreeNode();
|
---|
| 498 | logNode.AddSubTree(node);
|
---|
| 499 | return logNode;
|
---|
| 500 | }
|
---|
| 501 | }
|
---|
| 502 |
|
---|
| 503 |
|
---|
[4239] | 504 | // MakeFraction, MakeProduct and MakeSum take two already simplified trees and create a new simplified tree
|
---|
| 505 |
|
---|
| 506 | private SymbolicExpressionTreeNode MakeFraction(SymbolicExpressionTreeNode a, SymbolicExpressionTreeNode b) {
|
---|
[3442] | 507 | if (IsConstant(a) && IsConstant(b)) {
|
---|
[4239] | 508 | // fold constants
|
---|
[3442] | 509 | return MakeConstant(((ConstantTreeNode)a).Value / ((ConstantTreeNode)b).Value);
|
---|
[4239] | 510 | } if (IsConstant(a) && !((ConstantTreeNode)a).Value.IsAlmost(1.0)) {
|
---|
| 511 | return MakeFraction(MakeConstant(1.0), MakeProduct(b, Invert(a)));
|
---|
[3442] | 512 | } else if (IsVariable(a) && IsConstant(b)) {
|
---|
[4239] | 513 | // merge constant values into variable weights
|
---|
[3442] | 514 | var constB = ((ConstantTreeNode)b).Value;
|
---|
| 515 | ((VariableTreeNode)a).Weight /= constB;
|
---|
| 516 | return a;
|
---|
[4239] | 517 | } else if (IsAddition(a) && IsConstant(b)) {
|
---|
| 518 | return a.SubTrees
|
---|
[4398] | 519 | .Select(x => GetSimplifiedTree(x))
|
---|
[4239] | 520 | .Select(x => MakeFraction(x, b))
|
---|
| 521 | .Aggregate((c, d) => MakeSum(c, d));
|
---|
| 522 | } else if (IsMultiplication(a) && IsConstant(b)) {
|
---|
| 523 | return MakeProduct(a, Invert(b));
|
---|
| 524 | } else if (IsDivision(a) && IsConstant(b)) {
|
---|
| 525 | // (a1 / a2) / c => (a1 / (a2 * c))
|
---|
| 526 | Trace.Assert(a.SubTrees.Count == 2);
|
---|
| 527 | return MakeFraction(a.SubTrees[0], MakeProduct(a.SubTrees[1], b));
|
---|
| 528 | } else if (IsDivision(a) && IsDivision(b)) {
|
---|
| 529 | // (a1 / a2) / (b1 / b2) =>
|
---|
| 530 | Trace.Assert(a.SubTrees.Count == 2);
|
---|
| 531 | Trace.Assert(b.SubTrees.Count == 2);
|
---|
| 532 | return MakeFraction(MakeProduct(a.SubTrees[0], b.SubTrees[1]), MakeProduct(a.SubTrees[1], b.SubTrees[0]));
|
---|
| 533 | } else if (IsDivision(a)) {
|
---|
| 534 | // (a1 / a2) / b => (a1 / (a2 * b))
|
---|
| 535 | Trace.Assert(a.SubTrees.Count == 2);
|
---|
| 536 | return MakeFraction(a.SubTrees[0], MakeProduct(a.SubTrees[1], b));
|
---|
| 537 | } else if (IsDivision(b)) {
|
---|
| 538 | // a / (b1 / b2) => (a * b2) / b1
|
---|
| 539 | Trace.Assert(b.SubTrees.Count == 2);
|
---|
| 540 | return MakeFraction(MakeProduct(a, b.SubTrees[1]), b.SubTrees[0]);
|
---|
[3442] | 541 | } else {
|
---|
[3462] | 542 | var div = divSymbol.CreateTreeNode();
|
---|
[3985] | 543 | div.AddSubTree(a);
|
---|
| 544 | div.AddSubTree(b);
|
---|
[3442] | 545 | return div;
|
---|
| 546 | }
|
---|
| 547 | }
|
---|
| 548 |
|
---|
[4239] | 549 | private SymbolicExpressionTreeNode MakeSum(SymbolicExpressionTreeNode a, SymbolicExpressionTreeNode b) {
|
---|
[3442] | 550 | if (IsConstant(a) && IsConstant(b)) {
|
---|
[4239] | 551 | // fold constants
|
---|
[3442] | 552 | ((ConstantTreeNode)a).Value += ((ConstantTreeNode)b).Value;
|
---|
| 553 | return a;
|
---|
| 554 | } else if (IsConstant(a)) {
|
---|
| 555 | // c + x => x + c
|
---|
| 556 | // b is not constant => make sure constant is on the right
|
---|
[4239] | 557 | return MakeSum(b, a);
|
---|
[3442] | 558 | } else if (IsConstant(b) && ((ConstantTreeNode)b).Value.IsAlmost(0.0)) {
|
---|
| 559 | // x + 0 => x
|
---|
| 560 | return a;
|
---|
| 561 | } else if (IsAddition(a) && IsAddition(b)) {
|
---|
| 562 | // merge additions
|
---|
[3462] | 563 | var add = addSymbol.CreateTreeNode();
|
---|
[3442] | 564 | for (int i = 0; i < a.SubTrees.Count - 1; i++) add.AddSubTree(a.SubTrees[i]);
|
---|
| 565 | for (int i = 0; i < b.SubTrees.Count - 1; i++) add.AddSubTree(b.SubTrees[i]);
|
---|
| 566 | if (IsConstant(a.SubTrees.Last()) && IsConstant(b.SubTrees.Last())) {
|
---|
[4239] | 567 | add.AddSubTree(MakeSum(a.SubTrees.Last(), b.SubTrees.Last()));
|
---|
[3442] | 568 | } else if (IsConstant(a.SubTrees.Last())) {
|
---|
| 569 | add.AddSubTree(b.SubTrees.Last());
|
---|
| 570 | add.AddSubTree(a.SubTrees.Last());
|
---|
| 571 | } else {
|
---|
| 572 | add.AddSubTree(a.SubTrees.Last());
|
---|
| 573 | add.AddSubTree(b.SubTrees.Last());
|
---|
| 574 | }
|
---|
[4239] | 575 | MergeVariablesInSum(add);
|
---|
[3442] | 576 | return add;
|
---|
| 577 | } else if (IsAddition(b)) {
|
---|
[4239] | 578 | return MakeSum(b, a);
|
---|
[3442] | 579 | } else if (IsAddition(a) && IsConstant(b)) {
|
---|
[4239] | 580 | // a is an addition and b is a constant => append b to a and make sure the constants are merged
|
---|
[3462] | 581 | var add = addSymbol.CreateTreeNode();
|
---|
[3442] | 582 | for (int i = 0; i < a.SubTrees.Count - 1; i++) add.AddSubTree(a.SubTrees[i]);
|
---|
| 583 | if (IsConstant(a.SubTrees.Last()))
|
---|
[4239] | 584 | add.AddSubTree(MakeSum(a.SubTrees.Last(), b));
|
---|
[3442] | 585 | else {
|
---|
| 586 | add.AddSubTree(a.SubTrees.Last());
|
---|
| 587 | add.AddSubTree(b);
|
---|
| 588 | }
|
---|
| 589 | return add;
|
---|
| 590 | } else if (IsAddition(a)) {
|
---|
[4239] | 591 | // a is already an addition => append b
|
---|
[3462] | 592 | var add = addSymbol.CreateTreeNode();
|
---|
[3442] | 593 | add.AddSubTree(b);
|
---|
| 594 | foreach (var subTree in a.SubTrees) {
|
---|
| 595 | add.AddSubTree(subTree);
|
---|
| 596 | }
|
---|
[4239] | 597 | MergeVariablesInSum(add);
|
---|
[3442] | 598 | return add;
|
---|
| 599 | } else {
|
---|
[3462] | 600 | var add = addSymbol.CreateTreeNode();
|
---|
[3985] | 601 | add.AddSubTree(a);
|
---|
| 602 | add.AddSubTree(b);
|
---|
[4239] | 603 | MergeVariablesInSum(add);
|
---|
[3442] | 604 | return add;
|
---|
| 605 | }
|
---|
| 606 | }
|
---|
| 607 |
|
---|
[4239] | 608 | // makes sure variable symbols in sums are combined
|
---|
| 609 | // possible improvment: combine sums of products where the products only reference the same variable
|
---|
| 610 | private void MergeVariablesInSum(SymbolicExpressionTreeNode sum) {
|
---|
| 611 | var subtrees = new List<SymbolicExpressionTreeNode>(sum.SubTrees);
|
---|
| 612 | while (sum.SubTrees.Count > 0) sum.RemoveSubTree(0);
|
---|
[3442] | 613 | var groupedVarNodes = from node in subtrees.OfType<VariableTreeNode>()
|
---|
[5377] | 614 | let lag = (node is LaggedVariableTreeNode) ? ((LaggedVariableTreeNode)node).Lag : 0
|
---|
| 615 | group node by node.VariableName + lag into g
|
---|
[3442] | 616 | select g;
|
---|
| 617 | var unchangedSubTrees = subtrees.Where(t => !(t is VariableTreeNode));
|
---|
| 618 |
|
---|
| 619 | foreach (var variableNodeGroup in groupedVarNodes) {
|
---|
| 620 | var weightSum = variableNodeGroup.Select(t => t.Weight).Sum();
|
---|
| 621 | var representative = variableNodeGroup.First();
|
---|
| 622 | representative.Weight = weightSum;
|
---|
[4239] | 623 | sum.AddSubTree(representative);
|
---|
[3442] | 624 | }
|
---|
| 625 | foreach (var unchangedSubtree in unchangedSubTrees)
|
---|
[4239] | 626 | sum.AddSubTree(unchangedSubtree);
|
---|
[3442] | 627 | }
|
---|
| 628 |
|
---|
[4239] | 629 |
|
---|
| 630 | private SymbolicExpressionTreeNode MakeProduct(SymbolicExpressionTreeNode a, SymbolicExpressionTreeNode b) {
|
---|
[3442] | 631 | if (IsConstant(a) && IsConstant(b)) {
|
---|
[4239] | 632 | // fold constants
|
---|
[3442] | 633 | ((ConstantTreeNode)a).Value *= ((ConstantTreeNode)b).Value;
|
---|
| 634 | return a;
|
---|
| 635 | } else if (IsConstant(a)) {
|
---|
[4239] | 636 | // a * $ => $ * a
|
---|
| 637 | return MakeProduct(b, a);
|
---|
[3442] | 638 | } else if (IsConstant(b) && ((ConstantTreeNode)b).Value.IsAlmost(1.0)) {
|
---|
[4239] | 639 | // $ * 1.0 => $
|
---|
[3442] | 640 | return a;
|
---|
| 641 | } else if (IsConstant(b) && IsVariable(a)) {
|
---|
[4239] | 642 | // multiply constants into variables weights
|
---|
[3442] | 643 | ((VariableTreeNode)a).Weight *= ((ConstantTreeNode)b).Value;
|
---|
| 644 | return a;
|
---|
| 645 | } else if (IsConstant(b) && IsAddition(a)) {
|
---|
[4239] | 646 | // multiply constants into additions
|
---|
| 647 | return a.SubTrees.Select(x => MakeProduct(x, b)).Aggregate((c, d) => MakeSum(c, d));
|
---|
[4068] | 648 | } else if (IsDivision(a) && IsDivision(b)) {
|
---|
[4239] | 649 | // (a1 / a2) * (b1 / b2) => (a1 * b1) / (a2 * b2)
|
---|
| 650 | Trace.Assert(a.SubTrees.Count == 2);
|
---|
| 651 | Trace.Assert(b.SubTrees.Count == 2);
|
---|
| 652 | return MakeFraction(MakeProduct(a.SubTrees[0], b.SubTrees[0]), MakeProduct(a.SubTrees[1], b.SubTrees[1]));
|
---|
[3442] | 653 | } else if (IsDivision(a)) {
|
---|
[4239] | 654 | // (a1 / a2) * b => (a1 * b) / a2
|
---|
[3442] | 655 | Trace.Assert(a.SubTrees.Count == 2);
|
---|
[4239] | 656 | return MakeFraction(MakeProduct(a.SubTrees[0], b), a.SubTrees[1]);
|
---|
[3442] | 657 | } else if (IsDivision(b)) {
|
---|
[4239] | 658 | // a * (b1 / b2) => (b1 * a) / b2
|
---|
[3442] | 659 | Trace.Assert(b.SubTrees.Count == 2);
|
---|
[4239] | 660 | return MakeFraction(MakeProduct(b.SubTrees[0], a), b.SubTrees[1]);
|
---|
[3442] | 661 | } else if (IsMultiplication(a) && IsMultiplication(b)) {
|
---|
[4239] | 662 | // merge multiplications (make sure constants are merged)
|
---|
[3462] | 663 | var mul = mulSymbol.CreateTreeNode();
|
---|
[4239] | 664 | for (int i = 0; i < a.SubTrees.Count; i++) mul.AddSubTree(a.SubTrees[i]);
|
---|
| 665 | for (int i = 0; i < b.SubTrees.Count; i++) mul.AddSubTree(b.SubTrees[i]);
|
---|
| 666 | MergeVariablesAndConstantsInProduct(mul);
|
---|
[3442] | 667 | return mul;
|
---|
[4239] | 668 | } else if (IsMultiplication(b)) {
|
---|
| 669 | return MakeProduct(b, a);
|
---|
[3442] | 670 | } else if (IsMultiplication(a)) {
|
---|
[4239] | 671 | // a is already an multiplication => append b
|
---|
| 672 | a.AddSubTree(b);
|
---|
| 673 | MergeVariablesAndConstantsInProduct(a);
|
---|
| 674 | return a;
|
---|
[3442] | 675 | } else {
|
---|
[3462] | 676 | var mul = mulSymbol.CreateTreeNode();
|
---|
[3442] | 677 | mul.SubTrees.Add(a);
|
---|
| 678 | mul.SubTrees.Add(b);
|
---|
[4239] | 679 | MergeVariablesAndConstantsInProduct(mul);
|
---|
[3442] | 680 | return mul;
|
---|
| 681 | }
|
---|
| 682 | }
|
---|
[4239] | 683 | #endregion
|
---|
[3442] | 684 |
|
---|
[4239] | 685 | // helper to combine the constant factors in products and to combine variables (powers of 2, 3...)
|
---|
| 686 | private void MergeVariablesAndConstantsInProduct(SymbolicExpressionTreeNode prod) {
|
---|
| 687 | var subtrees = new List<SymbolicExpressionTreeNode>(prod.SubTrees);
|
---|
| 688 | while (prod.SubTrees.Count > 0) prod.RemoveSubTree(0);
|
---|
| 689 | var groupedVarNodes = from node in subtrees.OfType<VariableTreeNode>()
|
---|
[5377] | 690 | let lag = (node is LaggedVariableTreeNode) ? ((LaggedVariableTreeNode)node).Lag : 0
|
---|
| 691 | group node by node.VariableName + lag into g
|
---|
[4239] | 692 | orderby g.Count()
|
---|
| 693 | select g;
|
---|
| 694 | var constantProduct = (from node in subtrees.OfType<VariableTreeNode>()
|
---|
| 695 | select node.Weight)
|
---|
| 696 | .Concat(from node in subtrees.OfType<ConstantTreeNode>()
|
---|
| 697 | select node.Value)
|
---|
| 698 | .DefaultIfEmpty(1.0)
|
---|
| 699 | .Aggregate((c1, c2) => c1 * c2);
|
---|
[3442] | 700 |
|
---|
[4239] | 701 | var unchangedSubTrees = from tree in subtrees
|
---|
| 702 | where !(tree is VariableTreeNode)
|
---|
| 703 | where !(tree is ConstantTreeNode)
|
---|
| 704 | select tree;
|
---|
[3442] | 705 |
|
---|
[4239] | 706 | foreach (var variableNodeGroup in groupedVarNodes) {
|
---|
| 707 | var representative = variableNodeGroup.First();
|
---|
| 708 | representative.Weight = 1.0;
|
---|
| 709 | if (variableNodeGroup.Count() > 1) {
|
---|
| 710 | var poly = mulSymbol.CreateTreeNode();
|
---|
| 711 | for (int p = 0; p < variableNodeGroup.Count(); p++) {
|
---|
| 712 | poly.AddSubTree((SymbolicExpressionTreeNode)representative.Clone());
|
---|
| 713 | }
|
---|
| 714 | prod.AddSubTree(poly);
|
---|
| 715 | } else {
|
---|
| 716 | prod.AddSubTree(representative);
|
---|
| 717 | }
|
---|
| 718 | }
|
---|
[3442] | 719 |
|
---|
[4239] | 720 | foreach (var unchangedSubtree in unchangedSubTrees)
|
---|
| 721 | prod.AddSubTree(unchangedSubtree);
|
---|
[3442] | 722 |
|
---|
[4239] | 723 | if (!constantProduct.IsAlmost(1.0)) {
|
---|
| 724 | prod.AddSubTree(MakeConstant(constantProduct));
|
---|
| 725 | }
|
---|
[3442] | 726 | }
|
---|
| 727 |
|
---|
[4239] | 728 |
|
---|
| 729 | #region helper functions
|
---|
| 730 | /// <summary>
|
---|
| 731 | /// x => x * -1
|
---|
| 732 | /// Doesn't create new trees and manipulates x
|
---|
| 733 | /// </summary>
|
---|
| 734 | /// <param name="x"></param>
|
---|
| 735 | /// <returns>-x</returns>
|
---|
| 736 | private SymbolicExpressionTreeNode Negate(SymbolicExpressionTreeNode x) {
|
---|
| 737 | if (IsConstant(x)) {
|
---|
| 738 | ((ConstantTreeNode)x).Value *= -1;
|
---|
| 739 | } else if (IsVariable(x)) {
|
---|
| 740 | var variableTree = (VariableTreeNode)x;
|
---|
| 741 | variableTree.Weight *= -1.0;
|
---|
| 742 | } else if (IsAddition(x)) {
|
---|
| 743 | // (x0 + x1 + .. + xn) * -1 => (-x0 + -x1 + .. + -xn)
|
---|
[5108] | 744 | for (int i = 0; i < x.SubTrees.Count; i++)
|
---|
| 745 | x.SubTrees[i] = Negate(x.SubTrees[i]);
|
---|
[4239] | 746 | } else if (IsMultiplication(x) || IsDivision(x)) {
|
---|
| 747 | // x0 * x1 * .. * xn * -1 => x0 * x1 * .. * -xn
|
---|
[5108] | 748 | x.SubTrees[x.SubTrees.Count - 1] = Negate(x.SubTrees.Last()); // last is maybe a constant, prefer to negate the constant
|
---|
[4239] | 749 | } else {
|
---|
| 750 | // any other function
|
---|
| 751 | return MakeProduct(x, MakeConstant(-1));
|
---|
| 752 | }
|
---|
| 753 | return x;
|
---|
[3442] | 754 | }
|
---|
[3876] | 755 |
|
---|
[4239] | 756 | /// <summary>
|
---|
| 757 | /// x => 1/x
|
---|
| 758 | /// Doesn't create new trees and manipulates x
|
---|
| 759 | /// </summary>
|
---|
| 760 | /// <param name="x"></param>
|
---|
| 761 | /// <returns></returns>
|
---|
| 762 | private SymbolicExpressionTreeNode Invert(SymbolicExpressionTreeNode x) {
|
---|
| 763 | if (IsConstant(x)) {
|
---|
| 764 | return MakeConstant(1.0 / ((ConstantTreeNode)x).Value);
|
---|
| 765 | } else if (IsDivision(x)) {
|
---|
| 766 | Trace.Assert(x.SubTrees.Count == 2);
|
---|
| 767 | return MakeFraction(x.SubTrees[1], x.SubTrees[0]);
|
---|
| 768 | } else {
|
---|
| 769 | // any other function
|
---|
| 770 | return MakeFraction(MakeConstant(1), x);
|
---|
| 771 | }
|
---|
[3876] | 772 | }
|
---|
[3442] | 773 |
|
---|
| 774 | private SymbolicExpressionTreeNode MakeConstant(double value) {
|
---|
[3462] | 775 | ConstantTreeNode constantTreeNode = (ConstantTreeNode)(constSymbol.CreateTreeNode());
|
---|
[3442] | 776 | constantTreeNode.Value = value;
|
---|
| 777 | return (SymbolicExpressionTreeNode)constantTreeNode;
|
---|
| 778 | }
|
---|
| 779 |
|
---|
| 780 | private SymbolicExpressionTreeNode MakeVariable(double weight, string name) {
|
---|
[3462] | 781 | var tree = (VariableTreeNode)varSymbol.CreateTreeNode();
|
---|
[3442] | 782 | tree.Weight = weight;
|
---|
| 783 | tree.VariableName = name;
|
---|
| 784 | return tree;
|
---|
| 785 | }
|
---|
[4239] | 786 | #endregion
|
---|
[3442] | 787 | }
|
---|
| 788 | }
|
---|