[14843] | 1 | #region License Information
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| 2 |
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| 3 | /* HeuristicLab
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[17180] | 4 | * Copyright (C) Heuristic and Evolutionary Algorithms Laboratory (HEAL)
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[14843] | 5 | *
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| 6 | * This file is part of HeuristicLab.
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| 7 | *
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| 8 | * HeuristicLab is free software: you can redistribute it and/or modify
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| 9 | * it under the terms of the GNU General Public License as published by
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| 10 | * the Free Software Foundation, either version 3 of the License, or
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| 11 | * (at your option) any later version.
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| 12 | *
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| 13 | * HeuristicLab is distributed in the hope that it will be useful,
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| 14 | * but WITHOUT ANY WARRANTY; without even the implied warranty of
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| 15 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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| 16 | * GNU General Public License for more details.
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| 17 | *
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| 18 | * You should have received a copy of the GNU General Public License
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| 19 | * along with HeuristicLab. If not, see <http://www.gnu.org/licenses/>.
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| 20 | */
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| 21 |
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| 22 | #endregion
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| 23 |
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| 24 | using System;
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| 25 | using System.Collections.Generic;
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| 26 | using System.Linq;
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| 27 | using HeuristicLab.Common;
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| 28 | using HeuristicLab.Encodings.SymbolicExpressionTreeEncoding;
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| 29 |
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[17604] | 30 | using DoubleVector = MathNet.Numerics.LinearAlgebra.Vector<double>;
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| 31 |
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[14843] | 32 | namespace HeuristicLab.Problems.DataAnalysis.Symbolic {
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| 33 | /// <summary>
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| 34 | /// Simplifier for symbolic expressions
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| 35 | /// </summary>
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[17593] | 36 | public class VectorTreeSimplifier {
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[14949] | 37 | private static readonly Addition addSymbol = new Addition();
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| 38 | private static readonly Multiplication mulSymbol = new Multiplication();
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| 39 | private static readonly Division divSymbol = new Division();
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| 40 | private static readonly Constant constSymbol = new Constant();
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[16356] | 41 | private static readonly Absolute absSymbol = new Absolute();
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[14949] | 42 | private static readonly Logarithm logSymbol = new Logarithm();
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| 43 | private static readonly Exponential expSymbol = new Exponential();
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| 44 | private static readonly Root rootSymbol = new Root();
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| 45 | private static readonly Square sqrSymbol = new Square();
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| 46 | private static readonly SquareRoot sqrtSymbol = new SquareRoot();
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[16360] | 47 | private static readonly AnalyticQuotient aqSymbol = new AnalyticQuotient();
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[16356] | 48 | private static readonly Cube cubeSymbol = new Cube();
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| 49 | private static readonly CubeRoot cubeRootSymbol = new CubeRoot();
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[14949] | 50 | private static readonly Power powSymbol = new Power();
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| 51 | private static readonly Sine sineSymbol = new Sine();
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| 52 | private static readonly Cosine cosineSymbol = new Cosine();
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| 53 | private static readonly Tangent tanSymbol = new Tangent();
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| 54 | private static readonly IfThenElse ifThenElseSymbol = new IfThenElse();
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| 55 | private static readonly And andSymbol = new And();
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| 56 | private static readonly Or orSymbol = new Or();
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| 57 | private static readonly Not notSymbol = new Not();
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| 58 | private static readonly GreaterThan gtSymbol = new GreaterThan();
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| 59 | private static readonly LessThan ltSymbol = new LessThan();
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| 60 | private static readonly Integral integralSymbol = new Integral();
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| 61 | private static readonly LaggedVariable laggedVariableSymbol = new LaggedVariable();
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| 62 | private static readonly TimeLag timeLagSymbol = new TimeLag();
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[17593] | 63 | private static readonly Sum sumSymbol = new Sum();
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| 64 | private static readonly Mean meanSymbol = new Mean();
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| 65 | private static readonly Length lengthSymbol = new Length();
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[17602] | 66 | private static readonly StandardDeviation standardDeviationSymbol = new StandardDeviation();
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| 67 | private static readonly Variance varianceSymbol = new Variance();
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[14843] | 68 |
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[17593] | 69 | private readonly SymbolicDataAnalysisExpressionTreeVectorInterpreter interpreter;
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[14949] | 70 |
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[17604] | 71 | public VectorTreeSimplifier(SymbolicDataAnalysisExpressionTreeVectorInterpreter interpreter) {
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[17593] | 72 | this.interpreter = interpreter;
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| 73 | }
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| 74 |
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| 75 | public ISymbolicExpressionTree Simplify(ISymbolicExpressionTree originalTree) {
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[14843] | 76 | var clone = (ISymbolicExpressionTreeNode)originalTree.Root.Clone();
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| 77 | // macro expand (initially no argument trees)
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| 78 | var macroExpandedTree = MacroExpand(clone, clone.GetSubtree(0), new List<ISymbolicExpressionTreeNode>());
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| 79 | ISymbolicExpressionTreeNode rootNode = (new ProgramRootSymbol()).CreateTreeNode();
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| 80 | rootNode.AddSubtree(GetSimplifiedTree(macroExpandedTree));
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| 81 |
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| 82 | #if DEBUG
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| 83 | // check that each node is only referenced once
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| 84 | var nodes = rootNode.IterateNodesPrefix().ToArray();
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[14949] | 85 | foreach (var n in nodes) if (nodes.Count(ni => ni == n) > 1) throw new InvalidOperationException();
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[14843] | 86 | #endif
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| 87 | return new SymbolicExpressionTree(rootNode);
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| 88 | }
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| 89 |
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| 90 | // the argumentTrees list contains already expanded trees used as arguments for invocations
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[14949] | 91 | private static ISymbolicExpressionTreeNode MacroExpand(ISymbolicExpressionTreeNode root, ISymbolicExpressionTreeNode node,
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[14843] | 92 | IList<ISymbolicExpressionTreeNode> argumentTrees) {
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| 93 | List<ISymbolicExpressionTreeNode> subtrees = new List<ISymbolicExpressionTreeNode>(node.Subtrees);
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| 94 | while (node.SubtreeCount > 0) node.RemoveSubtree(0);
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| 95 | if (node.Symbol is InvokeFunction) {
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| 96 | var invokeSym = node.Symbol as InvokeFunction;
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| 97 | var defunNode = FindFunctionDefinition(root, invokeSym.FunctionName);
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| 98 | var macroExpandedArguments = new List<ISymbolicExpressionTreeNode>();
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| 99 | foreach (var subtree in subtrees) {
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| 100 | macroExpandedArguments.Add(MacroExpand(root, subtree, argumentTrees));
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| 101 | }
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| 102 | return MacroExpand(root, defunNode, macroExpandedArguments);
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| 103 | } else if (node.Symbol is Argument) {
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| 104 | var argSym = node.Symbol as Argument;
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| 105 | // return the correct argument sub-tree (already macro-expanded)
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| 106 | return (SymbolicExpressionTreeNode)argumentTrees[argSym.ArgumentIndex].Clone();
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| 107 | } else {
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| 108 | // recursive application
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| 109 | foreach (var subtree in subtrees) {
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| 110 | node.AddSubtree(MacroExpand(root, subtree, argumentTrees));
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| 111 | }
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| 112 | return node;
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| 113 | }
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| 114 | }
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| 115 |
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[14949] | 116 | private static ISymbolicExpressionTreeNode FindFunctionDefinition(ISymbolicExpressionTreeNode root, string functionName) {
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[14843] | 117 | foreach (var subtree in root.Subtrees.OfType<DefunTreeNode>()) {
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| 118 | if (subtree.FunctionName == functionName) return subtree.GetSubtree(0);
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| 119 | }
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| 120 |
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| 121 | throw new ArgumentException("Definition of function " + functionName + " not found.");
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| 122 | }
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| 123 |
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| 124 | #region symbol predicates
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| 125 |
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| 126 | // arithmetic
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[14949] | 127 | private static bool IsDivision(ISymbolicExpressionTreeNode node) {
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[14843] | 128 | return node.Symbol is Division;
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| 129 | }
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| 130 |
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[14949] | 131 | private static bool IsMultiplication(ISymbolicExpressionTreeNode node) {
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[14843] | 132 | return node.Symbol is Multiplication;
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| 133 | }
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| 134 |
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[14949] | 135 | private static bool IsSubtraction(ISymbolicExpressionTreeNode node) {
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[14843] | 136 | return node.Symbol is Subtraction;
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| 137 | }
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| 138 |
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[14949] | 139 | private static bool IsAddition(ISymbolicExpressionTreeNode node) {
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[14843] | 140 | return node.Symbol is Addition;
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| 141 | }
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| 142 |
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[14949] | 143 | private static bool IsAverage(ISymbolicExpressionTreeNode node) {
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[14843] | 144 | return node.Symbol is Average;
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| 145 | }
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| 146 |
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[16356] | 147 | private static bool IsAbsolute(ISymbolicExpressionTreeNode node) {
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| 148 | return node.Symbol is Absolute;
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| 149 | }
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| 150 |
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[14843] | 151 | // exponential
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[14949] | 152 | private static bool IsLog(ISymbolicExpressionTreeNode node) {
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[14843] | 153 | return node.Symbol is Logarithm;
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| 154 | }
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| 155 |
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[14949] | 156 | private static bool IsExp(ISymbolicExpressionTreeNode node) {
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[14843] | 157 | return node.Symbol is Exponential;
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| 158 | }
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| 159 |
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[14949] | 160 | private static bool IsRoot(ISymbolicExpressionTreeNode node) {
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[14843] | 161 | return node.Symbol is Root;
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| 162 | }
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| 163 |
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[14949] | 164 | private static bool IsSquare(ISymbolicExpressionTreeNode node) {
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[14843] | 165 | return node.Symbol is Square;
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| 166 | }
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| 167 |
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[14949] | 168 | private static bool IsSquareRoot(ISymbolicExpressionTreeNode node) {
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[14843] | 169 | return node.Symbol is SquareRoot;
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| 170 | }
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| 171 |
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[16356] | 172 | private static bool IsCube(ISymbolicExpressionTreeNode node) {
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| 173 | return node.Symbol is Cube;
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| 174 | }
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| 175 |
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| 176 | private static bool IsCubeRoot(ISymbolicExpressionTreeNode node) {
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| 177 | return node.Symbol is CubeRoot;
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| 178 | }
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| 179 |
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[14949] | 180 | private static bool IsPower(ISymbolicExpressionTreeNode node) {
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[14843] | 181 | return node.Symbol is Power;
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| 182 | }
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| 183 |
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| 184 | // trigonometric
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[14949] | 185 | private static bool IsSine(ISymbolicExpressionTreeNode node) {
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[14843] | 186 | return node.Symbol is Sine;
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| 187 | }
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| 188 |
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[14949] | 189 | private static bool IsCosine(ISymbolicExpressionTreeNode node) {
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[14843] | 190 | return node.Symbol is Cosine;
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| 191 | }
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| 192 |
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[14949] | 193 | private static bool IsTangent(ISymbolicExpressionTreeNode node) {
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[14843] | 194 | return node.Symbol is Tangent;
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| 195 | }
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| 196 |
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[16356] | 197 | private static bool IsAnalyticalQuotient(ISymbolicExpressionTreeNode node) {
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[16360] | 198 | return node.Symbol is AnalyticQuotient;
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[16356] | 199 | }
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| 200 |
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[14843] | 201 | // boolean
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[14949] | 202 | private static bool IsIfThenElse(ISymbolicExpressionTreeNode node) {
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[14843] | 203 | return node.Symbol is IfThenElse;
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| 204 | }
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| 205 |
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[14949] | 206 | private static bool IsAnd(ISymbolicExpressionTreeNode node) {
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[14843] | 207 | return node.Symbol is And;
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| 208 | }
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| 209 |
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[14949] | 210 | private static bool IsOr(ISymbolicExpressionTreeNode node) {
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[14843] | 211 | return node.Symbol is Or;
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| 212 | }
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| 213 |
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[14949] | 214 | private static bool IsNot(ISymbolicExpressionTreeNode node) {
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[14843] | 215 | return node.Symbol is Not;
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| 216 | }
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| 217 |
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| 218 | // comparison
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[14949] | 219 | private static bool IsGreaterThan(ISymbolicExpressionTreeNode node) {
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[14843] | 220 | return node.Symbol is GreaterThan;
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| 221 | }
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| 222 |
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[14949] | 223 | private static bool IsLessThan(ISymbolicExpressionTreeNode node) {
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[14843] | 224 | return node.Symbol is LessThan;
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| 225 | }
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| 226 |
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[14949] | 227 | private static bool IsBoolean(ISymbolicExpressionTreeNode node) {
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[14843] | 228 | return
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| 229 | node.Symbol is GreaterThan ||
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| 230 | node.Symbol is LessThan ||
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| 231 | node.Symbol is And ||
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| 232 | node.Symbol is Or;
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| 233 | }
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| 234 |
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| 235 | // terminals
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[14949] | 236 | private static bool IsVariable(ISymbolicExpressionTreeNode node) {
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[14843] | 237 | return node.Symbol is Variable;
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| 238 | }
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| 239 |
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[14949] | 240 | private static bool IsVariableBase(ISymbolicExpressionTreeNode node) {
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[14843] | 241 | return node is VariableTreeNodeBase;
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| 242 | }
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| 243 |
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[14949] | 244 | private static bool IsFactor(ISymbolicExpressionTreeNode node) {
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[14843] | 245 | return node is FactorVariableTreeNode;
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| 246 | }
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| 247 |
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[14949] | 248 | private static bool IsBinFactor(ISymbolicExpressionTreeNode node) {
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[14843] | 249 | return node is BinaryFactorVariableTreeNode;
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| 250 | }
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| 251 |
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[14949] | 252 | private static bool IsConstant(ISymbolicExpressionTreeNode node) {
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[14843] | 253 | return node.Symbol is Constant;
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| 254 | }
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| 255 |
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| 256 | // dynamic
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[14949] | 257 | private static bool IsTimeLag(ISymbolicExpressionTreeNode node) {
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[14843] | 258 | return node.Symbol is TimeLag;
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| 259 | }
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| 260 |
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[14949] | 261 | private static bool IsIntegral(ISymbolicExpressionTreeNode node) {
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[14843] | 262 | return node.Symbol is Integral;
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| 263 | }
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| 264 |
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[17593] | 265 | private static bool IsSum(ISymbolicExpressionTreeNode node) {
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| 266 | return node.Symbol is Sum;
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| 267 | }
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| 268 |
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| 269 | private static bool IsMean(ISymbolicExpressionTreeNode node) {
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| 270 | return node.Symbol is Mean;
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| 271 | }
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[17597] | 272 |
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| 273 | private static bool IsLength(ISymbolicExpressionTreeNode node) {
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| 274 | return node.Symbol is Length;
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| 275 | }
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[17602] | 276 |
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| 277 | private static bool IsStandardDeviation(ISymbolicExpressionTreeNode node) {
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| 278 | return node.Symbol is StandardDeviation;
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| 279 | }
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| 280 |
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| 281 | private static bool IsVariance(ISymbolicExpressionTreeNode node) {
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| 282 | return node.Symbol is Variance;
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| 283 | }
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[14843] | 284 | #endregion
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| 285 |
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[17593] | 286 | #region type predicates
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| 287 | public bool IsScalarNode(ISymbolicExpressionTreeNode node) {
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[17604] | 288 | return interpreter.GetNodeType(node) == typeof(double);
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[17593] | 289 | }
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| 290 | public bool IsVectorNode(ISymbolicExpressionTreeNode node) {
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[17604] | 291 | return interpreter.GetNodeType(node) == typeof(DoubleVector);
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[17593] | 292 | }
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| 293 | #endregion
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| 294 |
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[14843] | 295 | /// <summary>
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| 296 | /// Creates a new simplified tree
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| 297 | /// </summary>
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| 298 | /// <param name="original"></param>
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| 299 | /// <returns></returns>
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[17593] | 300 | public ISymbolicExpressionTreeNode GetSimplifiedTree(ISymbolicExpressionTreeNode original) {
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[14843] | 301 | if (IsConstant(original) || IsVariableBase(original)) {
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| 302 | return (ISymbolicExpressionTreeNode)original.Clone();
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[16356] | 303 | } else if (IsAbsolute(original)) {
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| 304 | return SimplifyAbsolute(original);
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[14843] | 305 | } else if (IsAddition(original)) {
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| 306 | return SimplifyAddition(original);
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| 307 | } else if (IsSubtraction(original)) {
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| 308 | return SimplifySubtraction(original);
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| 309 | } else if (IsMultiplication(original)) {
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| 310 | return SimplifyMultiplication(original);
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| 311 | } else if (IsDivision(original)) {
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| 312 | return SimplifyDivision(original);
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| 313 | } else if (IsAverage(original)) {
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| 314 | return SimplifyAverage(original);
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| 315 | } else if (IsLog(original)) {
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| 316 | return SimplifyLog(original);
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| 317 | } else if (IsExp(original)) {
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| 318 | return SimplifyExp(original);
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| 319 | } else if (IsSquare(original)) {
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| 320 | return SimplifySquare(original);
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| 321 | } else if (IsSquareRoot(original)) {
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| 322 | return SimplifySquareRoot(original);
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[16356] | 323 | } else if (IsCube(original)) {
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| 324 | return SimplifyCube(original);
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| 325 | } else if (IsCubeRoot(original)) {
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| 326 | return SimplifyCubeRoot(original);
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[14843] | 327 | } else if (IsPower(original)) {
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| 328 | return SimplifyPower(original);
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| 329 | } else if (IsRoot(original)) {
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| 330 | return SimplifyRoot(original);
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| 331 | } else if (IsSine(original)) {
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| 332 | return SimplifySine(original);
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| 333 | } else if (IsCosine(original)) {
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| 334 | return SimplifyCosine(original);
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| 335 | } else if (IsTangent(original)) {
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| 336 | return SimplifyTangent(original);
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[16356] | 337 | } else if (IsAnalyticalQuotient(original)) {
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| 338 | return SimplifyAnalyticalQuotient(original);
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[14843] | 339 | } else if (IsIfThenElse(original)) {
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| 340 | return SimplifyIfThenElse(original);
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| 341 | } else if (IsGreaterThan(original)) {
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| 342 | return SimplifyGreaterThan(original);
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| 343 | } else if (IsLessThan(original)) {
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| 344 | return SimplifyLessThan(original);
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| 345 | } else if (IsAnd(original)) {
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| 346 | return SimplifyAnd(original);
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| 347 | } else if (IsOr(original)) {
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| 348 | return SimplifyOr(original);
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| 349 | } else if (IsNot(original)) {
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| 350 | return SimplifyNot(original);
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| 351 | } else if (IsTimeLag(original)) {
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| 352 | return SimplifyTimeLag(original);
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| 353 | } else if (IsIntegral(original)) {
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| 354 | return SimplifyIntegral(original);
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[17593] | 355 | } else if (IsSum(original)) {
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| 356 | return SimplifySumAggregation(original);
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| 357 | } else if (IsMean(original)) {
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| 358 | return SimplifyMeanAggregation(original);
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[17597] | 359 | } else if (IsLength(original)) {
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| 360 | return SimplifyLengthAggregation(original);
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[17602] | 361 | } else if (IsStandardDeviation(original)) {
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| 362 | return SimplifyStandardDeviationAggregation(original);
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| 363 | } else if (IsVariance(original)) {
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| 364 | return SimplifyVarianceAggregation(original);
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[14843] | 365 | } else {
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| 366 | return SimplifyAny(original);
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| 367 | }
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| 368 | }
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| 369 |
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| 370 | #region specific simplification routines
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| 371 |
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[17593] | 372 | private ISymbolicExpressionTreeNode SimplifyAny(ISymbolicExpressionTreeNode original) {
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[14843] | 373 | // can't simplify this function but simplify all subtrees
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| 374 | List<ISymbolicExpressionTreeNode> subtrees = new List<ISymbolicExpressionTreeNode>(original.Subtrees);
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| 375 | while (original.Subtrees.Count() > 0) original.RemoveSubtree(0);
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| 376 | var clone = (SymbolicExpressionTreeNode)original.Clone();
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| 377 | List<ISymbolicExpressionTreeNode> simplifiedSubtrees = new List<ISymbolicExpressionTreeNode>();
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| 378 | foreach (var subtree in subtrees) {
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| 379 | simplifiedSubtrees.Add(GetSimplifiedTree(subtree));
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| 380 | original.AddSubtree(subtree);
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| 381 | }
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| 382 | foreach (var simplifiedSubtree in simplifiedSubtrees) {
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| 383 | clone.AddSubtree(simplifiedSubtree);
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| 384 | }
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| 385 | if (simplifiedSubtrees.TrueForAll(t => IsConstant(t))) {
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| 386 | SimplifyConstantExpression(clone);
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| 387 | }
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| 388 | return clone;
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| 389 | }
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| 390 |
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[17593] | 391 | private ISymbolicExpressionTreeNode SimplifyConstantExpression(ISymbolicExpressionTreeNode original) {
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[14843] | 392 | // not yet implemented
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| 393 | return original;
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| 394 | }
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| 395 |
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[17593] | 396 | private ISymbolicExpressionTreeNode SimplifyAverage(ISymbolicExpressionTreeNode original) {
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[14843] | 397 | if (original.Subtrees.Count() == 1) {
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| 398 | return GetSimplifiedTree(original.GetSubtree(0));
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| 399 | } else {
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| 400 | // simplify expressions x0..xn
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| 401 | // make sum(x0..xn) / n
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| 402 | var sum = original.Subtrees
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| 403 | .Select(GetSimplifiedTree)
|
---|
| 404 | .Aggregate(MakeSum);
|
---|
| 405 | return MakeFraction(sum, MakeConstant(original.Subtrees.Count()));
|
---|
| 406 | }
|
---|
| 407 | }
|
---|
| 408 |
|
---|
[17593] | 409 | private ISymbolicExpressionTreeNode SimplifyDivision(ISymbolicExpressionTreeNode original) {
|
---|
[14843] | 410 | if (original.Subtrees.Count() == 1) {
|
---|
| 411 | return Invert(GetSimplifiedTree(original.GetSubtree(0)));
|
---|
| 412 | } else {
|
---|
| 413 | // simplify expressions x0..xn
|
---|
| 414 | // make multiplication (x0 * 1/(x1 * x1 * .. * xn))
|
---|
| 415 | var first = original.GetSubtree(0);
|
---|
| 416 | var second = original.GetSubtree(1);
|
---|
| 417 | var remaining = original.Subtrees.Skip(2);
|
---|
| 418 | return
|
---|
| 419 | MakeProduct(GetSimplifiedTree(first),
|
---|
| 420 | Invert(remaining.Aggregate(GetSimplifiedTree(second), (a, b) => MakeProduct(a, GetSimplifiedTree(b)))));
|
---|
| 421 | }
|
---|
| 422 | }
|
---|
| 423 |
|
---|
[17593] | 424 | private ISymbolicExpressionTreeNode SimplifyMultiplication(ISymbolicExpressionTreeNode original) {
|
---|
[14843] | 425 | if (original.Subtrees.Count() == 1) {
|
---|
| 426 | return GetSimplifiedTree(original.GetSubtree(0));
|
---|
| 427 | } else {
|
---|
| 428 | return original.Subtrees
|
---|
| 429 | .Select(GetSimplifiedTree)
|
---|
| 430 | .Aggregate(MakeProduct);
|
---|
| 431 | }
|
---|
| 432 | }
|
---|
| 433 |
|
---|
[17593] | 434 | private ISymbolicExpressionTreeNode SimplifySubtraction(ISymbolicExpressionTreeNode original) {
|
---|
[14843] | 435 | if (original.Subtrees.Count() == 1) {
|
---|
| 436 | return Negate(GetSimplifiedTree(original.GetSubtree(0)));
|
---|
| 437 | } else {
|
---|
| 438 | // simplify expressions x0..xn
|
---|
| 439 | // make addition (x0,-x1..-xn)
|
---|
| 440 | var first = original.Subtrees.First();
|
---|
| 441 | var remaining = original.Subtrees.Skip(1);
|
---|
| 442 | return remaining.Aggregate(GetSimplifiedTree(first), (a, b) => MakeSum(a, Negate(GetSimplifiedTree(b))));
|
---|
| 443 | }
|
---|
| 444 | }
|
---|
| 445 |
|
---|
[17593] | 446 | private ISymbolicExpressionTreeNode SimplifyAddition(ISymbolicExpressionTreeNode original) {
|
---|
[14843] | 447 | if (original.Subtrees.Count() == 1) {
|
---|
| 448 | return GetSimplifiedTree(original.GetSubtree(0));
|
---|
| 449 | } else {
|
---|
| 450 | // simplify expression x0..xn
|
---|
| 451 | // make addition (x0..xn)
|
---|
| 452 | return original.Subtrees
|
---|
| 453 | .Select(GetSimplifiedTree)
|
---|
| 454 | .Aggregate(MakeSum);
|
---|
| 455 | }
|
---|
| 456 | }
|
---|
| 457 |
|
---|
[17593] | 458 | private ISymbolicExpressionTreeNode SimplifyAbsolute(ISymbolicExpressionTreeNode original) {
|
---|
[16356] | 459 | return MakeAbs(GetSimplifiedTree(original.GetSubtree(0)));
|
---|
| 460 | }
|
---|
| 461 |
|
---|
[17593] | 462 | private ISymbolicExpressionTreeNode SimplifyNot(ISymbolicExpressionTreeNode original) {
|
---|
[14843] | 463 | return MakeNot(GetSimplifiedTree(original.GetSubtree(0)));
|
---|
| 464 | }
|
---|
| 465 |
|
---|
[17593] | 466 | private ISymbolicExpressionTreeNode SimplifyOr(ISymbolicExpressionTreeNode original) {
|
---|
[14843] | 467 | return original.Subtrees
|
---|
| 468 | .Select(GetSimplifiedTree)
|
---|
| 469 | .Aggregate(MakeOr);
|
---|
| 470 | }
|
---|
| 471 |
|
---|
[17593] | 472 | private ISymbolicExpressionTreeNode SimplifyAnd(ISymbolicExpressionTreeNode original) {
|
---|
[14843] | 473 | return original.Subtrees
|
---|
| 474 | .Select(GetSimplifiedTree)
|
---|
| 475 | .Aggregate(MakeAnd);
|
---|
| 476 | }
|
---|
| 477 |
|
---|
[17593] | 478 | private ISymbolicExpressionTreeNode SimplifyLessThan(ISymbolicExpressionTreeNode original) {
|
---|
[14843] | 479 | return MakeLessThan(GetSimplifiedTree(original.GetSubtree(0)), GetSimplifiedTree(original.GetSubtree(1)));
|
---|
| 480 | }
|
---|
| 481 |
|
---|
[17593] | 482 | private ISymbolicExpressionTreeNode SimplifyGreaterThan(ISymbolicExpressionTreeNode original) {
|
---|
[14843] | 483 | return MakeGreaterThan(GetSimplifiedTree(original.GetSubtree(0)), GetSimplifiedTree(original.GetSubtree(1)));
|
---|
| 484 | }
|
---|
| 485 |
|
---|
[17593] | 486 | private ISymbolicExpressionTreeNode SimplifyIfThenElse(ISymbolicExpressionTreeNode original) {
|
---|
[14843] | 487 | return MakeIfThenElse(GetSimplifiedTree(original.GetSubtree(0)), GetSimplifiedTree(original.GetSubtree(1)),
|
---|
| 488 | GetSimplifiedTree(original.GetSubtree(2)));
|
---|
| 489 | }
|
---|
| 490 |
|
---|
[17593] | 491 | private ISymbolicExpressionTreeNode SimplifyTangent(ISymbolicExpressionTreeNode original) {
|
---|
[14843] | 492 | return MakeTangent(GetSimplifiedTree(original.GetSubtree(0)));
|
---|
| 493 | }
|
---|
| 494 |
|
---|
[17593] | 495 | private ISymbolicExpressionTreeNode SimplifyCosine(ISymbolicExpressionTreeNode original) {
|
---|
[14843] | 496 | return MakeCosine(GetSimplifiedTree(original.GetSubtree(0)));
|
---|
| 497 | }
|
---|
| 498 |
|
---|
[17593] | 499 | private ISymbolicExpressionTreeNode SimplifySine(ISymbolicExpressionTreeNode original) {
|
---|
[14843] | 500 | return MakeSine(GetSimplifiedTree(original.GetSubtree(0)));
|
---|
| 501 | }
|
---|
| 502 |
|
---|
[17593] | 503 | private ISymbolicExpressionTreeNode SimplifyExp(ISymbolicExpressionTreeNode original) {
|
---|
[14843] | 504 | return MakeExp(GetSimplifiedTree(original.GetSubtree(0)));
|
---|
| 505 | }
|
---|
| 506 |
|
---|
[17593] | 507 | private ISymbolicExpressionTreeNode SimplifySquare(ISymbolicExpressionTreeNode original) {
|
---|
[14843] | 508 | return MakeSquare(GetSimplifiedTree(original.GetSubtree(0)));
|
---|
| 509 | }
|
---|
| 510 |
|
---|
[17593] | 511 | private ISymbolicExpressionTreeNode SimplifySquareRoot(ISymbolicExpressionTreeNode original) {
|
---|
[14843] | 512 | return MakeSquareRoot(GetSimplifiedTree(original.GetSubtree(0)));
|
---|
| 513 | }
|
---|
[17593] | 514 | private ISymbolicExpressionTreeNode SimplifyCube(ISymbolicExpressionTreeNode original) {
|
---|
[16356] | 515 | return MakeCube(GetSimplifiedTree(original.GetSubtree(0)));
|
---|
| 516 | }
|
---|
[14843] | 517 |
|
---|
[17593] | 518 | private ISymbolicExpressionTreeNode SimplifyCubeRoot(ISymbolicExpressionTreeNode original) {
|
---|
[16356] | 519 | return MakeCubeRoot(GetSimplifiedTree(original.GetSubtree(0)));
|
---|
| 520 | }
|
---|
| 521 |
|
---|
[17593] | 522 | private ISymbolicExpressionTreeNode SimplifyLog(ISymbolicExpressionTreeNode original) {
|
---|
[14843] | 523 | return MakeLog(GetSimplifiedTree(original.GetSubtree(0)));
|
---|
| 524 | }
|
---|
| 525 |
|
---|
[17593] | 526 | private ISymbolicExpressionTreeNode SimplifyRoot(ISymbolicExpressionTreeNode original) {
|
---|
[14843] | 527 | return MakeRoot(GetSimplifiedTree(original.GetSubtree(0)), GetSimplifiedTree(original.GetSubtree(1)));
|
---|
| 528 | }
|
---|
| 529 |
|
---|
[17593] | 530 | private ISymbolicExpressionTreeNode SimplifyPower(ISymbolicExpressionTreeNode original) {
|
---|
[14843] | 531 | return MakePower(GetSimplifiedTree(original.GetSubtree(0)), GetSimplifiedTree(original.GetSubtree(1)));
|
---|
| 532 | }
|
---|
| 533 |
|
---|
[17593] | 534 | private ISymbolicExpressionTreeNode SimplifyAnalyticalQuotient(ISymbolicExpressionTreeNode original) {
|
---|
[16356] | 535 | return MakeAnalyticalQuotient(GetSimplifiedTree(original.GetSubtree(0)), GetSimplifiedTree(original.GetSubtree(1)));
|
---|
| 536 | }
|
---|
| 537 |
|
---|
[17593] | 538 | private ISymbolicExpressionTreeNode SimplifyTimeLag(ISymbolicExpressionTreeNode original) {
|
---|
[14843] | 539 | var laggedTreeNode = original as ILaggedTreeNode;
|
---|
| 540 | var simplifiedSubtree = GetSimplifiedTree(original.GetSubtree(0));
|
---|
| 541 | if (!ContainsVariableCondition(simplifiedSubtree)) {
|
---|
| 542 | return AddLagToDynamicNodes(simplifiedSubtree, laggedTreeNode.Lag);
|
---|
| 543 | } else {
|
---|
| 544 | return MakeTimeLag(simplifiedSubtree, laggedTreeNode.Lag);
|
---|
| 545 | }
|
---|
| 546 | }
|
---|
| 547 |
|
---|
[17593] | 548 | private ISymbolicExpressionTreeNode SimplifyIntegral(ISymbolicExpressionTreeNode original) {
|
---|
[14843] | 549 | var laggedTreeNode = original as ILaggedTreeNode;
|
---|
| 550 | var simplifiedSubtree = GetSimplifiedTree(original.GetSubtree(0));
|
---|
| 551 | if (IsConstant(simplifiedSubtree)) {
|
---|
| 552 | return GetSimplifiedTree(MakeProduct(simplifiedSubtree, MakeConstant(-laggedTreeNode.Lag)));
|
---|
| 553 | } else {
|
---|
| 554 | return MakeIntegral(simplifiedSubtree, laggedTreeNode.Lag);
|
---|
| 555 | }
|
---|
| 556 | }
|
---|
| 557 |
|
---|
[17593] | 558 | private ISymbolicExpressionTreeNode SimplifySumAggregation(ISymbolicExpressionTreeNode original) {
|
---|
| 559 | return MakeSumAggregation(GetSimplifiedTree(original.GetSubtree(0)));
|
---|
| 560 | }
|
---|
| 561 |
|
---|
| 562 | private ISymbolicExpressionTreeNode SimplifyMeanAggregation(ISymbolicExpressionTreeNode original) {
|
---|
| 563 | return MakeMeanAggregation(GetSimplifiedTree(original.GetSubtree(0)));
|
---|
| 564 | }
|
---|
| 565 |
|
---|
[17597] | 566 | private ISymbolicExpressionTreeNode SimplifyLengthAggregation(ISymbolicExpressionTreeNode original) {
|
---|
| 567 | return MakeLengthAggregation(GetSimplifiedTree(original.GetSubtree(0)));
|
---|
| 568 | }
|
---|
[17602] | 569 |
|
---|
| 570 | private ISymbolicExpressionTreeNode SimplifyStandardDeviationAggregation(ISymbolicExpressionTreeNode original) {
|
---|
| 571 | return MakeStandardDeviationAggregation(GetSimplifiedTree(original.GetSubtree(0)));
|
---|
| 572 | }
|
---|
| 573 |
|
---|
| 574 | private ISymbolicExpressionTreeNode SimplifyVarianceAggregation(ISymbolicExpressionTreeNode original) {
|
---|
| 575 | return MakeVarianceAggregation(GetSimplifiedTree(original.GetSubtree(0)));
|
---|
| 576 | }
|
---|
[14843] | 577 | #endregion
|
---|
| 578 |
|
---|
| 579 | #region low level tree restructuring
|
---|
| 580 |
|
---|
[17593] | 581 | private ISymbolicExpressionTreeNode MakeTimeLag(ISymbolicExpressionTreeNode subtree, int lag) {
|
---|
[14843] | 582 | if (lag == 0) return subtree;
|
---|
| 583 | if (IsConstant(subtree)) return subtree;
|
---|
| 584 | var lagNode = (LaggedTreeNode)timeLagSymbol.CreateTreeNode();
|
---|
| 585 | lagNode.Lag = lag;
|
---|
| 586 | lagNode.AddSubtree(subtree);
|
---|
| 587 | return lagNode;
|
---|
| 588 | }
|
---|
| 589 |
|
---|
[17593] | 590 | private ISymbolicExpressionTreeNode MakeIntegral(ISymbolicExpressionTreeNode subtree, int lag) {
|
---|
[14843] | 591 | if (lag == 0) return subtree;
|
---|
| 592 | else if (lag == -1 || lag == 1) {
|
---|
| 593 | return MakeSum(subtree, AddLagToDynamicNodes((ISymbolicExpressionTreeNode)subtree.Clone(), lag));
|
---|
| 594 | } else {
|
---|
| 595 | var node = (LaggedTreeNode)integralSymbol.CreateTreeNode();
|
---|
| 596 | node.Lag = lag;
|
---|
| 597 | node.AddSubtree(subtree);
|
---|
| 598 | return node;
|
---|
| 599 | }
|
---|
| 600 | }
|
---|
| 601 |
|
---|
[17593] | 602 | private ISymbolicExpressionTreeNode MakeNot(ISymbolicExpressionTreeNode t) {
|
---|
[14843] | 603 | if (IsConstant(t)) {
|
---|
| 604 | var constNode = t as ConstantTreeNode;
|
---|
| 605 | if (constNode.Value > 0) return MakeConstant(-1.0);
|
---|
| 606 | else return MakeConstant(1.0);
|
---|
| 607 | } else if (IsNot(t)) {
|
---|
| 608 | return t.GetSubtree(0);
|
---|
| 609 | } else if (!IsBoolean(t)) {
|
---|
| 610 | var gtNode = gtSymbol.CreateTreeNode();
|
---|
| 611 | gtNode.AddSubtree(t);
|
---|
| 612 | gtNode.AddSubtree(MakeConstant(0.0));
|
---|
| 613 | var notNode = notSymbol.CreateTreeNode();
|
---|
| 614 | notNode.AddSubtree(gtNode);
|
---|
| 615 | return notNode;
|
---|
| 616 | } else {
|
---|
| 617 | var notNode = notSymbol.CreateTreeNode();
|
---|
| 618 | notNode.AddSubtree(t);
|
---|
| 619 | return notNode;
|
---|
| 620 | }
|
---|
| 621 | }
|
---|
| 622 |
|
---|
[17593] | 623 | private ISymbolicExpressionTreeNode MakeOr(ISymbolicExpressionTreeNode a, ISymbolicExpressionTreeNode b) {
|
---|
[14843] | 624 | if (IsConstant(a) && IsConstant(b)) {
|
---|
| 625 | var constA = a as ConstantTreeNode;
|
---|
| 626 | var constB = b as ConstantTreeNode;
|
---|
| 627 | if (constA.Value > 0.0 || constB.Value > 0.0) {
|
---|
| 628 | return MakeConstant(1.0);
|
---|
| 629 | } else {
|
---|
| 630 | return MakeConstant(-1.0);
|
---|
| 631 | }
|
---|
| 632 | } else if (IsConstant(a)) {
|
---|
| 633 | return MakeOr(b, a);
|
---|
| 634 | } else if (IsConstant(b)) {
|
---|
| 635 | var constT = b as ConstantTreeNode;
|
---|
| 636 | if (constT.Value > 0.0) {
|
---|
| 637 | // boolean expression is necessarily true
|
---|
| 638 | return MakeConstant(1.0);
|
---|
| 639 | } else {
|
---|
| 640 | // the constant value has no effect on the result of the boolean condition so we can drop the constant term
|
---|
| 641 | var orNode = orSymbol.CreateTreeNode();
|
---|
| 642 | orNode.AddSubtree(a);
|
---|
| 643 | return orNode;
|
---|
| 644 | }
|
---|
| 645 | } else {
|
---|
| 646 | var orNode = orSymbol.CreateTreeNode();
|
---|
| 647 | orNode.AddSubtree(a);
|
---|
| 648 | orNode.AddSubtree(b);
|
---|
| 649 | return orNode;
|
---|
| 650 | }
|
---|
| 651 | }
|
---|
| 652 |
|
---|
[17593] | 653 | private ISymbolicExpressionTreeNode MakeAnd(ISymbolicExpressionTreeNode a, ISymbolicExpressionTreeNode b) {
|
---|
[14843] | 654 | if (IsConstant(a) && IsConstant(b)) {
|
---|
| 655 | var constA = a as ConstantTreeNode;
|
---|
| 656 | var constB = b as ConstantTreeNode;
|
---|
| 657 | if (constA.Value > 0.0 && constB.Value > 0.0) {
|
---|
| 658 | return MakeConstant(1.0);
|
---|
| 659 | } else {
|
---|
| 660 | return MakeConstant(-1.0);
|
---|
| 661 | }
|
---|
| 662 | } else if (IsConstant(a)) {
|
---|
| 663 | return MakeAnd(b, a);
|
---|
| 664 | } else if (IsConstant(b)) {
|
---|
| 665 | var constB = b as ConstantTreeNode;
|
---|
| 666 | if (constB.Value > 0.0) {
|
---|
| 667 | // the constant value has no effect on the result of the boolean condition so we can drop the constant term
|
---|
| 668 | var andNode = andSymbol.CreateTreeNode();
|
---|
| 669 | andNode.AddSubtree(a);
|
---|
| 670 | return andNode;
|
---|
| 671 | } else {
|
---|
| 672 | // boolean expression is necessarily false
|
---|
| 673 | return MakeConstant(-1.0);
|
---|
| 674 | }
|
---|
| 675 | } else {
|
---|
| 676 | var andNode = andSymbol.CreateTreeNode();
|
---|
| 677 | andNode.AddSubtree(a);
|
---|
| 678 | andNode.AddSubtree(b);
|
---|
| 679 | return andNode;
|
---|
| 680 | }
|
---|
| 681 | }
|
---|
| 682 |
|
---|
[17593] | 683 | private ISymbolicExpressionTreeNode MakeLessThan(ISymbolicExpressionTreeNode leftSide,
|
---|
[14843] | 684 | ISymbolicExpressionTreeNode rightSide) {
|
---|
| 685 | if (IsConstant(leftSide) && IsConstant(rightSide)) {
|
---|
| 686 | var lsConst = leftSide as ConstantTreeNode;
|
---|
| 687 | var rsConst = rightSide as ConstantTreeNode;
|
---|
| 688 | if (lsConst.Value < rsConst.Value) return MakeConstant(1.0);
|
---|
| 689 | else return MakeConstant(-1.0);
|
---|
| 690 | } else {
|
---|
| 691 | var ltNode = ltSymbol.CreateTreeNode();
|
---|
| 692 | ltNode.AddSubtree(leftSide);
|
---|
| 693 | ltNode.AddSubtree(rightSide);
|
---|
| 694 | return ltNode;
|
---|
| 695 | }
|
---|
| 696 | }
|
---|
| 697 |
|
---|
[17593] | 698 | private ISymbolicExpressionTreeNode MakeGreaterThan(ISymbolicExpressionTreeNode leftSide,
|
---|
[14843] | 699 | ISymbolicExpressionTreeNode rightSide) {
|
---|
| 700 | if (IsConstant(leftSide) && IsConstant(rightSide)) {
|
---|
| 701 | var lsConst = leftSide as ConstantTreeNode;
|
---|
| 702 | var rsConst = rightSide as ConstantTreeNode;
|
---|
| 703 | if (lsConst.Value > rsConst.Value) return MakeConstant(1.0);
|
---|
| 704 | else return MakeConstant(-1.0);
|
---|
| 705 | } else {
|
---|
| 706 | var gtNode = gtSymbol.CreateTreeNode();
|
---|
| 707 | gtNode.AddSubtree(leftSide);
|
---|
| 708 | gtNode.AddSubtree(rightSide);
|
---|
| 709 | return gtNode;
|
---|
| 710 | }
|
---|
| 711 | }
|
---|
| 712 |
|
---|
[17593] | 713 | private ISymbolicExpressionTreeNode MakeIfThenElse(ISymbolicExpressionTreeNode condition,
|
---|
[14843] | 714 | ISymbolicExpressionTreeNode trueBranch, ISymbolicExpressionTreeNode falseBranch) {
|
---|
| 715 | if (IsConstant(condition)) {
|
---|
| 716 | var constT = condition as ConstantTreeNode;
|
---|
| 717 | if (constT.Value > 0.0) return trueBranch;
|
---|
| 718 | else return falseBranch;
|
---|
| 719 | } else {
|
---|
| 720 | var ifNode = ifThenElseSymbol.CreateTreeNode();
|
---|
| 721 | if (IsBoolean(condition)) {
|
---|
| 722 | ifNode.AddSubtree(condition);
|
---|
| 723 | } else {
|
---|
| 724 | var gtNode = gtSymbol.CreateTreeNode();
|
---|
| 725 | gtNode.AddSubtree(condition);
|
---|
| 726 | gtNode.AddSubtree(MakeConstant(0.0));
|
---|
| 727 | ifNode.AddSubtree(gtNode);
|
---|
| 728 | }
|
---|
| 729 | ifNode.AddSubtree(trueBranch);
|
---|
| 730 | ifNode.AddSubtree(falseBranch);
|
---|
| 731 | return ifNode;
|
---|
| 732 | }
|
---|
| 733 | }
|
---|
| 734 |
|
---|
[17593] | 735 | private ISymbolicExpressionTreeNode MakeSine(ISymbolicExpressionTreeNode node) {
|
---|
[14843] | 736 | if (IsConstant(node)) {
|
---|
| 737 | var constT = node as ConstantTreeNode;
|
---|
| 738 | return MakeConstant(Math.Sin(constT.Value));
|
---|
| 739 | } else if (IsFactor(node)) {
|
---|
| 740 | var factor = node as FactorVariableTreeNode;
|
---|
| 741 | return MakeFactor(factor.Symbol, factor.VariableName, factor.Weights.Select(Math.Sin));
|
---|
| 742 | } else if (IsBinFactor(node)) {
|
---|
| 743 | var binFactor = node as BinaryFactorVariableTreeNode;
|
---|
| 744 | return MakeBinFactor(binFactor.Symbol, binFactor.VariableName, binFactor.VariableValue, Math.Sin(binFactor.Weight));
|
---|
| 745 | } else {
|
---|
| 746 | var sineNode = sineSymbol.CreateTreeNode();
|
---|
| 747 | sineNode.AddSubtree(node);
|
---|
| 748 | return sineNode;
|
---|
| 749 | }
|
---|
| 750 | }
|
---|
| 751 |
|
---|
[17593] | 752 | private ISymbolicExpressionTreeNode MakeTangent(ISymbolicExpressionTreeNode node) {
|
---|
[14843] | 753 | if (IsConstant(node)) {
|
---|
| 754 | var constT = node as ConstantTreeNode;
|
---|
| 755 | return MakeConstant(Math.Tan(constT.Value));
|
---|
| 756 | } else if (IsFactor(node)) {
|
---|
| 757 | var factor = node as FactorVariableTreeNode;
|
---|
| 758 | return MakeFactor(factor.Symbol, factor.VariableName, factor.Weights.Select(Math.Tan));
|
---|
| 759 | } else if (IsBinFactor(node)) {
|
---|
| 760 | var binFactor = node as BinaryFactorVariableTreeNode;
|
---|
| 761 | return MakeBinFactor(binFactor.Symbol, binFactor.VariableName, binFactor.VariableValue, Math.Tan(binFactor.Weight));
|
---|
| 762 | } else {
|
---|
| 763 | var tanNode = tanSymbol.CreateTreeNode();
|
---|
| 764 | tanNode.AddSubtree(node);
|
---|
| 765 | return tanNode;
|
---|
| 766 | }
|
---|
| 767 | }
|
---|
| 768 |
|
---|
[17593] | 769 | private ISymbolicExpressionTreeNode MakeCosine(ISymbolicExpressionTreeNode node) {
|
---|
[14843] | 770 | if (IsConstant(node)) {
|
---|
| 771 | var constT = node as ConstantTreeNode;
|
---|
| 772 | return MakeConstant(Math.Cos(constT.Value));
|
---|
| 773 | } else if (IsFactor(node)) {
|
---|
| 774 | var factor = node as FactorVariableTreeNode;
|
---|
| 775 | return MakeFactor(factor.Symbol, factor.VariableName, factor.Weights.Select(Math.Cos));
|
---|
| 776 | } else if (IsBinFactor(node)) {
|
---|
| 777 | var binFactor = node as BinaryFactorVariableTreeNode;
|
---|
| 778 | // cos(0) = 1 see similar case for Exp(binfactor)
|
---|
| 779 | return MakeSum(MakeBinFactor(binFactor.Symbol, binFactor.VariableName, binFactor.VariableValue, Math.Cos(binFactor.Weight) - 1),
|
---|
| 780 | MakeConstant(1.0));
|
---|
| 781 | } else {
|
---|
| 782 | var cosNode = cosineSymbol.CreateTreeNode();
|
---|
| 783 | cosNode.AddSubtree(node);
|
---|
| 784 | return cosNode;
|
---|
| 785 | }
|
---|
| 786 | }
|
---|
| 787 |
|
---|
[17593] | 788 | private ISymbolicExpressionTreeNode MakeExp(ISymbolicExpressionTreeNode node) {
|
---|
[14843] | 789 | if (IsConstant(node)) {
|
---|
| 790 | var constT = node as ConstantTreeNode;
|
---|
| 791 | return MakeConstant(Math.Exp(constT.Value));
|
---|
| 792 | } else if (IsFactor(node)) {
|
---|
| 793 | var factNode = node as FactorVariableTreeNode;
|
---|
| 794 | return MakeFactor(factNode.Symbol, factNode.VariableName, factNode.Weights.Select(w => Math.Exp(w)));
|
---|
| 795 | } else if (IsBinFactor(node)) {
|
---|
| 796 | // exp( binfactor w val=a) = if(val=a) exp(w) else exp(0) = binfactor( (exp(w) - 1) val a) + 1
|
---|
| 797 | var binFactor = node as BinaryFactorVariableTreeNode;
|
---|
| 798 | return
|
---|
| 799 | MakeSum(MakeBinFactor(binFactor.Symbol, binFactor.VariableName, binFactor.VariableValue, Math.Exp(binFactor.Weight) - 1), MakeConstant(1.0));
|
---|
| 800 | } else if (IsLog(node)) {
|
---|
| 801 | return node.GetSubtree(0);
|
---|
| 802 | } else if (IsAddition(node)) {
|
---|
| 803 | return node.Subtrees.Select(s => MakeExp(s)).Aggregate((s, t) => MakeProduct(s, t));
|
---|
| 804 | } else if (IsSubtraction(node)) {
|
---|
| 805 | return node.Subtrees.Select(s => MakeExp(s)).Aggregate((s, t) => MakeProduct(s, Negate(t)));
|
---|
| 806 | } else {
|
---|
| 807 | var expNode = expSymbol.CreateTreeNode();
|
---|
| 808 | expNode.AddSubtree(node);
|
---|
| 809 | return expNode;
|
---|
| 810 | }
|
---|
| 811 | }
|
---|
[17593] | 812 | private ISymbolicExpressionTreeNode MakeLog(ISymbolicExpressionTreeNode node) {
|
---|
[14843] | 813 | if (IsConstant(node)) {
|
---|
| 814 | var constT = node as ConstantTreeNode;
|
---|
| 815 | return MakeConstant(Math.Log(constT.Value));
|
---|
| 816 | } else if (IsFactor(node)) {
|
---|
| 817 | var factNode = node as FactorVariableTreeNode;
|
---|
| 818 | return MakeFactor(factNode.Symbol, factNode.VariableName, factNode.Weights.Select(w => Math.Log(w)));
|
---|
| 819 | } else if (IsExp(node)) {
|
---|
| 820 | return node.GetSubtree(0);
|
---|
| 821 | } else if (IsSquareRoot(node)) {
|
---|
| 822 | return MakeFraction(MakeLog(node.GetSubtree(0)), MakeConstant(2.0));
|
---|
| 823 | } else {
|
---|
| 824 | var logNode = logSymbol.CreateTreeNode();
|
---|
| 825 | logNode.AddSubtree(node);
|
---|
| 826 | return logNode;
|
---|
| 827 | }
|
---|
| 828 | }
|
---|
| 829 |
|
---|
[17593] | 830 | private ISymbolicExpressionTreeNode MakeSquare(ISymbolicExpressionTreeNode node) {
|
---|
[14843] | 831 | if (IsConstant(node)) {
|
---|
| 832 | var constT = node as ConstantTreeNode;
|
---|
| 833 | return MakeConstant(constT.Value * constT.Value);
|
---|
| 834 | } else if (IsFactor(node)) {
|
---|
| 835 | var factNode = node as FactorVariableTreeNode;
|
---|
| 836 | return MakeFactor(factNode.Symbol, factNode.VariableName, factNode.Weights.Select(w => w * w));
|
---|
| 837 | } else if (IsBinFactor(node)) {
|
---|
| 838 | var binFactor = node as BinaryFactorVariableTreeNode;
|
---|
| 839 | return MakeBinFactor(binFactor.Symbol, binFactor.VariableName, binFactor.VariableValue, binFactor.Weight * binFactor.Weight);
|
---|
| 840 | } else if (IsSquareRoot(node)) {
|
---|
| 841 | return node.GetSubtree(0);
|
---|
[16356] | 842 | } else if (IsMultiplication(node)) {
|
---|
| 843 | // sqr( x * y ) = sqr(x) * sqr(y)
|
---|
| 844 | var mulNode = mulSymbol.CreateTreeNode();
|
---|
| 845 | foreach (var subtree in node.Subtrees) {
|
---|
| 846 | mulNode.AddSubtree(MakeSquare(subtree));
|
---|
| 847 | }
|
---|
| 848 | return mulNode;
|
---|
| 849 | } else if (IsAbsolute(node)) {
|
---|
| 850 | return MakeSquare(node.GetSubtree(0)); // sqr(abs(x)) = sqr(x)
|
---|
| 851 | } else if (IsExp(node)) {
|
---|
| 852 | return MakeExp(MakeProduct(node.GetSubtree(0), MakeConstant(2.0))); // sqr(exp(x)) = exp(2x)
|
---|
| 853 | } else if (IsCube(node)) {
|
---|
| 854 | return MakePower(node.GetSubtree(0), MakeConstant(6));
|
---|
[14843] | 855 | } else {
|
---|
| 856 | var sqrNode = sqrSymbol.CreateTreeNode();
|
---|
| 857 | sqrNode.AddSubtree(node);
|
---|
| 858 | return sqrNode;
|
---|
| 859 | }
|
---|
| 860 | }
|
---|
| 861 |
|
---|
[17593] | 862 | private ISymbolicExpressionTreeNode MakeCube(ISymbolicExpressionTreeNode node) {
|
---|
[16356] | 863 | if (IsConstant(node)) {
|
---|
| 864 | var constT = node as ConstantTreeNode;
|
---|
| 865 | return MakeConstant(constT.Value * constT.Value * constT.Value);
|
---|
| 866 | } else if (IsFactor(node)) {
|
---|
| 867 | var factNode = node as FactorVariableTreeNode;
|
---|
| 868 | return MakeFactor(factNode.Symbol, factNode.VariableName, factNode.Weights.Select(w => w * w * w));
|
---|
| 869 | } else if (IsBinFactor(node)) {
|
---|
| 870 | var binFactor = node as BinaryFactorVariableTreeNode;
|
---|
| 871 | return MakeBinFactor(binFactor.Symbol, binFactor.VariableName, binFactor.VariableValue, binFactor.Weight * binFactor.Weight * binFactor.Weight);
|
---|
| 872 | } else if (IsCubeRoot(node)) {
|
---|
| 873 | return node.GetSubtree(0); // NOTE: not really accurate because cuberoot(x) with negative x is evaluated to NaN and after this simplification we evaluate as x
|
---|
| 874 | } else if (IsExp(node)) {
|
---|
| 875 | return MakeExp(MakeProduct(node.GetSubtree(0), MakeConstant(3)));
|
---|
| 876 | } else if (IsSquare(node)) {
|
---|
| 877 | return MakePower(node.GetSubtree(0), MakeConstant(6));
|
---|
| 878 | } else {
|
---|
| 879 | var cubeNode = cubeSymbol.CreateTreeNode();
|
---|
| 880 | cubeNode.AddSubtree(node);
|
---|
| 881 | return cubeNode;
|
---|
| 882 | }
|
---|
| 883 | }
|
---|
| 884 |
|
---|
[17593] | 885 | private ISymbolicExpressionTreeNode MakeAbs(ISymbolicExpressionTreeNode node) {
|
---|
[16356] | 886 | if (IsConstant(node)) {
|
---|
| 887 | var constT = node as ConstantTreeNode;
|
---|
| 888 | return MakeConstant(Math.Abs(constT.Value));
|
---|
| 889 | } else if (IsFactor(node)) {
|
---|
| 890 | var factNode = node as FactorVariableTreeNode;
|
---|
| 891 | return MakeFactor(factNode.Symbol, factNode.VariableName, factNode.Weights.Select(w => Math.Abs(w)));
|
---|
| 892 | } else if (IsBinFactor(node)) {
|
---|
| 893 | var binFactor = node as BinaryFactorVariableTreeNode;
|
---|
| 894 | return MakeBinFactor(binFactor.Symbol, binFactor.VariableName, binFactor.VariableValue, Math.Abs(binFactor.Weight));
|
---|
| 895 | } else if (IsSquare(node) || IsExp(node) || IsSquareRoot(node) || IsCubeRoot(node)) {
|
---|
| 896 | return node; // abs(sqr(x)) = sqr(x), abs(exp(x)) = exp(x) ...
|
---|
| 897 | } else if (IsMultiplication(node)) {
|
---|
| 898 | var mul = mulSymbol.CreateTreeNode();
|
---|
| 899 | foreach (var st in node.Subtrees) {
|
---|
| 900 | mul.AddSubtree(MakeAbs(st));
|
---|
| 901 | }
|
---|
| 902 | return mul;
|
---|
| 903 | } else if (IsDivision(node)) {
|
---|
| 904 | var div = divSymbol.CreateTreeNode();
|
---|
| 905 | foreach (var st in node.Subtrees) {
|
---|
| 906 | div.AddSubtree(MakeAbs(st));
|
---|
| 907 | }
|
---|
| 908 | return div;
|
---|
| 909 | } else {
|
---|
| 910 | var absNode = absSymbol.CreateTreeNode();
|
---|
| 911 | absNode.AddSubtree(node);
|
---|
| 912 | return absNode;
|
---|
| 913 | }
|
---|
| 914 | }
|
---|
| 915 |
|
---|
| 916 | // constant folding only
|
---|
[17593] | 917 | private ISymbolicExpressionTreeNode MakeAnalyticalQuotient(ISymbolicExpressionTreeNode a, ISymbolicExpressionTreeNode b) {
|
---|
[16356] | 918 | if (IsConstant(b)) {
|
---|
| 919 | var c = b as ConstantTreeNode;
|
---|
| 920 | return MakeFraction(a, MakeConstant(Math.Sqrt(1.0 + c.Value * c.Value)));
|
---|
| 921 | } else if (IsFactor(b)) {
|
---|
| 922 | var factNode = b as FactorVariableTreeNode;
|
---|
| 923 | return MakeFraction(a, MakeFactor(factNode.Symbol, factNode.VariableName, factNode.Weights.Select(w => Math.Sqrt(1.0 + w * w))));
|
---|
| 924 | } else if (IsBinFactor(b)) {
|
---|
| 925 | var binFactor = b as BinaryFactorVariableTreeNode;
|
---|
| 926 | return MakeFraction(a, MakeBinFactor(binFactor.Symbol, binFactor.VariableName, binFactor.VariableValue, Math.Sqrt(1.0 + binFactor.Weight * binFactor.Weight)));
|
---|
| 927 | } else {
|
---|
| 928 | var aqNode = aqSymbol.CreateTreeNode();
|
---|
| 929 | aqNode.AddSubtree(a);
|
---|
| 930 | aqNode.AddSubtree(b);
|
---|
| 931 | return aqNode;
|
---|
| 932 | }
|
---|
| 933 | }
|
---|
| 934 |
|
---|
[17593] | 935 | private ISymbolicExpressionTreeNode MakeSquareRoot(ISymbolicExpressionTreeNode node) {
|
---|
[14843] | 936 | if (IsConstant(node)) {
|
---|
| 937 | var constT = node as ConstantTreeNode;
|
---|
| 938 | return MakeConstant(Math.Sqrt(constT.Value));
|
---|
| 939 | } else if (IsFactor(node)) {
|
---|
| 940 | var factNode = node as FactorVariableTreeNode;
|
---|
| 941 | return MakeFactor(factNode.Symbol, factNode.VariableName, factNode.Weights.Select(w => Math.Sqrt(w)));
|
---|
| 942 | } else if (IsBinFactor(node)) {
|
---|
| 943 | var binFactor = node as BinaryFactorVariableTreeNode;
|
---|
| 944 | return MakeBinFactor(binFactor.Symbol, binFactor.VariableName, binFactor.VariableValue, Math.Sqrt(binFactor.Weight));
|
---|
| 945 | } else if (IsSquare(node)) {
|
---|
[16356] | 946 | return node.GetSubtree(0); // NOTE: not really accurate because sqrt(x) with negative x is evaluated to NaN and after this simplification we evaluate as x
|
---|
[14843] | 947 | } else {
|
---|
| 948 | var sqrtNode = sqrtSymbol.CreateTreeNode();
|
---|
| 949 | sqrtNode.AddSubtree(node);
|
---|
| 950 | return sqrtNode;
|
---|
| 951 | }
|
---|
| 952 | }
|
---|
| 953 |
|
---|
[17593] | 954 | private ISymbolicExpressionTreeNode MakeCubeRoot(ISymbolicExpressionTreeNode node) {
|
---|
[16356] | 955 | if (IsConstant(node)) {
|
---|
| 956 | var constT = node as ConstantTreeNode;
|
---|
| 957 | return MakeConstant(Math.Pow(constT.Value, 1.0 / 3.0));
|
---|
| 958 | } else if (IsFactor(node)) {
|
---|
| 959 | var factNode = node as FactorVariableTreeNode;
|
---|
| 960 | return MakeFactor(factNode.Symbol, factNode.VariableName, factNode.Weights.Select(w => Math.Pow(w, 1.0 / 3.0)));
|
---|
| 961 | } else if (IsBinFactor(node)) {
|
---|
| 962 | var binFactor = node as BinaryFactorVariableTreeNode;
|
---|
| 963 | return MakeBinFactor(binFactor.Symbol, binFactor.VariableName, binFactor.VariableValue, Math.Sqrt(Math.Pow(binFactor.Weight, 1.0 / 3.0)));
|
---|
| 964 | } else if (IsCube(node)) {
|
---|
| 965 | return node.GetSubtree(0);
|
---|
| 966 | } else {
|
---|
| 967 | var cubeRootNode = cubeRootSymbol.CreateTreeNode();
|
---|
| 968 | cubeRootNode.AddSubtree(node);
|
---|
| 969 | return cubeRootNode;
|
---|
| 970 | }
|
---|
| 971 | }
|
---|
| 972 |
|
---|
[17593] | 973 | private ISymbolicExpressionTreeNode MakeRoot(ISymbolicExpressionTreeNode a, ISymbolicExpressionTreeNode b) {
|
---|
[14843] | 974 | if (IsConstant(a) && IsConstant(b)) {
|
---|
| 975 | var constA = a as ConstantTreeNode;
|
---|
| 976 | var constB = b as ConstantTreeNode;
|
---|
| 977 | return MakeConstant(Math.Pow(constA.Value, 1.0 / Math.Round(constB.Value)));
|
---|
| 978 | } else if (IsFactor(a) && IsConstant(b)) {
|
---|
| 979 | var factNode = a as FactorVariableTreeNode;
|
---|
| 980 | var constNode = b as ConstantTreeNode;
|
---|
| 981 | return MakeFactor(factNode.Symbol, factNode.VariableName,
|
---|
| 982 | factNode.Weights.Select(w => Math.Pow(w, 1.0 / Math.Round(constNode.Value))));
|
---|
| 983 | } else if (IsBinFactor(a) && IsConstant(b)) {
|
---|
| 984 | var binFactor = a as BinaryFactorVariableTreeNode;
|
---|
| 985 | var constNode = b as ConstantTreeNode;
|
---|
| 986 | return MakeBinFactor(binFactor.Symbol, binFactor.VariableName, binFactor.VariableValue, Math.Pow(binFactor.Weight, 1.0 / Math.Round(constNode.Value)));
|
---|
| 987 | } else if (IsConstant(a) && IsFactor(b)) {
|
---|
| 988 | var constNode = a as ConstantTreeNode;
|
---|
| 989 | var factNode = b as FactorVariableTreeNode;
|
---|
| 990 | return MakeFactor(factNode.Symbol, factNode.VariableName, factNode.Weights.Select(w => Math.Pow(constNode.Value, 1.0 / Math.Round(w))));
|
---|
| 991 | } else if (IsConstant(a) && IsBinFactor(b)) {
|
---|
| 992 | var constNode = a as ConstantTreeNode;
|
---|
| 993 | var factNode = b as BinaryFactorVariableTreeNode;
|
---|
| 994 | return MakeBinFactor(factNode.Symbol, factNode.VariableName, factNode.VariableValue, Math.Pow(constNode.Value, 1.0 / Math.Round(factNode.Weight)));
|
---|
| 995 | } else if (IsFactor(a) && IsFactor(b) && AreSameTypeAndVariable(a, b)) {
|
---|
| 996 | var node0 = a as FactorVariableTreeNode;
|
---|
| 997 | var node1 = b as FactorVariableTreeNode;
|
---|
| 998 | return MakeFactor(node0.Symbol, node0.VariableName, node0.Weights.Zip(node1.Weights, (u, v) => Math.Pow(u, 1.0 / Math.Round(v))));
|
---|
| 999 | } else if (IsConstant(b)) {
|
---|
| 1000 | var constB = b as ConstantTreeNode;
|
---|
| 1001 | var constBValue = Math.Round(constB.Value);
|
---|
| 1002 | if (constBValue.IsAlmost(1.0)) {
|
---|
| 1003 | return a;
|
---|
| 1004 | } else if (constBValue.IsAlmost(0.0)) {
|
---|
| 1005 | return MakeConstant(1.0);
|
---|
| 1006 | } else if (constBValue.IsAlmost(-1.0)) {
|
---|
| 1007 | return MakeFraction(MakeConstant(1.0), a);
|
---|
| 1008 | } else if (constBValue < 0) {
|
---|
| 1009 | var rootNode = rootSymbol.CreateTreeNode();
|
---|
| 1010 | rootNode.AddSubtree(a);
|
---|
| 1011 | rootNode.AddSubtree(MakeConstant(-1.0 * constBValue));
|
---|
| 1012 | return MakeFraction(MakeConstant(1.0), rootNode);
|
---|
| 1013 | } else {
|
---|
| 1014 | var rootNode = rootSymbol.CreateTreeNode();
|
---|
| 1015 | rootNode.AddSubtree(a);
|
---|
| 1016 | rootNode.AddSubtree(MakeConstant(constBValue));
|
---|
| 1017 | return rootNode;
|
---|
| 1018 | }
|
---|
| 1019 | } else {
|
---|
| 1020 | var rootNode = rootSymbol.CreateTreeNode();
|
---|
| 1021 | rootNode.AddSubtree(a);
|
---|
| 1022 | rootNode.AddSubtree(b);
|
---|
| 1023 | return rootNode;
|
---|
| 1024 | }
|
---|
| 1025 | }
|
---|
| 1026 |
|
---|
| 1027 |
|
---|
[17593] | 1028 | private ISymbolicExpressionTreeNode MakePower(ISymbolicExpressionTreeNode a, ISymbolicExpressionTreeNode b) {
|
---|
[14843] | 1029 | if (IsConstant(a) && IsConstant(b)) {
|
---|
| 1030 | var constA = a as ConstantTreeNode;
|
---|
| 1031 | var constB = b as ConstantTreeNode;
|
---|
| 1032 | return MakeConstant(Math.Pow(constA.Value, Math.Round(constB.Value)));
|
---|
| 1033 | } else if (IsFactor(a) && IsConstant(b)) {
|
---|
| 1034 | var factNode = a as FactorVariableTreeNode;
|
---|
| 1035 | var constNode = b as ConstantTreeNode;
|
---|
| 1036 | return MakeFactor(factNode.Symbol, factNode.VariableName, factNode.Weights.Select(w => Math.Pow(w, Math.Round(constNode.Value))));
|
---|
| 1037 | } else if (IsBinFactor(a) && IsConstant(b)) {
|
---|
| 1038 | var binFactor = a as BinaryFactorVariableTreeNode;
|
---|
| 1039 | var constNode = b as ConstantTreeNode;
|
---|
| 1040 | return MakeBinFactor(binFactor.Symbol, binFactor.VariableName, binFactor.VariableValue, Math.Pow(binFactor.Weight, Math.Round(constNode.Value)));
|
---|
| 1041 | } else if (IsConstant(a) && IsFactor(b)) {
|
---|
| 1042 | var constNode = a as ConstantTreeNode;
|
---|
| 1043 | var factNode = b as FactorVariableTreeNode;
|
---|
| 1044 | return MakeFactor(factNode.Symbol, factNode.VariableName, factNode.Weights.Select(w => Math.Pow(constNode.Value, Math.Round(w))));
|
---|
| 1045 | } else if (IsConstant(a) && IsBinFactor(b)) {
|
---|
| 1046 | var constNode = a as ConstantTreeNode;
|
---|
| 1047 | var factNode = b as BinaryFactorVariableTreeNode;
|
---|
| 1048 | return MakeBinFactor(factNode.Symbol, factNode.VariableName, factNode.VariableValue, Math.Pow(constNode.Value, Math.Round(factNode.Weight)));
|
---|
| 1049 | } else if (IsFactor(a) && IsFactor(b) && AreSameTypeAndVariable(a, b)) {
|
---|
| 1050 | var node0 = a as FactorVariableTreeNode;
|
---|
| 1051 | var node1 = b as FactorVariableTreeNode;
|
---|
| 1052 | return MakeFactor(node0.Symbol, node0.VariableName, node0.Weights.Zip(node1.Weights, (u, v) => Math.Pow(u, Math.Round(v))));
|
---|
| 1053 | } else if (IsConstant(b)) {
|
---|
| 1054 | var constB = b as ConstantTreeNode;
|
---|
| 1055 | double exponent = Math.Round(constB.Value);
|
---|
| 1056 | if (exponent.IsAlmost(0.0)) {
|
---|
| 1057 | return MakeConstant(1.0);
|
---|
| 1058 | } else if (exponent.IsAlmost(1.0)) {
|
---|
| 1059 | return a;
|
---|
| 1060 | } else if (exponent.IsAlmost(-1.0)) {
|
---|
| 1061 | return MakeFraction(MakeConstant(1.0), a);
|
---|
| 1062 | } else if (exponent < 0) {
|
---|
| 1063 | var powNode = powSymbol.CreateTreeNode();
|
---|
| 1064 | powNode.AddSubtree(a);
|
---|
| 1065 | powNode.AddSubtree(MakeConstant(-1.0 * exponent));
|
---|
| 1066 | return MakeFraction(MakeConstant(1.0), powNode);
|
---|
| 1067 | } else {
|
---|
| 1068 | var powNode = powSymbol.CreateTreeNode();
|
---|
| 1069 | powNode.AddSubtree(a);
|
---|
| 1070 | powNode.AddSubtree(MakeConstant(exponent));
|
---|
| 1071 | return powNode;
|
---|
| 1072 | }
|
---|
| 1073 | } else {
|
---|
| 1074 | var powNode = powSymbol.CreateTreeNode();
|
---|
| 1075 | powNode.AddSubtree(a);
|
---|
| 1076 | powNode.AddSubtree(b);
|
---|
| 1077 | return powNode;
|
---|
| 1078 | }
|
---|
| 1079 | }
|
---|
| 1080 |
|
---|
| 1081 |
|
---|
| 1082 | // MakeFraction, MakeProduct and MakeSum take two already simplified trees and create a new simplified tree
|
---|
[17593] | 1083 | private ISymbolicExpressionTreeNode MakeFraction(ISymbolicExpressionTreeNode a, ISymbolicExpressionTreeNode b) {
|
---|
[14843] | 1084 | if (IsConstant(a) && IsConstant(b)) {
|
---|
| 1085 | // fold constants
|
---|
| 1086 | return MakeConstant(((ConstantTreeNode)a).Value / ((ConstantTreeNode)b).Value);
|
---|
| 1087 | } else if ((IsConstant(a) && !((ConstantTreeNode)a).Value.IsAlmost(1.0))) {
|
---|
| 1088 | return MakeFraction(MakeConstant(1.0), MakeProduct(b, Invert(a)));
|
---|
| 1089 | } else if (IsVariableBase(a) && IsConstant(b)) {
|
---|
| 1090 | // merge constant values into variable weights
|
---|
| 1091 | var constB = ((ConstantTreeNode)b).Value;
|
---|
| 1092 | ((VariableTreeNodeBase)a).Weight /= constB;
|
---|
| 1093 | return a;
|
---|
| 1094 | } else if (IsFactor(a) && IsConstant(b)) {
|
---|
| 1095 | var factNode = a as FactorVariableTreeNode;
|
---|
| 1096 | var constNode = b as ConstantTreeNode;
|
---|
| 1097 | return MakeFactor(factNode.Symbol, factNode.VariableName, factNode.Weights.Select(w => w / constNode.Value));
|
---|
| 1098 | } else if (IsBinFactor(a) && IsConstant(b)) {
|
---|
| 1099 | var factNode = a as BinaryFactorVariableTreeNode;
|
---|
| 1100 | var constNode = b as ConstantTreeNode;
|
---|
| 1101 | return MakeBinFactor(factNode.Symbol, factNode.VariableName, factNode.VariableValue, factNode.Weight / constNode.Value);
|
---|
| 1102 | } else if (IsFactor(a) && IsFactor(b) && AreSameTypeAndVariable(a, b)) {
|
---|
| 1103 | var node0 = a as FactorVariableTreeNode;
|
---|
| 1104 | var node1 = b as FactorVariableTreeNode;
|
---|
| 1105 | return MakeFactor(node0.Symbol, node0.VariableName, node0.Weights.Zip(node1.Weights, (u, v) => u / v));
|
---|
| 1106 | } else if (IsFactor(a) && IsBinFactor(b) && ((IVariableTreeNode)a).VariableName == ((IVariableTreeNode)b).VariableName) {
|
---|
| 1107 | var node0 = a as FactorVariableTreeNode;
|
---|
| 1108 | var node1 = b as BinaryFactorVariableTreeNode;
|
---|
| 1109 | var varValues = node0.Symbol.GetVariableValues(node0.VariableName).ToArray();
|
---|
| 1110 | var wi = Array.IndexOf(varValues, node1.VariableValue);
|
---|
| 1111 | if (wi < 0) throw new ArgumentException();
|
---|
| 1112 | var newWeighs = new double[varValues.Length];
|
---|
| 1113 | node0.Weights.CopyTo(newWeighs, 0);
|
---|
| 1114 | for (int i = 0; i < newWeighs.Length; i++)
|
---|
| 1115 | if (wi == i) newWeighs[i] /= node1.Weight;
|
---|
| 1116 | else newWeighs[i] /= 0.0;
|
---|
| 1117 | return MakeFactor(node0.Symbol, node0.VariableName, newWeighs);
|
---|
| 1118 | } else if (IsFactor(a)) {
|
---|
| 1119 | return MakeFraction(MakeConstant(1.0), MakeProduct(b, Invert(a)));
|
---|
| 1120 | } else if (IsVariableBase(a) && IsVariableBase(b) && AreSameTypeAndVariable(a, b) && !IsBinFactor(b)) {
|
---|
| 1121 | // cancel variables (not allowed for bin factors because of division by zero)
|
---|
| 1122 | var aVar = a as VariableTreeNode;
|
---|
| 1123 | var bVar = b as VariableTreeNode;
|
---|
| 1124 | return MakeConstant(aVar.Weight / bVar.Weight);
|
---|
| 1125 | } else if (IsAddition(a) && IsConstant(b)) {
|
---|
| 1126 | return a.Subtrees
|
---|
| 1127 | .Select(x => GetSimplifiedTree(x))
|
---|
| 1128 | .Select(x => MakeFraction(x, GetSimplifiedTree(b)))
|
---|
| 1129 | .Aggregate((c, d) => MakeSum(c, d));
|
---|
| 1130 | } else if (IsMultiplication(a) && IsConstant(b)) {
|
---|
| 1131 | return MakeProduct(a, Invert(b));
|
---|
| 1132 | } else if (IsDivision(a) && IsConstant(b)) {
|
---|
| 1133 | // (a1 / a2) / c => (a1 / (a2 * c))
|
---|
| 1134 | return MakeFraction(a.GetSubtree(0), MakeProduct(a.GetSubtree(1), b));
|
---|
| 1135 | } else if (IsDivision(a) && IsDivision(b)) {
|
---|
| 1136 | // (a1 / a2) / (b1 / b2) =>
|
---|
| 1137 | return MakeFraction(MakeProduct(a.GetSubtree(0), b.GetSubtree(1)), MakeProduct(a.GetSubtree(1), b.GetSubtree(0)));
|
---|
| 1138 | } else if (IsDivision(a)) {
|
---|
| 1139 | // (a1 / a2) / b => (a1 / (a2 * b))
|
---|
| 1140 | return MakeFraction(a.GetSubtree(0), MakeProduct(a.GetSubtree(1), b));
|
---|
| 1141 | } else if (IsDivision(b)) {
|
---|
| 1142 | // a / (b1 / b2) => (a * b2) / b1
|
---|
| 1143 | return MakeFraction(MakeProduct(a, b.GetSubtree(1)), b.GetSubtree(0));
|
---|
[16356] | 1144 | } else if (IsAnalyticalQuotient(a)) {
|
---|
| 1145 | return MakeAnalyticalQuotient(a.GetSubtree(0), MakeProduct(a.GetSubtree(1), b));
|
---|
[14843] | 1146 | } else {
|
---|
| 1147 | var div = divSymbol.CreateTreeNode();
|
---|
| 1148 | div.AddSubtree(a);
|
---|
| 1149 | div.AddSubtree(b);
|
---|
| 1150 | return div;
|
---|
| 1151 | }
|
---|
| 1152 | }
|
---|
| 1153 |
|
---|
[17593] | 1154 | private ISymbolicExpressionTreeNode MakeSum(ISymbolicExpressionTreeNode a, ISymbolicExpressionTreeNode b) {
|
---|
[14843] | 1155 | if (IsConstant(a) && IsConstant(b)) {
|
---|
| 1156 | // fold constants
|
---|
| 1157 | ((ConstantTreeNode)a).Value += ((ConstantTreeNode)b).Value;
|
---|
| 1158 | return a;
|
---|
| 1159 | } else if (IsConstant(a)) {
|
---|
| 1160 | // c + x => x + c
|
---|
| 1161 | // b is not constant => make sure constant is on the right
|
---|
| 1162 | return MakeSum(b, a);
|
---|
| 1163 | } else if (IsConstant(b) && ((ConstantTreeNode)b).Value.IsAlmost(0.0)) {
|
---|
| 1164 | // x + 0 => x
|
---|
| 1165 | return a;
|
---|
| 1166 | } else if (IsFactor(a) && IsConstant(b)) {
|
---|
| 1167 | var factNode = a as FactorVariableTreeNode;
|
---|
| 1168 | var constNode = b as ConstantTreeNode;
|
---|
| 1169 | return MakeFactor(factNode.Symbol, factNode.VariableName, factNode.Weights.Select((w) => w + constNode.Value));
|
---|
| 1170 | } else if (IsFactor(a) && IsFactor(b) && AreSameTypeAndVariable(a, b)) {
|
---|
| 1171 | var node0 = a as FactorVariableTreeNode;
|
---|
| 1172 | var node1 = b as FactorVariableTreeNode;
|
---|
| 1173 | return MakeFactor(node0.Symbol, node0.VariableName, node0.Weights.Zip(node1.Weights, (u, v) => u + v));
|
---|
| 1174 | } else if (IsBinFactor(a) && IsFactor(b)) {
|
---|
| 1175 | return MakeSum(b, a);
|
---|
| 1176 | } else if (IsFactor(a) && IsBinFactor(b) &&
|
---|
| 1177 | ((IVariableTreeNode)a).VariableName == ((IVariableTreeNode)b).VariableName) {
|
---|
| 1178 | var node0 = a as FactorVariableTreeNode;
|
---|
| 1179 | var node1 = b as BinaryFactorVariableTreeNode;
|
---|
| 1180 | var varValues = node0.Symbol.GetVariableValues(node0.VariableName).ToArray();
|
---|
| 1181 | var wi = Array.IndexOf(varValues, node1.VariableValue);
|
---|
| 1182 | if (wi < 0) throw new ArgumentException();
|
---|
| 1183 | var newWeighs = new double[varValues.Length];
|
---|
| 1184 | node0.Weights.CopyTo(newWeighs, 0);
|
---|
| 1185 | newWeighs[wi] += node1.Weight;
|
---|
| 1186 | return MakeFactor(node0.Symbol, node0.VariableName, newWeighs);
|
---|
| 1187 | } else if (IsAddition(a) && IsAddition(b)) {
|
---|
| 1188 | // merge additions
|
---|
| 1189 | var add = addSymbol.CreateTreeNode();
|
---|
| 1190 | // add all sub trees except for the last
|
---|
| 1191 | for (int i = 0; i < a.Subtrees.Count() - 1; i++) add.AddSubtree(a.GetSubtree(i));
|
---|
| 1192 | for (int i = 0; i < b.Subtrees.Count() - 1; i++) add.AddSubtree(b.GetSubtree(i));
|
---|
| 1193 | if (IsConstant(a.Subtrees.Last()) && IsConstant(b.Subtrees.Last())) {
|
---|
| 1194 | add.AddSubtree(MakeSum(a.Subtrees.Last(), b.Subtrees.Last()));
|
---|
| 1195 | } else if (IsConstant(a.Subtrees.Last())) {
|
---|
| 1196 | add.AddSubtree(b.Subtrees.Last());
|
---|
| 1197 | add.AddSubtree(a.Subtrees.Last());
|
---|
| 1198 | } else {
|
---|
| 1199 | add.AddSubtree(a.Subtrees.Last());
|
---|
| 1200 | add.AddSubtree(b.Subtrees.Last());
|
---|
| 1201 | }
|
---|
| 1202 | MergeVariablesInSum(add);
|
---|
| 1203 | if (add.Subtrees.Count() == 1) {
|
---|
| 1204 | return add.GetSubtree(0);
|
---|
| 1205 | } else {
|
---|
| 1206 | return add;
|
---|
| 1207 | }
|
---|
| 1208 | } else if (IsAddition(b)) {
|
---|
| 1209 | return MakeSum(b, a);
|
---|
| 1210 | } else if (IsAddition(a) && IsConstant(b)) {
|
---|
| 1211 | // a is an addition and b is a constant => append b to a and make sure the constants are merged
|
---|
| 1212 | var add = addSymbol.CreateTreeNode();
|
---|
| 1213 | // add all sub trees except for the last
|
---|
| 1214 | for (int i = 0; i < a.Subtrees.Count() - 1; i++) add.AddSubtree(a.GetSubtree(i));
|
---|
| 1215 | if (IsConstant(a.Subtrees.Last()))
|
---|
| 1216 | add.AddSubtree(MakeSum(a.Subtrees.Last(), b));
|
---|
| 1217 | else {
|
---|
| 1218 | add.AddSubtree(a.Subtrees.Last());
|
---|
| 1219 | add.AddSubtree(b);
|
---|
| 1220 | }
|
---|
| 1221 | return add;
|
---|
| 1222 | } else if (IsAddition(a)) {
|
---|
| 1223 | // a is already an addition => append b
|
---|
| 1224 | var add = addSymbol.CreateTreeNode();
|
---|
| 1225 | add.AddSubtree(b);
|
---|
| 1226 | foreach (var subtree in a.Subtrees) {
|
---|
| 1227 | add.AddSubtree(subtree);
|
---|
| 1228 | }
|
---|
| 1229 | MergeVariablesInSum(add);
|
---|
| 1230 | if (add.Subtrees.Count() == 1) {
|
---|
| 1231 | return add.GetSubtree(0);
|
---|
| 1232 | } else {
|
---|
| 1233 | return add;
|
---|
| 1234 | }
|
---|
| 1235 | } else {
|
---|
| 1236 | var add = addSymbol.CreateTreeNode();
|
---|
| 1237 | add.AddSubtree(a);
|
---|
| 1238 | add.AddSubtree(b);
|
---|
| 1239 | MergeVariablesInSum(add);
|
---|
| 1240 | if (add.Subtrees.Count() == 1) {
|
---|
| 1241 | return add.GetSubtree(0);
|
---|
| 1242 | } else {
|
---|
| 1243 | return add;
|
---|
| 1244 | }
|
---|
| 1245 | }
|
---|
| 1246 | }
|
---|
| 1247 |
|
---|
| 1248 | // makes sure variable symbols in sums are combined
|
---|
[17593] | 1249 | private void MergeVariablesInSum(ISymbolicExpressionTreeNode sum) {
|
---|
[14843] | 1250 | var subtrees = new List<ISymbolicExpressionTreeNode>(sum.Subtrees);
|
---|
| 1251 | while (sum.Subtrees.Any()) sum.RemoveSubtree(0);
|
---|
| 1252 | var groupedVarNodes = from node in subtrees.OfType<IVariableTreeNode>()
|
---|
| 1253 | where node.SubtreeCount == 0
|
---|
| 1254 | group node by GroupId(node) into g
|
---|
| 1255 | select g;
|
---|
| 1256 | var constant = (from node in subtrees.OfType<ConstantTreeNode>()
|
---|
| 1257 | select node.Value).DefaultIfEmpty(0.0).Sum();
|
---|
| 1258 | var unchangedSubtrees = subtrees.Where(t => t.SubtreeCount > 0 || !(t is IVariableTreeNode) && !(t is ConstantTreeNode));
|
---|
| 1259 |
|
---|
| 1260 | foreach (var variableNodeGroup in groupedVarNodes) {
|
---|
| 1261 | var firstNode = variableNodeGroup.First();
|
---|
| 1262 | if (firstNode is VariableTreeNodeBase) {
|
---|
| 1263 | var representative = firstNode as VariableTreeNodeBase;
|
---|
| 1264 | var weightSum = variableNodeGroup.Cast<VariableTreeNodeBase>().Select(t => t.Weight).Sum();
|
---|
| 1265 | representative.Weight = weightSum;
|
---|
| 1266 | sum.AddSubtree(representative);
|
---|
| 1267 | } else if (firstNode is FactorVariableTreeNode) {
|
---|
| 1268 | var representative = firstNode as FactorVariableTreeNode;
|
---|
| 1269 | foreach (var node in variableNodeGroup.Skip(1).Cast<FactorVariableTreeNode>()) {
|
---|
| 1270 | for (int j = 0; j < representative.Weights.Length; j++) {
|
---|
| 1271 | representative.Weights[j] += node.Weights[j];
|
---|
| 1272 | }
|
---|
| 1273 | }
|
---|
| 1274 | sum.AddSubtree(representative);
|
---|
| 1275 | }
|
---|
| 1276 | }
|
---|
| 1277 | foreach (var unchangedSubtree in unchangedSubtrees)
|
---|
| 1278 | sum.AddSubtree(unchangedSubtree);
|
---|
| 1279 | if (!constant.IsAlmost(0.0)) {
|
---|
| 1280 | sum.AddSubtree(MakeConstant(constant));
|
---|
| 1281 | }
|
---|
| 1282 | }
|
---|
| 1283 |
|
---|
| 1284 | // nodes referencing variables can be grouped if they have
|
---|
[17593] | 1285 | private string GroupId(IVariableTreeNode node) {
|
---|
[14843] | 1286 | var binaryFactorNode = node as BinaryFactorVariableTreeNode;
|
---|
| 1287 | var factorNode = node as FactorVariableTreeNode;
|
---|
| 1288 | var variableNode = node as VariableTreeNode;
|
---|
| 1289 | var laggedVarNode = node as LaggedVariableTreeNode;
|
---|
| 1290 | if (variableNode != null) {
|
---|
| 1291 | return "var " + variableNode.VariableName;
|
---|
| 1292 | } else if (binaryFactorNode != null) {
|
---|
| 1293 | return "binfactor " + binaryFactorNode.VariableName + " " + binaryFactorNode.VariableValue;
|
---|
| 1294 | } else if (factorNode != null) {
|
---|
| 1295 | return "factor " + factorNode.VariableName;
|
---|
| 1296 | } else if (laggedVarNode != null) {
|
---|
| 1297 | return "lagged " + laggedVarNode.VariableName + " " + laggedVarNode.Lag;
|
---|
| 1298 | } else {
|
---|
| 1299 | throw new NotSupportedException();
|
---|
| 1300 | }
|
---|
| 1301 | }
|
---|
| 1302 |
|
---|
| 1303 |
|
---|
[17593] | 1304 | private ISymbolicExpressionTreeNode MakeProduct(ISymbolicExpressionTreeNode a, ISymbolicExpressionTreeNode b) {
|
---|
[14843] | 1305 | if (IsConstant(a) && IsConstant(b)) {
|
---|
| 1306 | // fold constants
|
---|
| 1307 | return MakeConstant(((ConstantTreeNode)a).Value * ((ConstantTreeNode)b).Value);
|
---|
| 1308 | } else if (IsConstant(a)) {
|
---|
| 1309 | // a * $ => $ * a
|
---|
| 1310 | return MakeProduct(b, a);
|
---|
| 1311 | } else if (IsFactor(a) && IsFactor(b) && AreSameTypeAndVariable(a, b)) {
|
---|
| 1312 | var node0 = a as FactorVariableTreeNode;
|
---|
| 1313 | var node1 = b as FactorVariableTreeNode;
|
---|
| 1314 | return MakeFactor(node0.Symbol, node0.VariableName, node0.Weights.Zip(node1.Weights, (u, v) => u * v));
|
---|
| 1315 | } else if (IsBinFactor(a) && IsBinFactor(b) && AreSameTypeAndVariable(a, b)) {
|
---|
| 1316 | var node0 = a as BinaryFactorVariableTreeNode;
|
---|
| 1317 | var node1 = b as BinaryFactorVariableTreeNode;
|
---|
| 1318 | return MakeBinFactor(node0.Symbol, node0.VariableName, node0.VariableValue, node0.Weight * node1.Weight);
|
---|
| 1319 | } else if (IsFactor(a) && IsConstant(b)) {
|
---|
| 1320 | var node0 = a as FactorVariableTreeNode;
|
---|
| 1321 | var node1 = b as ConstantTreeNode;
|
---|
| 1322 | return MakeFactor(node0.Symbol, node0.VariableName, node0.Weights.Select(w => w * node1.Value));
|
---|
| 1323 | } else if (IsBinFactor(a) && IsConstant(b)) {
|
---|
| 1324 | var node0 = a as BinaryFactorVariableTreeNode;
|
---|
| 1325 | var node1 = b as ConstantTreeNode;
|
---|
| 1326 | return MakeBinFactor(node0.Symbol, node0.VariableName, node0.VariableValue, node0.Weight * node1.Value);
|
---|
| 1327 | } else if (IsBinFactor(a) && IsFactor(b)) {
|
---|
| 1328 | return MakeProduct(b, a);
|
---|
| 1329 | } else if (IsFactor(a) && IsBinFactor(b) &&
|
---|
| 1330 | ((IVariableTreeNode)a).VariableName == ((IVariableTreeNode)b).VariableName) {
|
---|
| 1331 | var node0 = a as FactorVariableTreeNode;
|
---|
| 1332 | var node1 = b as BinaryFactorVariableTreeNode;
|
---|
| 1333 | var varValues = node0.Symbol.GetVariableValues(node0.VariableName).ToArray();
|
---|
| 1334 | var wi = Array.IndexOf(varValues, node1.VariableValue);
|
---|
| 1335 | if (wi < 0) throw new ArgumentException();
|
---|
| 1336 | return MakeBinFactor(node1.Symbol, node1.VariableName, node1.VariableValue, node1.Weight * node0.Weights[wi]);
|
---|
| 1337 | } else if (IsConstant(b) && ((ConstantTreeNode)b).Value.IsAlmost(1.0)) {
|
---|
| 1338 | // $ * 1.0 => $
|
---|
| 1339 | return a;
|
---|
[16206] | 1340 | } else if (IsConstant(b) && ((ConstantTreeNode)b).Value.IsAlmost(0.0)) {
|
---|
| 1341 | return MakeConstant(0);
|
---|
[14843] | 1342 | } else if (IsConstant(b) && IsVariableBase(a)) {
|
---|
| 1343 | // multiply constants into variables weights
|
---|
| 1344 | ((VariableTreeNodeBase)a).Weight *= ((ConstantTreeNode)b).Value;
|
---|
| 1345 | return a;
|
---|
| 1346 | } else if (IsConstant(b) && IsAddition(a) ||
|
---|
| 1347 | IsFactor(b) && IsAddition(a) ||
|
---|
| 1348 | IsBinFactor(b) && IsAddition(a)) {
|
---|
| 1349 | // multiply constants into additions
|
---|
| 1350 | return a.Subtrees.Select(x => MakeProduct(GetSimplifiedTree(x), GetSimplifiedTree(b))).Aggregate((c, d) => MakeSum(c, d));
|
---|
| 1351 | } else if (IsDivision(a) && IsDivision(b)) {
|
---|
| 1352 | // (a1 / a2) * (b1 / b2) => (a1 * b1) / (a2 * b2)
|
---|
| 1353 | return MakeFraction(MakeProduct(a.GetSubtree(0), b.GetSubtree(0)), MakeProduct(a.GetSubtree(1), b.GetSubtree(1)));
|
---|
| 1354 | } else if (IsDivision(a)) {
|
---|
| 1355 | // (a1 / a2) * b => (a1 * b) / a2
|
---|
| 1356 | return MakeFraction(MakeProduct(a.GetSubtree(0), b), a.GetSubtree(1));
|
---|
| 1357 | } else if (IsDivision(b)) {
|
---|
| 1358 | // a * (b1 / b2) => (b1 * a) / b2
|
---|
| 1359 | return MakeFraction(MakeProduct(b.GetSubtree(0), a), b.GetSubtree(1));
|
---|
| 1360 | } else if (IsMultiplication(a) && IsMultiplication(b)) {
|
---|
| 1361 | // merge multiplications (make sure constants are merged)
|
---|
| 1362 | var mul = mulSymbol.CreateTreeNode();
|
---|
| 1363 | for (int i = 0; i < a.Subtrees.Count(); i++) mul.AddSubtree(a.GetSubtree(i));
|
---|
| 1364 | for (int i = 0; i < b.Subtrees.Count(); i++) mul.AddSubtree(b.GetSubtree(i));
|
---|
| 1365 | MergeVariablesAndConstantsInProduct(mul);
|
---|
| 1366 | return mul;
|
---|
| 1367 | } else if (IsMultiplication(b)) {
|
---|
| 1368 | return MakeProduct(b, a);
|
---|
| 1369 | } else if (IsMultiplication(a)) {
|
---|
| 1370 | // a is already an multiplication => append b
|
---|
| 1371 | a.AddSubtree(GetSimplifiedTree(b));
|
---|
| 1372 | MergeVariablesAndConstantsInProduct(a);
|
---|
| 1373 | return a;
|
---|
[16356] | 1374 | } else if (IsAbsolute(a) && IsAbsolute(b)) {
|
---|
| 1375 | return MakeAbs(MakeProduct(a.GetSubtree(0), b.GetSubtree(0)));
|
---|
| 1376 | } else if (IsAbsolute(a) && IsConstant(b)) {
|
---|
| 1377 | var constNode = b as ConstantTreeNode;
|
---|
| 1378 | var posF = Math.Abs(constNode.Value);
|
---|
| 1379 | if (constNode.Value > 0) {
|
---|
| 1380 | return MakeAbs(MakeProduct(a.GetSubtree(0), MakeConstant(posF)));
|
---|
| 1381 | } else {
|
---|
| 1382 | var mul = mulSymbol.CreateTreeNode();
|
---|
| 1383 | mul.AddSubtree(MakeAbs(MakeProduct(a.GetSubtree(0), MakeConstant(posF))));
|
---|
| 1384 | mul.AddSubtree(MakeConstant(-1.0));
|
---|
| 1385 | return mul;
|
---|
| 1386 | }
|
---|
| 1387 | } else if (IsAnalyticalQuotient(a)) {
|
---|
| 1388 | return MakeAnalyticalQuotient(MakeProduct(a.GetSubtree(0), b), a.GetSubtree(1));
|
---|
[14843] | 1389 | } else {
|
---|
| 1390 | var mul = mulSymbol.CreateTreeNode();
|
---|
| 1391 | mul.AddSubtree(a);
|
---|
| 1392 | mul.AddSubtree(b);
|
---|
| 1393 | MergeVariablesAndConstantsInProduct(mul);
|
---|
| 1394 | return mul;
|
---|
| 1395 | }
|
---|
| 1396 | }
|
---|
| 1397 |
|
---|
[17626] | 1398 | delegate ISymbolicExpressionTreeNode ScalarSimplifier(ISymbolicExpressionTreeNode scalar);
|
---|
| 1399 | delegate ISymbolicExpressionTreeNode VectorSimplifier(ISymbolicExpressionTreeNode vectorPart, ISymbolicExpressionTreeNode scalarPart);
|
---|
[17596] | 1400 |
|
---|
[17626] | 1401 | private ISymbolicExpressionTreeNode MakeAggregation(ISymbolicExpressionTreeNode node, Symbol aggregationSymbol,
|
---|
| 1402 | ScalarSimplifier simplifyScalar,
|
---|
| 1403 | VectorSimplifier simplifyAdditiveTerms,
|
---|
| 1404 | VectorSimplifier simplifyMultiplicativeFactors) {
|
---|
| 1405 |
|
---|
| 1406 | ISymbolicExpressionTreeNode MakeAggregationNode(ISymbolicExpressionTreeNode remainingNode) {
|
---|
| 1407 | var aggregationNode = aggregationSymbol.CreateTreeNode();
|
---|
| 1408 | aggregationNode.AddSubtree(GetSimplifiedTree(remainingNode));
|
---|
| 1409 | return aggregationNode;
|
---|
| 1410 | }
|
---|
| 1411 |
|
---|
| 1412 | ISymbolicExpressionTreeNode SimplifyArithmeticOperation(IEnumerable<ISymbolicExpressionTreeNode> terms,
|
---|
| 1413 | Func<ISymbolicExpressionTreeNode, ISymbolicExpressionTreeNode, ISymbolicExpressionTreeNode> aggregation,
|
---|
| 1414 | VectorSimplifier simplifyTerms) {
|
---|
[17593] | 1415 | var scalarTerms = terms.Where(IsScalarNode).ToList();
|
---|
| 1416 | var remainingTerms = terms.Except(scalarTerms).ToList();
|
---|
| 1417 |
|
---|
[17626] | 1418 | var scalarNode = scalarTerms.Any() ? scalarTerms.Aggregate(aggregation) : null;
|
---|
| 1419 | var remainingNode = remainingTerms.Aggregate(aggregation); // at least one term is remaining, otherwise "node" would have been scalar and earlier rule had applied
|
---|
[17593] | 1420 |
|
---|
[17626] | 1421 | if (scalarTerms.Any()) {
|
---|
| 1422 | return simplifyTerms(remainingNode, scalarNode);
|
---|
| 1423 | } else {
|
---|
| 1424 | return MakeAggregationNode(remainingNode);
|
---|
| 1425 | }
|
---|
| 1426 | }
|
---|
[17593] | 1427 |
|
---|
[17626] | 1428 | if (IsScalarNode(node)) {
|
---|
| 1429 | return simplifyScalar(GetSimplifiedTree(node));
|
---|
| 1430 | } else if (IsAddition(node) || IsSubtraction(node)) {
|
---|
| 1431 | var terms = node.Subtrees;
|
---|
| 1432 | if (IsSubtraction(node)) terms = InvertNodes(terms, Negate);
|
---|
| 1433 | return SimplifyArithmeticOperation(terms, MakeSum, simplifyAdditiveTerms);
|
---|
[17596] | 1434 | } else if (IsMultiplication(node) || IsDivision(node)) {
|
---|
[17593] | 1435 | var factors = node.Subtrees;
|
---|
[17597] | 1436 | if (IsDivision(node)) factors = InvertNodes(factors, Invert);
|
---|
[17626] | 1437 | return SimplifyArithmeticOperation(factors, MakeProduct, simplifyMultiplicativeFactors);
|
---|
| 1438 | } else if (node is VariableTreeNodeBase variableNode && !variableNode.Weight.IsAlmost(1.0)) { // weight is like multiplication
|
---|
[17597] | 1439 | var weight = variableNode.Weight;
|
---|
| 1440 | variableNode.Weight = 1.0;
|
---|
[17626] | 1441 | var factors = new[] { variableNode, MakeConstant(weight) };
|
---|
| 1442 | return SimplifyArithmeticOperation(factors, MakeProduct, simplifyMultiplicativeFactors);
|
---|
[17593] | 1443 | } else {
|
---|
[17626] | 1444 | return MakeAggregationNode(node);
|
---|
[17593] | 1445 | }
|
---|
| 1446 | }
|
---|
| 1447 |
|
---|
[17626] | 1448 | private ISymbolicExpressionTreeNode MakeSumAggregation(ISymbolicExpressionTreeNode node) {
|
---|
| 1449 | return MakeAggregation(node, sumSymbol,
|
---|
| 1450 | simplifyScalar: n => n,
|
---|
| 1451 | simplifyAdditiveTerms: (vectorNode, scalarNode) => {
|
---|
| 1452 | var lengthNode = MakeLengthAggregation(vectorNode);
|
---|
| 1453 | var scalarMulNode = MakeProduct(scalarNode, lengthNode);
|
---|
| 1454 | var sumNode = MakeSumAggregation(vectorNode);
|
---|
| 1455 | return MakeSum(scalarMulNode, sumNode);
|
---|
| 1456 | },
|
---|
| 1457 | simplifyMultiplicativeFactors: (vectorNode, scalarNode) => {
|
---|
| 1458 | var sumNode = MakeSumAggregation(vectorNode);
|
---|
| 1459 | return MakeProduct(scalarNode, sumNode);
|
---|
| 1460 | });
|
---|
| 1461 | }
|
---|
| 1462 |
|
---|
[17597] | 1463 | private ISymbolicExpressionTreeNode MakeMeanAggregation(ISymbolicExpressionTreeNode node) {
|
---|
[17626] | 1464 | return MakeAggregation(node, meanSymbol,
|
---|
| 1465 | simplifyScalar: n => n,
|
---|
| 1466 | simplifyAdditiveTerms: (vectorNode, scalarNode) => {
|
---|
[17597] | 1467 | var meanNode = MakeMeanAggregation(vectorNode);
|
---|
[17593] | 1468 | return MakeSum(scalarNode, meanNode);
|
---|
[17626] | 1469 | },
|
---|
| 1470 | simplifyMultiplicativeFactors: (vectorNode, scalarNode) => {
|
---|
[17597] | 1471 | var meanNode = MakeMeanAggregation(vectorNode);
|
---|
[17593] | 1472 | return MakeProduct(scalarNode, meanNode);
|
---|
[17626] | 1473 | });
|
---|
[17593] | 1474 | }
|
---|
| 1475 |
|
---|
[17597] | 1476 | private ISymbolicExpressionTreeNode MakeLengthAggregation(ISymbolicExpressionTreeNode node) {
|
---|
[17626] | 1477 | return MakeAggregation(node, lengthSymbol,
|
---|
| 1478 | simplifyScalar: _ => MakeConstant(1.0),
|
---|
| 1479 | simplifyAdditiveTerms: (vectorNode, _) => {
|
---|
| 1480 | return MakeLengthAggregation(vectorNode);
|
---|
| 1481 | },
|
---|
| 1482 | simplifyMultiplicativeFactors: (vectorNode, _) => {
|
---|
| 1483 | return MakeLengthAggregation(vectorNode);
|
---|
| 1484 | });
|
---|
[17597] | 1485 | }
|
---|
| 1486 |
|
---|
[17602] | 1487 | private ISymbolicExpressionTreeNode MakeStandardDeviationAggregation(ISymbolicExpressionTreeNode node) {
|
---|
[17626] | 1488 | return MakeAggregation(node, standardDeviationSymbol,
|
---|
| 1489 | simplifyScalar: _ => MakeConstant(0.0),
|
---|
| 1490 | simplifyAdditiveTerms: (vectorNode, _) => {
|
---|
| 1491 | return MakeStandardDeviationAggregation(vectorNode);
|
---|
| 1492 | },
|
---|
| 1493 | simplifyMultiplicativeFactors: (vectorNode, scalarNode) => {
|
---|
[17602] | 1494 | var stdevNode = MakeStandardDeviationAggregation(vectorNode);
|
---|
| 1495 | return MakeProduct(scalarNode, stdevNode);
|
---|
[17626] | 1496 | });
|
---|
[17602] | 1497 | }
|
---|
| 1498 |
|
---|
| 1499 | private ISymbolicExpressionTreeNode MakeVarianceAggregation(ISymbolicExpressionTreeNode node) {
|
---|
[17626] | 1500 | return MakeAggregation(node, varianceSymbol,
|
---|
| 1501 | simplifyScalar: _ => MakeConstant(0.0),
|
---|
| 1502 | simplifyAdditiveTerms: (vectorNode, _) => {
|
---|
| 1503 | return MakeVarianceAggregation(vectorNode);
|
---|
| 1504 | },
|
---|
| 1505 | simplifyMultiplicativeFactors: (vectorNode, scalarNode) => {
|
---|
[17602] | 1506 | var varNode = MakeVarianceAggregation(vectorNode);
|
---|
| 1507 | return MakeProduct(MakeSquare(scalarNode), varNode);
|
---|
[17626] | 1508 | });
|
---|
[17602] | 1509 | }
|
---|
[14843] | 1510 | #endregion
|
---|
| 1511 |
|
---|
| 1512 | #region helper functions
|
---|
| 1513 |
|
---|
[17593] | 1514 | private bool ContainsVariableCondition(ISymbolicExpressionTreeNode node) {
|
---|
[14843] | 1515 | if (node.Symbol is VariableCondition) return true;
|
---|
| 1516 | foreach (var subtree in node.Subtrees)
|
---|
| 1517 | if (ContainsVariableCondition(subtree)) return true;
|
---|
| 1518 | return false;
|
---|
| 1519 | }
|
---|
| 1520 |
|
---|
[17593] | 1521 | private ISymbolicExpressionTreeNode AddLagToDynamicNodes(ISymbolicExpressionTreeNode node, int lag) {
|
---|
[14843] | 1522 | var laggedTreeNode = node as ILaggedTreeNode;
|
---|
| 1523 | var variableNode = node as VariableTreeNode;
|
---|
| 1524 | var variableConditionNode = node as VariableConditionTreeNode;
|
---|
| 1525 | if (laggedTreeNode != null)
|
---|
| 1526 | laggedTreeNode.Lag += lag;
|
---|
| 1527 | else if (variableNode != null) {
|
---|
| 1528 | var laggedVariableNode = (LaggedVariableTreeNode)laggedVariableSymbol.CreateTreeNode();
|
---|
| 1529 | laggedVariableNode.Lag = lag;
|
---|
| 1530 | laggedVariableNode.VariableName = variableNode.VariableName;
|
---|
| 1531 | return laggedVariableNode;
|
---|
| 1532 | } else if (variableConditionNode != null) {
|
---|
| 1533 | throw new NotSupportedException("Removal of time lags around variable condition symbols is not allowed.");
|
---|
| 1534 | }
|
---|
| 1535 | var subtrees = new List<ISymbolicExpressionTreeNode>(node.Subtrees);
|
---|
| 1536 | while (node.SubtreeCount > 0) node.RemoveSubtree(0);
|
---|
| 1537 | foreach (var subtree in subtrees) {
|
---|
| 1538 | node.AddSubtree(AddLagToDynamicNodes(subtree, lag));
|
---|
| 1539 | }
|
---|
| 1540 | return node;
|
---|
| 1541 | }
|
---|
| 1542 |
|
---|
[17593] | 1543 | private bool AreSameTypeAndVariable(ISymbolicExpressionTreeNode a, ISymbolicExpressionTreeNode b) {
|
---|
[14843] | 1544 | return GroupId((IVariableTreeNode)a) == GroupId((IVariableTreeNode)b);
|
---|
| 1545 | }
|
---|
| 1546 |
|
---|
| 1547 | // helper to combine the constant factors in products and to combine variables (powers of 2, 3...)
|
---|
[17593] | 1548 | private void MergeVariablesAndConstantsInProduct(ISymbolicExpressionTreeNode prod) {
|
---|
[14843] | 1549 | var subtrees = new List<ISymbolicExpressionTreeNode>(prod.Subtrees);
|
---|
| 1550 | while (prod.Subtrees.Any()) prod.RemoveSubtree(0);
|
---|
| 1551 | var groupedVarNodes = from node in subtrees.OfType<IVariableTreeNode>()
|
---|
| 1552 | where node.SubtreeCount == 0
|
---|
| 1553 | group node by GroupId(node) into g
|
---|
| 1554 | orderby g.Count()
|
---|
| 1555 | select g;
|
---|
| 1556 | var constantProduct = (from node in subtrees.OfType<VariableTreeNodeBase>()
|
---|
| 1557 | select node.Weight)
|
---|
| 1558 | .Concat(from node in subtrees.OfType<ConstantTreeNode>()
|
---|
| 1559 | select node.Value)
|
---|
| 1560 | .DefaultIfEmpty(1.0)
|
---|
| 1561 | .Aggregate((c1, c2) => c1 * c2);
|
---|
| 1562 |
|
---|
| 1563 | var unchangedSubtrees = from tree in subtrees
|
---|
| 1564 | where tree.SubtreeCount > 0 || !(tree is IVariableTreeNode) && !(tree is ConstantTreeNode)
|
---|
| 1565 | select tree;
|
---|
| 1566 |
|
---|
| 1567 | foreach (var variableNodeGroup in groupedVarNodes) {
|
---|
| 1568 | var firstNode = variableNodeGroup.First();
|
---|
| 1569 | if (firstNode is VariableTreeNodeBase) {
|
---|
| 1570 | var representative = (VariableTreeNodeBase)firstNode;
|
---|
| 1571 | representative.Weight = 1.0;
|
---|
| 1572 | if (variableNodeGroup.Count() > 1) {
|
---|
| 1573 | var poly = mulSymbol.CreateTreeNode();
|
---|
| 1574 | for (int p = 0; p < variableNodeGroup.Count(); p++) {
|
---|
| 1575 | poly.AddSubtree((ISymbolicExpressionTreeNode)representative.Clone());
|
---|
| 1576 | }
|
---|
| 1577 | prod.AddSubtree(poly);
|
---|
| 1578 | } else {
|
---|
| 1579 | prod.AddSubtree(representative);
|
---|
| 1580 | }
|
---|
| 1581 | } else if (firstNode is FactorVariableTreeNode) {
|
---|
| 1582 | var representative = (FactorVariableTreeNode)firstNode;
|
---|
| 1583 | foreach (var node in variableNodeGroup.Skip(1).Cast<FactorVariableTreeNode>()) {
|
---|
| 1584 | for (int j = 0; j < representative.Weights.Length; j++) {
|
---|
| 1585 | representative.Weights[j] *= node.Weights[j];
|
---|
| 1586 | }
|
---|
| 1587 | }
|
---|
| 1588 | for (int j = 0; j < representative.Weights.Length; j++) {
|
---|
| 1589 | representative.Weights[j] *= constantProduct;
|
---|
| 1590 | }
|
---|
| 1591 | constantProduct = 1.0;
|
---|
| 1592 | // if the product already contains a factor it is not necessary to multiply a constant below
|
---|
| 1593 | prod.AddSubtree(representative);
|
---|
| 1594 | }
|
---|
| 1595 | }
|
---|
| 1596 |
|
---|
| 1597 | foreach (var unchangedSubtree in unchangedSubtrees)
|
---|
| 1598 | prod.AddSubtree(unchangedSubtree);
|
---|
| 1599 |
|
---|
| 1600 | if (!constantProduct.IsAlmost(1.0)) {
|
---|
| 1601 | prod.AddSubtree(MakeConstant(constantProduct));
|
---|
| 1602 | }
|
---|
| 1603 | }
|
---|
| 1604 |
|
---|
| 1605 |
|
---|
| 1606 | /// <summary>
|
---|
| 1607 | /// x => x * -1
|
---|
| 1608 | /// Is only used in cases where it is not necessary to create new tree nodes. Manipulates x directly.
|
---|
| 1609 | /// </summary>
|
---|
| 1610 | /// <param name="x"></param>
|
---|
| 1611 | /// <returns>-x</returns>
|
---|
[17593] | 1612 | private ISymbolicExpressionTreeNode Negate(ISymbolicExpressionTreeNode x) {
|
---|
[14843] | 1613 | if (IsConstant(x)) {
|
---|
| 1614 | ((ConstantTreeNode)x).Value *= -1;
|
---|
| 1615 | } else if (IsVariableBase(x)) {
|
---|
| 1616 | var variableTree = (VariableTreeNodeBase)x;
|
---|
| 1617 | variableTree.Weight *= -1.0;
|
---|
| 1618 | } else if (IsFactor(x)) {
|
---|
| 1619 | var factorNode = (FactorVariableTreeNode)x;
|
---|
| 1620 | for (int i = 0; i < factorNode.Weights.Length; i++) factorNode.Weights[i] *= -1;
|
---|
| 1621 | } else if (IsBinFactor(x)) {
|
---|
| 1622 | var factorNode = (BinaryFactorVariableTreeNode)x;
|
---|
| 1623 | factorNode.Weight *= -1;
|
---|
| 1624 | } else if (IsAddition(x)) {
|
---|
| 1625 | // (x0 + x1 + .. + xn) * -1 => (-x0 + -x1 + .. + -xn)
|
---|
| 1626 | var subtrees = new List<ISymbolicExpressionTreeNode>(x.Subtrees);
|
---|
| 1627 | while (x.Subtrees.Any()) x.RemoveSubtree(0);
|
---|
| 1628 | foreach (var subtree in subtrees) {
|
---|
| 1629 | x.AddSubtree(Negate(subtree));
|
---|
| 1630 | }
|
---|
| 1631 | } else if (IsMultiplication(x) || IsDivision(x)) {
|
---|
| 1632 | // x0 * x1 * .. * xn * -1 => x0 * x1 * .. * -xn
|
---|
| 1633 | var lastSubTree = x.Subtrees.Last();
|
---|
| 1634 | x.RemoveSubtree(x.SubtreeCount - 1);
|
---|
| 1635 | x.AddSubtree(Negate(lastSubTree)); // last is maybe a constant, prefer to negate the constant
|
---|
| 1636 | } else {
|
---|
| 1637 | // any other function
|
---|
| 1638 | return MakeProduct(x, MakeConstant(-1));
|
---|
| 1639 | }
|
---|
| 1640 | return x;
|
---|
| 1641 | }
|
---|
| 1642 |
|
---|
| 1643 | /// <summary>
|
---|
| 1644 | /// x => 1/x
|
---|
| 1645 | /// Must create new tree nodes
|
---|
| 1646 | /// </summary>
|
---|
| 1647 | /// <param name="x"></param>
|
---|
| 1648 | /// <returns></returns>
|
---|
[17593] | 1649 | private ISymbolicExpressionTreeNode Invert(ISymbolicExpressionTreeNode x) {
|
---|
[14843] | 1650 | if (IsConstant(x)) {
|
---|
| 1651 | return MakeConstant(1.0 / ((ConstantTreeNode)x).Value);
|
---|
| 1652 | } else if (IsFactor(x)) {
|
---|
| 1653 | var factorNode = (FactorVariableTreeNode)x;
|
---|
| 1654 | return MakeFactor(factorNode.Symbol, factorNode.VariableName, factorNode.Weights.Select(w => 1.0 / w));
|
---|
| 1655 | } else if (IsDivision(x)) {
|
---|
| 1656 | return MakeFraction(x.GetSubtree(1), x.GetSubtree(0));
|
---|
| 1657 | } else {
|
---|
| 1658 | // any other function
|
---|
| 1659 | return MakeFraction(MakeConstant(1), x);
|
---|
| 1660 | }
|
---|
| 1661 | }
|
---|
| 1662 |
|
---|
[17597] | 1663 | private static ISymbolicExpressionTreeNode MakeConstant(double value) {
|
---|
[14843] | 1664 | ConstantTreeNode constantTreeNode = (ConstantTreeNode)(constSymbol.CreateTreeNode());
|
---|
| 1665 | constantTreeNode.Value = value;
|
---|
| 1666 | return constantTreeNode;
|
---|
| 1667 | }
|
---|
| 1668 |
|
---|
[17597] | 1669 | private static ISymbolicExpressionTreeNode MakeFactor(FactorVariable sy, string variableName, IEnumerable<double> weights) {
|
---|
[14843] | 1670 | var tree = (FactorVariableTreeNode)sy.CreateTreeNode();
|
---|
| 1671 | tree.VariableName = variableName;
|
---|
| 1672 | tree.Weights = weights.ToArray();
|
---|
| 1673 | return tree;
|
---|
| 1674 | }
|
---|
[17597] | 1675 | private static ISymbolicExpressionTreeNode MakeBinFactor(BinaryFactorVariable sy, string variableName, string variableValue, double weight) {
|
---|
[14843] | 1676 | var tree = (BinaryFactorVariableTreeNode)sy.CreateTreeNode();
|
---|
| 1677 | tree.VariableName = variableName;
|
---|
| 1678 | tree.VariableValue = variableValue;
|
---|
| 1679 | tree.Weight = weight;
|
---|
| 1680 | return tree;
|
---|
| 1681 | }
|
---|
[17597] | 1682 | private static IEnumerable<ISymbolicExpressionTreeNode> InvertNodes(IEnumerable<ISymbolicExpressionTreeNode> nodes, Func<ISymbolicExpressionTreeNode, ISymbolicExpressionTreeNode> invertFunc) {
|
---|
| 1683 | if (nodes.Count() == 1)
|
---|
| 1684 | return nodes.Select(invertFunc);
|
---|
| 1685 | var first = nodes.First().ToEnumerable();
|
---|
| 1686 | var remaining = nodes.Skip(1).Select(invertFunc);
|
---|
| 1687 | return first.Concat(remaining);
|
---|
| 1688 | }
|
---|
[14843] | 1689 |
|
---|
| 1690 | #endregion
|
---|
| 1691 | }
|
---|
| 1692 | }
|
---|