[14843] | 1 | #region License Information
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| 2 |
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| 3 | /* HeuristicLab
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[17181] | 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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| 30 | namespace HeuristicLab.Problems.DataAnalysis.Symbolic {
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| 31 | /// <summary>
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| 32 | /// Simplifier for symbolic expressions
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| 33 | /// </summary>
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| 34 | public class TreeSimplifier {
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[15145] | 35 | private static readonly Addition addSymbol = new Addition();
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| 36 | private static readonly Multiplication mulSymbol = new Multiplication();
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| 37 | private static readonly Division divSymbol = new Division();
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| 38 | private static readonly Constant constSymbol = new Constant();
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[17072] | 39 | private static readonly Absolute absSymbol = new Absolute();
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[15145] | 40 | private static readonly Logarithm logSymbol = new Logarithm();
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| 41 | private static readonly Exponential expSymbol = new Exponential();
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| 42 | private static readonly Root rootSymbol = new Root();
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| 43 | private static readonly Square sqrSymbol = new Square();
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| 44 | private static readonly SquareRoot sqrtSymbol = new SquareRoot();
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[17072] | 45 | private static readonly AnalyticQuotient aqSymbol = new AnalyticQuotient();
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| 46 | private static readonly Cube cubeSymbol = new Cube();
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| 47 | private static readonly CubeRoot cubeRootSymbol = new CubeRoot();
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[15145] | 48 | private static readonly Power powSymbol = new Power();
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| 49 | private static readonly Sine sineSymbol = new Sine();
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| 50 | private static readonly Cosine cosineSymbol = new Cosine();
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| 51 | private static readonly Tangent tanSymbol = new Tangent();
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| 52 | private static readonly IfThenElse ifThenElseSymbol = new IfThenElse();
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| 53 | private static readonly And andSymbol = new And();
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| 54 | private static readonly Or orSymbol = new Or();
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| 55 | private static readonly Not notSymbol = new Not();
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| 56 | private static readonly GreaterThan gtSymbol = new GreaterThan();
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| 57 | private static readonly LessThan ltSymbol = new LessThan();
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| 58 | private static readonly Integral integralSymbol = new Integral();
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| 59 | private static readonly LaggedVariable laggedVariableSymbol = new LaggedVariable();
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| 60 | private static readonly TimeLag timeLagSymbol = new TimeLag();
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[14843] | 61 |
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[15145] | 62 | [Obsolete("Use static method TreeSimplifier.Simplify instead")]
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| 63 | public TreeSimplifier() { }
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| 64 |
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| 65 | public static ISymbolicExpressionTree Simplify(ISymbolicExpressionTree originalTree) {
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[14843] | 66 | var clone = (ISymbolicExpressionTreeNode)originalTree.Root.Clone();
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| 67 | // macro expand (initially no argument trees)
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| 68 | var macroExpandedTree = MacroExpand(clone, clone.GetSubtree(0), new List<ISymbolicExpressionTreeNode>());
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| 69 | ISymbolicExpressionTreeNode rootNode = (new ProgramRootSymbol()).CreateTreeNode();
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| 70 | rootNode.AddSubtree(GetSimplifiedTree(macroExpandedTree));
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| 71 |
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| 72 | #if DEBUG
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| 73 | // check that each node is only referenced once
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| 74 | var nodes = rootNode.IterateNodesPrefix().ToArray();
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[15145] | 75 | foreach (var n in nodes) if (nodes.Count(ni => ni == n) > 1) throw new InvalidOperationException();
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[14843] | 76 | #endif
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| 77 | return new SymbolicExpressionTree(rootNode);
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| 78 | }
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| 79 |
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| 80 | // the argumentTrees list contains already expanded trees used as arguments for invocations
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[15145] | 81 | private static ISymbolicExpressionTreeNode MacroExpand(ISymbolicExpressionTreeNode root, ISymbolicExpressionTreeNode node,
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[14843] | 82 | IList<ISymbolicExpressionTreeNode> argumentTrees) {
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| 83 | List<ISymbolicExpressionTreeNode> subtrees = new List<ISymbolicExpressionTreeNode>(node.Subtrees);
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| 84 | while (node.SubtreeCount > 0) node.RemoveSubtree(0);
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| 85 | if (node.Symbol is InvokeFunction) {
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| 86 | var invokeSym = node.Symbol as InvokeFunction;
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| 87 | var defunNode = FindFunctionDefinition(root, invokeSym.FunctionName);
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| 88 | var macroExpandedArguments = new List<ISymbolicExpressionTreeNode>();
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| 89 | foreach (var subtree in subtrees) {
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| 90 | macroExpandedArguments.Add(MacroExpand(root, subtree, argumentTrees));
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| 91 | }
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| 92 | return MacroExpand(root, defunNode, macroExpandedArguments);
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| 93 | } else if (node.Symbol is Argument) {
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| 94 | var argSym = node.Symbol as Argument;
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| 95 | // return the correct argument sub-tree (already macro-expanded)
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| 96 | return (SymbolicExpressionTreeNode)argumentTrees[argSym.ArgumentIndex].Clone();
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| 97 | } else {
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| 98 | // recursive application
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| 99 | foreach (var subtree in subtrees) {
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| 100 | node.AddSubtree(MacroExpand(root, subtree, argumentTrees));
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| 101 | }
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| 102 | return node;
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| 103 | }
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| 104 | }
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| 105 |
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[15145] | 106 | private static ISymbolicExpressionTreeNode FindFunctionDefinition(ISymbolicExpressionTreeNode root, string functionName) {
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[14843] | 107 | foreach (var subtree in root.Subtrees.OfType<DefunTreeNode>()) {
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| 108 | if (subtree.FunctionName == functionName) return subtree.GetSubtree(0);
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| 109 | }
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| 110 |
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| 111 | throw new ArgumentException("Definition of function " + functionName + " not found.");
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| 112 | }
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| 113 |
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| 114 | #region symbol predicates
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| 115 |
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| 116 | // arithmetic
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[15145] | 117 | private static bool IsDivision(ISymbolicExpressionTreeNode node) {
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[14843] | 118 | return node.Symbol is Division;
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| 119 | }
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| 120 |
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[15145] | 121 | private static bool IsMultiplication(ISymbolicExpressionTreeNode node) {
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[14843] | 122 | return node.Symbol is Multiplication;
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| 123 | }
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| 124 |
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[15145] | 125 | private static bool IsSubtraction(ISymbolicExpressionTreeNode node) {
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[14843] | 126 | return node.Symbol is Subtraction;
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| 127 | }
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| 128 |
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[15145] | 129 | private static bool IsAddition(ISymbolicExpressionTreeNode node) {
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[14843] | 130 | return node.Symbol is Addition;
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| 131 | }
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| 132 |
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[15145] | 133 | private static bool IsAverage(ISymbolicExpressionTreeNode node) {
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[14843] | 134 | return node.Symbol is Average;
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| 135 | }
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| 136 |
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[17072] | 137 | private static bool IsAbsolute(ISymbolicExpressionTreeNode node) {
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| 138 | return node.Symbol is Absolute;
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| 139 | }
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| 140 |
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[14843] | 141 | // exponential
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[15145] | 142 | private static bool IsLog(ISymbolicExpressionTreeNode node) {
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[14843] | 143 | return node.Symbol is Logarithm;
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| 144 | }
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| 145 |
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[15145] | 146 | private static bool IsExp(ISymbolicExpressionTreeNode node) {
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[14843] | 147 | return node.Symbol is Exponential;
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| 148 | }
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| 149 |
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[15145] | 150 | private static bool IsRoot(ISymbolicExpressionTreeNode node) {
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[14843] | 151 | return node.Symbol is Root;
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| 152 | }
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| 153 |
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[15145] | 154 | private static bool IsSquare(ISymbolicExpressionTreeNode node) {
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[14843] | 155 | return node.Symbol is Square;
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| 156 | }
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| 157 |
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[15145] | 158 | private static bool IsSquareRoot(ISymbolicExpressionTreeNode node) {
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[14843] | 159 | return node.Symbol is SquareRoot;
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| 160 | }
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| 161 |
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[17072] | 162 | private static bool IsCube(ISymbolicExpressionTreeNode node) {
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| 163 | return node.Symbol is Cube;
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| 164 | }
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| 165 |
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| 166 | private static bool IsCubeRoot(ISymbolicExpressionTreeNode node) {
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| 167 | return node.Symbol is CubeRoot;
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| 168 | }
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| 169 |
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[15145] | 170 | private static bool IsPower(ISymbolicExpressionTreeNode node) {
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[14843] | 171 | return node.Symbol is Power;
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| 172 | }
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| 173 |
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| 174 | // trigonometric
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[15145] | 175 | private static bool IsSine(ISymbolicExpressionTreeNode node) {
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[14843] | 176 | return node.Symbol is Sine;
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| 177 | }
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| 178 |
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[15145] | 179 | private static bool IsCosine(ISymbolicExpressionTreeNode node) {
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[14843] | 180 | return node.Symbol is Cosine;
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| 181 | }
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| 182 |
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[15145] | 183 | private static bool IsTangent(ISymbolicExpressionTreeNode node) {
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[14843] | 184 | return node.Symbol is Tangent;
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| 185 | }
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| 186 |
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[17072] | 187 | private static bool IsAnalyticalQuotient(ISymbolicExpressionTreeNode node) {
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| 188 | return node.Symbol is AnalyticQuotient;
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| 189 | }
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| 190 |
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[14843] | 191 | // boolean
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[15145] | 192 | private static bool IsIfThenElse(ISymbolicExpressionTreeNode node) {
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[14843] | 193 | return node.Symbol is IfThenElse;
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| 194 | }
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| 195 |
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[15145] | 196 | private static bool IsAnd(ISymbolicExpressionTreeNode node) {
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[14843] | 197 | return node.Symbol is And;
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| 198 | }
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| 199 |
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[15145] | 200 | private static bool IsOr(ISymbolicExpressionTreeNode node) {
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[14843] | 201 | return node.Symbol is Or;
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| 202 | }
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| 203 |
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[15145] | 204 | private static bool IsNot(ISymbolicExpressionTreeNode node) {
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[14843] | 205 | return node.Symbol is Not;
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| 206 | }
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| 207 |
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| 208 | // comparison
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[15145] | 209 | private static bool IsGreaterThan(ISymbolicExpressionTreeNode node) {
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[14843] | 210 | return node.Symbol is GreaterThan;
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| 211 | }
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| 212 |
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[15145] | 213 | private static bool IsLessThan(ISymbolicExpressionTreeNode node) {
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[14843] | 214 | return node.Symbol is LessThan;
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| 215 | }
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| 216 |
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[15145] | 217 | private static bool IsBoolean(ISymbolicExpressionTreeNode node) {
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[14843] | 218 | return
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| 219 | node.Symbol is GreaterThan ||
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| 220 | node.Symbol is LessThan ||
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| 221 | node.Symbol is And ||
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| 222 | node.Symbol is Or;
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| 223 | }
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| 224 |
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| 225 | // terminals
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[15145] | 226 | private static bool IsVariable(ISymbolicExpressionTreeNode node) {
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[14843] | 227 | return node.Symbol is Variable;
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| 228 | }
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| 229 |
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[15145] | 230 | private static bool IsVariableBase(ISymbolicExpressionTreeNode node) {
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[14843] | 231 | return node is VariableTreeNodeBase;
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| 232 | }
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| 233 |
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[15145] | 234 | private static bool IsFactor(ISymbolicExpressionTreeNode node) {
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[14843] | 235 | return node is FactorVariableTreeNode;
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| 236 | }
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| 237 |
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[15145] | 238 | private static bool IsBinFactor(ISymbolicExpressionTreeNode node) {
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[14843] | 239 | return node is BinaryFactorVariableTreeNode;
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| 240 | }
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| 241 |
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[15145] | 242 | private static bool IsConstant(ISymbolicExpressionTreeNode node) {
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[14843] | 243 | return node.Symbol is Constant;
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| 244 | }
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| 245 |
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| 246 | // dynamic
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[15145] | 247 | private static bool IsTimeLag(ISymbolicExpressionTreeNode node) {
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[14843] | 248 | return node.Symbol is TimeLag;
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| 249 | }
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| 250 |
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[15145] | 251 | private static bool IsIntegral(ISymbolicExpressionTreeNode node) {
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[14843] | 252 | return node.Symbol is Integral;
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| 253 | }
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| 254 |
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| 255 | #endregion
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| 256 |
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| 257 | /// <summary>
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| 258 | /// Creates a new simplified tree
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| 259 | /// </summary>
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| 260 | /// <param name="original"></param>
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| 261 | /// <returns></returns>
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[15145] | 262 | public static ISymbolicExpressionTreeNode GetSimplifiedTree(ISymbolicExpressionTreeNode original) {
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[14843] | 263 | if (IsConstant(original) || IsVariableBase(original)) {
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| 264 | return (ISymbolicExpressionTreeNode)original.Clone();
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[17072] | 265 | } else if (IsAbsolute(original)) {
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| 266 | return SimplifyAbsolute(original);
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[14843] | 267 | } else if (IsAddition(original)) {
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| 268 | return SimplifyAddition(original);
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| 269 | } else if (IsSubtraction(original)) {
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| 270 | return SimplifySubtraction(original);
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| 271 | } else if (IsMultiplication(original)) {
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| 272 | return SimplifyMultiplication(original);
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| 273 | } else if (IsDivision(original)) {
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| 274 | return SimplifyDivision(original);
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| 275 | } else if (IsAverage(original)) {
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| 276 | return SimplifyAverage(original);
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| 277 | } else if (IsLog(original)) {
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| 278 | return SimplifyLog(original);
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| 279 | } else if (IsExp(original)) {
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| 280 | return SimplifyExp(original);
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| 281 | } else if (IsSquare(original)) {
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| 282 | return SimplifySquare(original);
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| 283 | } else if (IsSquareRoot(original)) {
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| 284 | return SimplifySquareRoot(original);
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[17072] | 285 | } else if (IsCube(original)) {
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| 286 | return SimplifyCube(original);
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| 287 | } else if (IsCubeRoot(original)) {
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| 288 | return SimplifyCubeRoot(original);
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[14843] | 289 | } else if (IsPower(original)) {
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| 290 | return SimplifyPower(original);
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| 291 | } else if (IsRoot(original)) {
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| 292 | return SimplifyRoot(original);
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| 293 | } else if (IsSine(original)) {
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| 294 | return SimplifySine(original);
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| 295 | } else if (IsCosine(original)) {
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| 296 | return SimplifyCosine(original);
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| 297 | } else if (IsTangent(original)) {
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| 298 | return SimplifyTangent(original);
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[17072] | 299 | } else if (IsAnalyticalQuotient(original)) {
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| 300 | return SimplifyAnalyticalQuotient(original);
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[14843] | 301 | } else if (IsIfThenElse(original)) {
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| 302 | return SimplifyIfThenElse(original);
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| 303 | } else if (IsGreaterThan(original)) {
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| 304 | return SimplifyGreaterThan(original);
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| 305 | } else if (IsLessThan(original)) {
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| 306 | return SimplifyLessThan(original);
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| 307 | } else if (IsAnd(original)) {
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| 308 | return SimplifyAnd(original);
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| 309 | } else if (IsOr(original)) {
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| 310 | return SimplifyOr(original);
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| 311 | } else if (IsNot(original)) {
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| 312 | return SimplifyNot(original);
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| 313 | } else if (IsTimeLag(original)) {
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| 314 | return SimplifyTimeLag(original);
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| 315 | } else if (IsIntegral(original)) {
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| 316 | return SimplifyIntegral(original);
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| 317 | } else {
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| 318 | return SimplifyAny(original);
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| 319 | }
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| 320 | }
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| 321 |
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| 322 | #region specific simplification routines
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| 323 |
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[15145] | 324 | private static ISymbolicExpressionTreeNode SimplifyAny(ISymbolicExpressionTreeNode original) {
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[14843] | 325 | // can't simplify this function but simplify all subtrees
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| 326 | List<ISymbolicExpressionTreeNode> subtrees = new List<ISymbolicExpressionTreeNode>(original.Subtrees);
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| 327 | while (original.Subtrees.Count() > 0) original.RemoveSubtree(0);
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| 328 | var clone = (SymbolicExpressionTreeNode)original.Clone();
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| 329 | List<ISymbolicExpressionTreeNode> simplifiedSubtrees = new List<ISymbolicExpressionTreeNode>();
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| 330 | foreach (var subtree in subtrees) {
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| 331 | simplifiedSubtrees.Add(GetSimplifiedTree(subtree));
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| 332 | original.AddSubtree(subtree);
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| 333 | }
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| 334 | foreach (var simplifiedSubtree in simplifiedSubtrees) {
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| 335 | clone.AddSubtree(simplifiedSubtree);
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| 336 | }
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| 337 | if (simplifiedSubtrees.TrueForAll(t => IsConstant(t))) {
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| 338 | SimplifyConstantExpression(clone);
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| 339 | }
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| 340 | return clone;
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| 341 | }
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| 342 |
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[15145] | 343 | private static ISymbolicExpressionTreeNode SimplifyConstantExpression(ISymbolicExpressionTreeNode original) {
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[14843] | 344 | // not yet implemented
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| 345 | return original;
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| 346 | }
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| 347 |
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[15145] | 348 | private static ISymbolicExpressionTreeNode SimplifyAverage(ISymbolicExpressionTreeNode original) {
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[14843] | 349 | if (original.Subtrees.Count() == 1) {
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| 350 | return GetSimplifiedTree(original.GetSubtree(0));
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| 351 | } else {
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| 352 | // simplify expressions x0..xn
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| 353 | // make sum(x0..xn) / n
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| 354 | var sum = original.Subtrees
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| 355 | .Select(GetSimplifiedTree)
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| 356 | .Aggregate(MakeSum);
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| 357 | return MakeFraction(sum, MakeConstant(original.Subtrees.Count()));
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| 358 | }
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| 359 | }
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| 360 |
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[15145] | 361 | private static ISymbolicExpressionTreeNode SimplifyDivision(ISymbolicExpressionTreeNode original) {
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[14843] | 362 | if (original.Subtrees.Count() == 1) {
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| 363 | return Invert(GetSimplifiedTree(original.GetSubtree(0)));
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| 364 | } else {
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| 365 | // simplify expressions x0..xn
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| 366 | // make multiplication (x0 * 1/(x1 * x1 * .. * xn))
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| 367 | var first = original.GetSubtree(0);
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| 368 | var second = original.GetSubtree(1);
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| 369 | var remaining = original.Subtrees.Skip(2);
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| 370 | return
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| 371 | MakeProduct(GetSimplifiedTree(first),
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| 372 | Invert(remaining.Aggregate(GetSimplifiedTree(second), (a, b) => MakeProduct(a, GetSimplifiedTree(b)))));
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| 373 | }
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| 374 | }
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| 375 |
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[15145] | 376 | private static ISymbolicExpressionTreeNode SimplifyMultiplication(ISymbolicExpressionTreeNode original) {
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[14843] | 377 | if (original.Subtrees.Count() == 1) {
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| 378 | return GetSimplifiedTree(original.GetSubtree(0));
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| 379 | } else {
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| 380 | return original.Subtrees
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| 381 | .Select(GetSimplifiedTree)
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| 382 | .Aggregate(MakeProduct);
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| 383 | }
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| 384 | }
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| 385 |
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[15145] | 386 | private static ISymbolicExpressionTreeNode SimplifySubtraction(ISymbolicExpressionTreeNode original) {
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[14843] | 387 | if (original.Subtrees.Count() == 1) {
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| 388 | return Negate(GetSimplifiedTree(original.GetSubtree(0)));
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| 389 | } else {
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| 390 | // simplify expressions x0..xn
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| 391 | // make addition (x0,-x1..-xn)
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| 392 | var first = original.Subtrees.First();
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| 393 | var remaining = original.Subtrees.Skip(1);
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| 394 | return remaining.Aggregate(GetSimplifiedTree(first), (a, b) => MakeSum(a, Negate(GetSimplifiedTree(b))));
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| 395 | }
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| 396 | }
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| 397 |
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[15145] | 398 | private static ISymbolicExpressionTreeNode SimplifyAddition(ISymbolicExpressionTreeNode original) {
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[14843] | 399 | if (original.Subtrees.Count() == 1) {
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| 400 | return GetSimplifiedTree(original.GetSubtree(0));
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| 401 | } else {
|
---|
| 402 | // simplify expression x0..xn
|
---|
| 403 | // make addition (x0..xn)
|
---|
| 404 | return original.Subtrees
|
---|
| 405 | .Select(GetSimplifiedTree)
|
---|
| 406 | .Aggregate(MakeSum);
|
---|
| 407 | }
|
---|
| 408 | }
|
---|
| 409 |
|
---|
[17072] | 410 | private static ISymbolicExpressionTreeNode SimplifyAbsolute(ISymbolicExpressionTreeNode original) {
|
---|
| 411 | return MakeAbs(GetSimplifiedTree(original.GetSubtree(0)));
|
---|
| 412 | }
|
---|
| 413 |
|
---|
[15145] | 414 | private static ISymbolicExpressionTreeNode SimplifyNot(ISymbolicExpressionTreeNode original) {
|
---|
[14843] | 415 | return MakeNot(GetSimplifiedTree(original.GetSubtree(0)));
|
---|
| 416 | }
|
---|
| 417 |
|
---|
[15145] | 418 | private static ISymbolicExpressionTreeNode SimplifyOr(ISymbolicExpressionTreeNode original) {
|
---|
[14843] | 419 | return original.Subtrees
|
---|
| 420 | .Select(GetSimplifiedTree)
|
---|
| 421 | .Aggregate(MakeOr);
|
---|
| 422 | }
|
---|
| 423 |
|
---|
[15145] | 424 | private static ISymbolicExpressionTreeNode SimplifyAnd(ISymbolicExpressionTreeNode original) {
|
---|
[14843] | 425 | return original.Subtrees
|
---|
| 426 | .Select(GetSimplifiedTree)
|
---|
| 427 | .Aggregate(MakeAnd);
|
---|
| 428 | }
|
---|
| 429 |
|
---|
[15145] | 430 | private static ISymbolicExpressionTreeNode SimplifyLessThan(ISymbolicExpressionTreeNode original) {
|
---|
[14843] | 431 | return MakeLessThan(GetSimplifiedTree(original.GetSubtree(0)), GetSimplifiedTree(original.GetSubtree(1)));
|
---|
| 432 | }
|
---|
| 433 |
|
---|
[15145] | 434 | private static ISymbolicExpressionTreeNode SimplifyGreaterThan(ISymbolicExpressionTreeNode original) {
|
---|
[14843] | 435 | return MakeGreaterThan(GetSimplifiedTree(original.GetSubtree(0)), GetSimplifiedTree(original.GetSubtree(1)));
|
---|
| 436 | }
|
---|
| 437 |
|
---|
[15145] | 438 | private static ISymbolicExpressionTreeNode SimplifyIfThenElse(ISymbolicExpressionTreeNode original) {
|
---|
[14843] | 439 | return MakeIfThenElse(GetSimplifiedTree(original.GetSubtree(0)), GetSimplifiedTree(original.GetSubtree(1)),
|
---|
| 440 | GetSimplifiedTree(original.GetSubtree(2)));
|
---|
| 441 | }
|
---|
| 442 |
|
---|
[15145] | 443 | private static ISymbolicExpressionTreeNode SimplifyTangent(ISymbolicExpressionTreeNode original) {
|
---|
[14843] | 444 | return MakeTangent(GetSimplifiedTree(original.GetSubtree(0)));
|
---|
| 445 | }
|
---|
| 446 |
|
---|
[15145] | 447 | private static ISymbolicExpressionTreeNode SimplifyCosine(ISymbolicExpressionTreeNode original) {
|
---|
[14843] | 448 | return MakeCosine(GetSimplifiedTree(original.GetSubtree(0)));
|
---|
| 449 | }
|
---|
| 450 |
|
---|
[15145] | 451 | private static ISymbolicExpressionTreeNode SimplifySine(ISymbolicExpressionTreeNode original) {
|
---|
[14843] | 452 | return MakeSine(GetSimplifiedTree(original.GetSubtree(0)));
|
---|
| 453 | }
|
---|
| 454 |
|
---|
[15145] | 455 | private static ISymbolicExpressionTreeNode SimplifyExp(ISymbolicExpressionTreeNode original) {
|
---|
[14843] | 456 | return MakeExp(GetSimplifiedTree(original.GetSubtree(0)));
|
---|
| 457 | }
|
---|
| 458 |
|
---|
[15145] | 459 | private static ISymbolicExpressionTreeNode SimplifySquare(ISymbolicExpressionTreeNode original) {
|
---|
[14843] | 460 | return MakeSquare(GetSimplifiedTree(original.GetSubtree(0)));
|
---|
| 461 | }
|
---|
| 462 |
|
---|
[15145] | 463 | private static ISymbolicExpressionTreeNode SimplifySquareRoot(ISymbolicExpressionTreeNode original) {
|
---|
[14843] | 464 | return MakeSquareRoot(GetSimplifiedTree(original.GetSubtree(0)));
|
---|
| 465 | }
|
---|
[17072] | 466 | private static ISymbolicExpressionTreeNode SimplifyCube(ISymbolicExpressionTreeNode original) {
|
---|
| 467 | return MakeCube(GetSimplifiedTree(original.GetSubtree(0)));
|
---|
| 468 | }
|
---|
[14843] | 469 |
|
---|
[17072] | 470 | private static ISymbolicExpressionTreeNode SimplifyCubeRoot(ISymbolicExpressionTreeNode original) {
|
---|
| 471 | return MakeCubeRoot(GetSimplifiedTree(original.GetSubtree(0)));
|
---|
| 472 | }
|
---|
| 473 |
|
---|
[15145] | 474 | private static ISymbolicExpressionTreeNode SimplifyLog(ISymbolicExpressionTreeNode original) {
|
---|
[14843] | 475 | return MakeLog(GetSimplifiedTree(original.GetSubtree(0)));
|
---|
| 476 | }
|
---|
| 477 |
|
---|
[15145] | 478 | private static ISymbolicExpressionTreeNode SimplifyRoot(ISymbolicExpressionTreeNode original) {
|
---|
[14843] | 479 | return MakeRoot(GetSimplifiedTree(original.GetSubtree(0)), GetSimplifiedTree(original.GetSubtree(1)));
|
---|
| 480 | }
|
---|
| 481 |
|
---|
[15145] | 482 | private static ISymbolicExpressionTreeNode SimplifyPower(ISymbolicExpressionTreeNode original) {
|
---|
[14843] | 483 | return MakePower(GetSimplifiedTree(original.GetSubtree(0)), GetSimplifiedTree(original.GetSubtree(1)));
|
---|
| 484 | }
|
---|
| 485 |
|
---|
[17072] | 486 | private static ISymbolicExpressionTreeNode SimplifyAnalyticalQuotient(ISymbolicExpressionTreeNode original) {
|
---|
| 487 | return MakeAnalyticalQuotient(GetSimplifiedTree(original.GetSubtree(0)), GetSimplifiedTree(original.GetSubtree(1)));
|
---|
| 488 | }
|
---|
| 489 |
|
---|
[15145] | 490 | private static ISymbolicExpressionTreeNode SimplifyTimeLag(ISymbolicExpressionTreeNode original) {
|
---|
[14843] | 491 | var laggedTreeNode = original as ILaggedTreeNode;
|
---|
| 492 | var simplifiedSubtree = GetSimplifiedTree(original.GetSubtree(0));
|
---|
| 493 | if (!ContainsVariableCondition(simplifiedSubtree)) {
|
---|
| 494 | return AddLagToDynamicNodes(simplifiedSubtree, laggedTreeNode.Lag);
|
---|
| 495 | } else {
|
---|
| 496 | return MakeTimeLag(simplifiedSubtree, laggedTreeNode.Lag);
|
---|
| 497 | }
|
---|
| 498 | }
|
---|
| 499 |
|
---|
[15145] | 500 | private static ISymbolicExpressionTreeNode SimplifyIntegral(ISymbolicExpressionTreeNode original) {
|
---|
[14843] | 501 | var laggedTreeNode = original as ILaggedTreeNode;
|
---|
| 502 | var simplifiedSubtree = GetSimplifiedTree(original.GetSubtree(0));
|
---|
| 503 | if (IsConstant(simplifiedSubtree)) {
|
---|
| 504 | return GetSimplifiedTree(MakeProduct(simplifiedSubtree, MakeConstant(-laggedTreeNode.Lag)));
|
---|
| 505 | } else {
|
---|
| 506 | return MakeIntegral(simplifiedSubtree, laggedTreeNode.Lag);
|
---|
| 507 | }
|
---|
| 508 | }
|
---|
| 509 |
|
---|
| 510 | #endregion
|
---|
| 511 |
|
---|
| 512 | #region low level tree restructuring
|
---|
| 513 |
|
---|
[15145] | 514 | private static ISymbolicExpressionTreeNode MakeTimeLag(ISymbolicExpressionTreeNode subtree, int lag) {
|
---|
[14843] | 515 | if (lag == 0) return subtree;
|
---|
| 516 | if (IsConstant(subtree)) return subtree;
|
---|
| 517 | var lagNode = (LaggedTreeNode)timeLagSymbol.CreateTreeNode();
|
---|
| 518 | lagNode.Lag = lag;
|
---|
| 519 | lagNode.AddSubtree(subtree);
|
---|
| 520 | return lagNode;
|
---|
| 521 | }
|
---|
| 522 |
|
---|
[15145] | 523 | private static ISymbolicExpressionTreeNode MakeIntegral(ISymbolicExpressionTreeNode subtree, int lag) {
|
---|
[14843] | 524 | if (lag == 0) return subtree;
|
---|
| 525 | else if (lag == -1 || lag == 1) {
|
---|
| 526 | return MakeSum(subtree, AddLagToDynamicNodes((ISymbolicExpressionTreeNode)subtree.Clone(), lag));
|
---|
| 527 | } else {
|
---|
| 528 | var node = (LaggedTreeNode)integralSymbol.CreateTreeNode();
|
---|
| 529 | node.Lag = lag;
|
---|
| 530 | node.AddSubtree(subtree);
|
---|
| 531 | return node;
|
---|
| 532 | }
|
---|
| 533 | }
|
---|
| 534 |
|
---|
[15145] | 535 | private static ISymbolicExpressionTreeNode MakeNot(ISymbolicExpressionTreeNode t) {
|
---|
[14843] | 536 | if (IsConstant(t)) {
|
---|
| 537 | var constNode = t as ConstantTreeNode;
|
---|
| 538 | if (constNode.Value > 0) return MakeConstant(-1.0);
|
---|
| 539 | else return MakeConstant(1.0);
|
---|
| 540 | } else if (IsNot(t)) {
|
---|
| 541 | return t.GetSubtree(0);
|
---|
| 542 | } else if (!IsBoolean(t)) {
|
---|
| 543 | var gtNode = gtSymbol.CreateTreeNode();
|
---|
| 544 | gtNode.AddSubtree(t);
|
---|
| 545 | gtNode.AddSubtree(MakeConstant(0.0));
|
---|
| 546 | var notNode = notSymbol.CreateTreeNode();
|
---|
| 547 | notNode.AddSubtree(gtNode);
|
---|
| 548 | return notNode;
|
---|
| 549 | } else {
|
---|
| 550 | var notNode = notSymbol.CreateTreeNode();
|
---|
| 551 | notNode.AddSubtree(t);
|
---|
| 552 | return notNode;
|
---|
| 553 | }
|
---|
| 554 | }
|
---|
| 555 |
|
---|
[15145] | 556 | private static ISymbolicExpressionTreeNode MakeOr(ISymbolicExpressionTreeNode a, ISymbolicExpressionTreeNode b) {
|
---|
[14843] | 557 | if (IsConstant(a) && IsConstant(b)) {
|
---|
| 558 | var constA = a as ConstantTreeNode;
|
---|
| 559 | var constB = b as ConstantTreeNode;
|
---|
| 560 | if (constA.Value > 0.0 || constB.Value > 0.0) {
|
---|
| 561 | return MakeConstant(1.0);
|
---|
| 562 | } else {
|
---|
| 563 | return MakeConstant(-1.0);
|
---|
| 564 | }
|
---|
| 565 | } else if (IsConstant(a)) {
|
---|
| 566 | return MakeOr(b, a);
|
---|
| 567 | } else if (IsConstant(b)) {
|
---|
| 568 | var constT = b as ConstantTreeNode;
|
---|
| 569 | if (constT.Value > 0.0) {
|
---|
| 570 | // boolean expression is necessarily true
|
---|
| 571 | return MakeConstant(1.0);
|
---|
| 572 | } else {
|
---|
| 573 | // the constant value has no effect on the result of the boolean condition so we can drop the constant term
|
---|
| 574 | var orNode = orSymbol.CreateTreeNode();
|
---|
| 575 | orNode.AddSubtree(a);
|
---|
| 576 | return orNode;
|
---|
| 577 | }
|
---|
| 578 | } else {
|
---|
| 579 | var orNode = orSymbol.CreateTreeNode();
|
---|
| 580 | orNode.AddSubtree(a);
|
---|
| 581 | orNode.AddSubtree(b);
|
---|
| 582 | return orNode;
|
---|
| 583 | }
|
---|
| 584 | }
|
---|
| 585 |
|
---|
[15145] | 586 | private static ISymbolicExpressionTreeNode MakeAnd(ISymbolicExpressionTreeNode a, ISymbolicExpressionTreeNode b) {
|
---|
[14843] | 587 | if (IsConstant(a) && IsConstant(b)) {
|
---|
| 588 | var constA = a as ConstantTreeNode;
|
---|
| 589 | var constB = b as ConstantTreeNode;
|
---|
| 590 | if (constA.Value > 0.0 && constB.Value > 0.0) {
|
---|
| 591 | return MakeConstant(1.0);
|
---|
| 592 | } else {
|
---|
| 593 | return MakeConstant(-1.0);
|
---|
| 594 | }
|
---|
| 595 | } else if (IsConstant(a)) {
|
---|
| 596 | return MakeAnd(b, a);
|
---|
| 597 | } else if (IsConstant(b)) {
|
---|
| 598 | var constB = b as ConstantTreeNode;
|
---|
| 599 | if (constB.Value > 0.0) {
|
---|
| 600 | // the constant value has no effect on the result of the boolean condition so we can drop the constant term
|
---|
| 601 | var andNode = andSymbol.CreateTreeNode();
|
---|
| 602 | andNode.AddSubtree(a);
|
---|
| 603 | return andNode;
|
---|
| 604 | } else {
|
---|
| 605 | // boolean expression is necessarily false
|
---|
| 606 | return MakeConstant(-1.0);
|
---|
| 607 | }
|
---|
| 608 | } else {
|
---|
| 609 | var andNode = andSymbol.CreateTreeNode();
|
---|
| 610 | andNode.AddSubtree(a);
|
---|
| 611 | andNode.AddSubtree(b);
|
---|
| 612 | return andNode;
|
---|
| 613 | }
|
---|
| 614 | }
|
---|
| 615 |
|
---|
[15145] | 616 | private static ISymbolicExpressionTreeNode MakeLessThan(ISymbolicExpressionTreeNode leftSide,
|
---|
[14843] | 617 | ISymbolicExpressionTreeNode rightSide) {
|
---|
| 618 | if (IsConstant(leftSide) && IsConstant(rightSide)) {
|
---|
| 619 | var lsConst = leftSide as ConstantTreeNode;
|
---|
| 620 | var rsConst = rightSide as ConstantTreeNode;
|
---|
| 621 | if (lsConst.Value < rsConst.Value) return MakeConstant(1.0);
|
---|
| 622 | else return MakeConstant(-1.0);
|
---|
| 623 | } else {
|
---|
| 624 | var ltNode = ltSymbol.CreateTreeNode();
|
---|
| 625 | ltNode.AddSubtree(leftSide);
|
---|
| 626 | ltNode.AddSubtree(rightSide);
|
---|
| 627 | return ltNode;
|
---|
| 628 | }
|
---|
| 629 | }
|
---|
| 630 |
|
---|
[15145] | 631 | private static ISymbolicExpressionTreeNode MakeGreaterThan(ISymbolicExpressionTreeNode leftSide,
|
---|
[14843] | 632 | ISymbolicExpressionTreeNode rightSide) {
|
---|
| 633 | if (IsConstant(leftSide) && IsConstant(rightSide)) {
|
---|
| 634 | var lsConst = leftSide as ConstantTreeNode;
|
---|
| 635 | var rsConst = rightSide as ConstantTreeNode;
|
---|
| 636 | if (lsConst.Value > rsConst.Value) return MakeConstant(1.0);
|
---|
| 637 | else return MakeConstant(-1.0);
|
---|
| 638 | } else {
|
---|
| 639 | var gtNode = gtSymbol.CreateTreeNode();
|
---|
| 640 | gtNode.AddSubtree(leftSide);
|
---|
| 641 | gtNode.AddSubtree(rightSide);
|
---|
| 642 | return gtNode;
|
---|
| 643 | }
|
---|
| 644 | }
|
---|
| 645 |
|
---|
[15145] | 646 | private static ISymbolicExpressionTreeNode MakeIfThenElse(ISymbolicExpressionTreeNode condition,
|
---|
[14843] | 647 | ISymbolicExpressionTreeNode trueBranch, ISymbolicExpressionTreeNode falseBranch) {
|
---|
| 648 | if (IsConstant(condition)) {
|
---|
| 649 | var constT = condition as ConstantTreeNode;
|
---|
| 650 | if (constT.Value > 0.0) return trueBranch;
|
---|
| 651 | else return falseBranch;
|
---|
| 652 | } else {
|
---|
| 653 | var ifNode = ifThenElseSymbol.CreateTreeNode();
|
---|
| 654 | if (IsBoolean(condition)) {
|
---|
| 655 | ifNode.AddSubtree(condition);
|
---|
| 656 | } else {
|
---|
| 657 | var gtNode = gtSymbol.CreateTreeNode();
|
---|
| 658 | gtNode.AddSubtree(condition);
|
---|
| 659 | gtNode.AddSubtree(MakeConstant(0.0));
|
---|
| 660 | ifNode.AddSubtree(gtNode);
|
---|
| 661 | }
|
---|
| 662 | ifNode.AddSubtree(trueBranch);
|
---|
| 663 | ifNode.AddSubtree(falseBranch);
|
---|
| 664 | return ifNode;
|
---|
| 665 | }
|
---|
| 666 | }
|
---|
| 667 |
|
---|
[15145] | 668 | private static ISymbolicExpressionTreeNode MakeSine(ISymbolicExpressionTreeNode node) {
|
---|
[14843] | 669 | if (IsConstant(node)) {
|
---|
| 670 | var constT = node as ConstantTreeNode;
|
---|
| 671 | return MakeConstant(Math.Sin(constT.Value));
|
---|
| 672 | } else if (IsFactor(node)) {
|
---|
| 673 | var factor = node as FactorVariableTreeNode;
|
---|
| 674 | return MakeFactor(factor.Symbol, factor.VariableName, factor.Weights.Select(Math.Sin));
|
---|
| 675 | } else if (IsBinFactor(node)) {
|
---|
| 676 | var binFactor = node as BinaryFactorVariableTreeNode;
|
---|
| 677 | return MakeBinFactor(binFactor.Symbol, binFactor.VariableName, binFactor.VariableValue, Math.Sin(binFactor.Weight));
|
---|
| 678 | } else {
|
---|
| 679 | var sineNode = sineSymbol.CreateTreeNode();
|
---|
| 680 | sineNode.AddSubtree(node);
|
---|
| 681 | return sineNode;
|
---|
| 682 | }
|
---|
| 683 | }
|
---|
| 684 |
|
---|
[15145] | 685 | private static ISymbolicExpressionTreeNode MakeTangent(ISymbolicExpressionTreeNode node) {
|
---|
[14843] | 686 | if (IsConstant(node)) {
|
---|
| 687 | var constT = node as ConstantTreeNode;
|
---|
| 688 | return MakeConstant(Math.Tan(constT.Value));
|
---|
| 689 | } else if (IsFactor(node)) {
|
---|
| 690 | var factor = node as FactorVariableTreeNode;
|
---|
| 691 | return MakeFactor(factor.Symbol, factor.VariableName, factor.Weights.Select(Math.Tan));
|
---|
| 692 | } else if (IsBinFactor(node)) {
|
---|
| 693 | var binFactor = node as BinaryFactorVariableTreeNode;
|
---|
| 694 | return MakeBinFactor(binFactor.Symbol, binFactor.VariableName, binFactor.VariableValue, Math.Tan(binFactor.Weight));
|
---|
| 695 | } else {
|
---|
| 696 | var tanNode = tanSymbol.CreateTreeNode();
|
---|
| 697 | tanNode.AddSubtree(node);
|
---|
| 698 | return tanNode;
|
---|
| 699 | }
|
---|
| 700 | }
|
---|
| 701 |
|
---|
[15145] | 702 | private static ISymbolicExpressionTreeNode MakeCosine(ISymbolicExpressionTreeNode node) {
|
---|
[14843] | 703 | if (IsConstant(node)) {
|
---|
| 704 | var constT = node as ConstantTreeNode;
|
---|
| 705 | return MakeConstant(Math.Cos(constT.Value));
|
---|
| 706 | } else if (IsFactor(node)) {
|
---|
| 707 | var factor = node as FactorVariableTreeNode;
|
---|
| 708 | return MakeFactor(factor.Symbol, factor.VariableName, factor.Weights.Select(Math.Cos));
|
---|
| 709 | } else if (IsBinFactor(node)) {
|
---|
| 710 | var binFactor = node as BinaryFactorVariableTreeNode;
|
---|
| 711 | // cos(0) = 1 see similar case for Exp(binfactor)
|
---|
| 712 | return MakeSum(MakeBinFactor(binFactor.Symbol, binFactor.VariableName, binFactor.VariableValue, Math.Cos(binFactor.Weight) - 1),
|
---|
| 713 | MakeConstant(1.0));
|
---|
| 714 | } else {
|
---|
| 715 | var cosNode = cosineSymbol.CreateTreeNode();
|
---|
| 716 | cosNode.AddSubtree(node);
|
---|
| 717 | return cosNode;
|
---|
| 718 | }
|
---|
| 719 | }
|
---|
| 720 |
|
---|
[15145] | 721 | private static ISymbolicExpressionTreeNode MakeExp(ISymbolicExpressionTreeNode node) {
|
---|
[14843] | 722 | if (IsConstant(node)) {
|
---|
| 723 | var constT = node as ConstantTreeNode;
|
---|
| 724 | return MakeConstant(Math.Exp(constT.Value));
|
---|
| 725 | } else if (IsFactor(node)) {
|
---|
| 726 | var factNode = node as FactorVariableTreeNode;
|
---|
| 727 | return MakeFactor(factNode.Symbol, factNode.VariableName, factNode.Weights.Select(w => Math.Exp(w)));
|
---|
| 728 | } else if (IsBinFactor(node)) {
|
---|
| 729 | // exp( binfactor w val=a) = if(val=a) exp(w) else exp(0) = binfactor( (exp(w) - 1) val a) + 1
|
---|
| 730 | var binFactor = node as BinaryFactorVariableTreeNode;
|
---|
| 731 | return
|
---|
| 732 | MakeSum(MakeBinFactor(binFactor.Symbol, binFactor.VariableName, binFactor.VariableValue, Math.Exp(binFactor.Weight) - 1), MakeConstant(1.0));
|
---|
| 733 | } else if (IsLog(node)) {
|
---|
| 734 | return node.GetSubtree(0);
|
---|
| 735 | } else if (IsAddition(node)) {
|
---|
| 736 | return node.Subtrees.Select(s => MakeExp(s)).Aggregate((s, t) => MakeProduct(s, t));
|
---|
| 737 | } else if (IsSubtraction(node)) {
|
---|
| 738 | return node.Subtrees.Select(s => MakeExp(s)).Aggregate((s, t) => MakeProduct(s, Negate(t)));
|
---|
| 739 | } else {
|
---|
| 740 | var expNode = expSymbol.CreateTreeNode();
|
---|
| 741 | expNode.AddSubtree(node);
|
---|
| 742 | return expNode;
|
---|
| 743 | }
|
---|
| 744 | }
|
---|
[15145] | 745 | private static ISymbolicExpressionTreeNode MakeLog(ISymbolicExpressionTreeNode node) {
|
---|
[14843] | 746 | if (IsConstant(node)) {
|
---|
| 747 | var constT = node as ConstantTreeNode;
|
---|
| 748 | return MakeConstant(Math.Log(constT.Value));
|
---|
| 749 | } else if (IsFactor(node)) {
|
---|
| 750 | var factNode = node as FactorVariableTreeNode;
|
---|
| 751 | return MakeFactor(factNode.Symbol, factNode.VariableName, factNode.Weights.Select(w => Math.Log(w)));
|
---|
| 752 | } else if (IsExp(node)) {
|
---|
| 753 | return node.GetSubtree(0);
|
---|
| 754 | } else if (IsSquareRoot(node)) {
|
---|
| 755 | return MakeFraction(MakeLog(node.GetSubtree(0)), MakeConstant(2.0));
|
---|
| 756 | } else {
|
---|
| 757 | var logNode = logSymbol.CreateTreeNode();
|
---|
| 758 | logNode.AddSubtree(node);
|
---|
| 759 | return logNode;
|
---|
| 760 | }
|
---|
| 761 | }
|
---|
| 762 |
|
---|
[15145] | 763 | private static ISymbolicExpressionTreeNode MakeSquare(ISymbolicExpressionTreeNode node) {
|
---|
[14843] | 764 | if (IsConstant(node)) {
|
---|
| 765 | var constT = node as ConstantTreeNode;
|
---|
| 766 | return MakeConstant(constT.Value * constT.Value);
|
---|
| 767 | } else if (IsFactor(node)) {
|
---|
| 768 | var factNode = node as FactorVariableTreeNode;
|
---|
| 769 | return MakeFactor(factNode.Symbol, factNode.VariableName, factNode.Weights.Select(w => w * w));
|
---|
| 770 | } else if (IsBinFactor(node)) {
|
---|
| 771 | var binFactor = node as BinaryFactorVariableTreeNode;
|
---|
| 772 | return MakeBinFactor(binFactor.Symbol, binFactor.VariableName, binFactor.VariableValue, binFactor.Weight * binFactor.Weight);
|
---|
| 773 | } else if (IsSquareRoot(node)) {
|
---|
| 774 | return node.GetSubtree(0);
|
---|
[17072] | 775 | } else if (IsMultiplication(node)) {
|
---|
| 776 | // sqr( x * y ) = sqr(x) * sqr(y)
|
---|
| 777 | var mulNode = mulSymbol.CreateTreeNode();
|
---|
| 778 | foreach (var subtree in node.Subtrees) {
|
---|
| 779 | mulNode.AddSubtree(MakeSquare(subtree));
|
---|
| 780 | }
|
---|
| 781 | return mulNode;
|
---|
| 782 | } else if (IsAbsolute(node)) {
|
---|
| 783 | return MakeSquare(node.GetSubtree(0)); // sqr(abs(x)) = sqr(x)
|
---|
| 784 | } else if (IsExp(node)) {
|
---|
| 785 | return MakeExp(MakeProduct(node.GetSubtree(0), MakeConstant(2.0))); // sqr(exp(x)) = exp(2x)
|
---|
| 786 | } else if (IsCube(node)) {
|
---|
| 787 | return MakePower(node.GetSubtree(0), MakeConstant(6));
|
---|
[14843] | 788 | } else {
|
---|
| 789 | var sqrNode = sqrSymbol.CreateTreeNode();
|
---|
| 790 | sqrNode.AddSubtree(node);
|
---|
| 791 | return sqrNode;
|
---|
| 792 | }
|
---|
| 793 | }
|
---|
| 794 |
|
---|
[17072] | 795 | private static ISymbolicExpressionTreeNode MakeCube(ISymbolicExpressionTreeNode node) {
|
---|
| 796 | if (IsConstant(node)) {
|
---|
| 797 | var constT = node as ConstantTreeNode;
|
---|
| 798 | return MakeConstant(constT.Value * constT.Value * constT.Value);
|
---|
| 799 | } else if (IsFactor(node)) {
|
---|
| 800 | var factNode = node as FactorVariableTreeNode;
|
---|
| 801 | return MakeFactor(factNode.Symbol, factNode.VariableName, factNode.Weights.Select(w => w * w * w));
|
---|
| 802 | } else if (IsBinFactor(node)) {
|
---|
| 803 | var binFactor = node as BinaryFactorVariableTreeNode;
|
---|
| 804 | return MakeBinFactor(binFactor.Symbol, binFactor.VariableName, binFactor.VariableValue, binFactor.Weight * binFactor.Weight * binFactor.Weight);
|
---|
| 805 | } else if (IsCubeRoot(node)) {
|
---|
| 806 | 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
|
---|
| 807 | } else if (IsExp(node)) {
|
---|
| 808 | return MakeExp(MakeProduct(node.GetSubtree(0), MakeConstant(3)));
|
---|
| 809 | } else if (IsSquare(node)) {
|
---|
| 810 | return MakePower(node.GetSubtree(0), MakeConstant(6));
|
---|
| 811 | } else {
|
---|
| 812 | var cubeNode = cubeSymbol.CreateTreeNode();
|
---|
| 813 | cubeNode.AddSubtree(node);
|
---|
| 814 | return cubeNode;
|
---|
| 815 | }
|
---|
| 816 | }
|
---|
| 817 |
|
---|
| 818 | private static ISymbolicExpressionTreeNode MakeAbs(ISymbolicExpressionTreeNode node) {
|
---|
| 819 | if (IsConstant(node)) {
|
---|
| 820 | var constT = node as ConstantTreeNode;
|
---|
| 821 | return MakeConstant(Math.Abs(constT.Value));
|
---|
| 822 | } else if (IsFactor(node)) {
|
---|
| 823 | var factNode = node as FactorVariableTreeNode;
|
---|
| 824 | return MakeFactor(factNode.Symbol, factNode.VariableName, factNode.Weights.Select(w => Math.Abs(w)));
|
---|
| 825 | } else if (IsBinFactor(node)) {
|
---|
| 826 | var binFactor = node as BinaryFactorVariableTreeNode;
|
---|
| 827 | return MakeBinFactor(binFactor.Symbol, binFactor.VariableName, binFactor.VariableValue, Math.Abs(binFactor.Weight));
|
---|
| 828 | } else if (IsSquare(node) || IsExp(node) || IsSquareRoot(node) || IsCubeRoot(node)) {
|
---|
| 829 | return node; // abs(sqr(x)) = sqr(x), abs(exp(x)) = exp(x) ...
|
---|
| 830 | } else if (IsMultiplication(node)) {
|
---|
| 831 | var mul = mulSymbol.CreateTreeNode();
|
---|
| 832 | foreach (var st in node.Subtrees) {
|
---|
| 833 | mul.AddSubtree(MakeAbs(st));
|
---|
| 834 | }
|
---|
| 835 | return mul;
|
---|
| 836 | } else if (IsDivision(node)) {
|
---|
| 837 | var div = divSymbol.CreateTreeNode();
|
---|
| 838 | foreach (var st in node.Subtrees) {
|
---|
| 839 | div.AddSubtree(MakeAbs(st));
|
---|
| 840 | }
|
---|
| 841 | return div;
|
---|
| 842 | } else {
|
---|
| 843 | var absNode = absSymbol.CreateTreeNode();
|
---|
| 844 | absNode.AddSubtree(node);
|
---|
| 845 | return absNode;
|
---|
| 846 | }
|
---|
| 847 | }
|
---|
| 848 |
|
---|
| 849 | // constant folding only
|
---|
| 850 | private static ISymbolicExpressionTreeNode MakeAnalyticalQuotient(ISymbolicExpressionTreeNode a, ISymbolicExpressionTreeNode b) {
|
---|
| 851 | if (IsConstant(b)) {
|
---|
| 852 | var c = b as ConstantTreeNode;
|
---|
| 853 | return MakeFraction(a, MakeConstant(Math.Sqrt(1.0 + c.Value * c.Value)));
|
---|
| 854 | } else if (IsFactor(b)) {
|
---|
| 855 | var factNode = b as FactorVariableTreeNode;
|
---|
| 856 | return MakeFraction(a, MakeFactor(factNode.Symbol, factNode.VariableName, factNode.Weights.Select(w => Math.Sqrt(1.0 + w * w))));
|
---|
| 857 | } else if (IsBinFactor(b)) {
|
---|
| 858 | var binFactor = b as BinaryFactorVariableTreeNode;
|
---|
| 859 | return MakeFraction(a, MakeBinFactor(binFactor.Symbol, binFactor.VariableName, binFactor.VariableValue, Math.Sqrt(1.0 + binFactor.Weight * binFactor.Weight)));
|
---|
| 860 | } else {
|
---|
| 861 | var aqNode = aqSymbol.CreateTreeNode();
|
---|
| 862 | aqNode.AddSubtree(a);
|
---|
| 863 | aqNode.AddSubtree(b);
|
---|
| 864 | return aqNode;
|
---|
| 865 | }
|
---|
| 866 | }
|
---|
| 867 |
|
---|
[15145] | 868 | private static ISymbolicExpressionTreeNode MakeSquareRoot(ISymbolicExpressionTreeNode node) {
|
---|
[14843] | 869 | if (IsConstant(node)) {
|
---|
| 870 | var constT = node as ConstantTreeNode;
|
---|
| 871 | return MakeConstant(Math.Sqrt(constT.Value));
|
---|
| 872 | } else if (IsFactor(node)) {
|
---|
| 873 | var factNode = node as FactorVariableTreeNode;
|
---|
| 874 | return MakeFactor(factNode.Symbol, factNode.VariableName, factNode.Weights.Select(w => Math.Sqrt(w)));
|
---|
| 875 | } else if (IsBinFactor(node)) {
|
---|
| 876 | var binFactor = node as BinaryFactorVariableTreeNode;
|
---|
| 877 | return MakeBinFactor(binFactor.Symbol, binFactor.VariableName, binFactor.VariableValue, Math.Sqrt(binFactor.Weight));
|
---|
| 878 | } else if (IsSquare(node)) {
|
---|
[17072] | 879 | 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] | 880 | } else {
|
---|
| 881 | var sqrtNode = sqrtSymbol.CreateTreeNode();
|
---|
| 882 | sqrtNode.AddSubtree(node);
|
---|
| 883 | return sqrtNode;
|
---|
| 884 | }
|
---|
| 885 | }
|
---|
| 886 |
|
---|
[17072] | 887 | private static ISymbolicExpressionTreeNode MakeCubeRoot(ISymbolicExpressionTreeNode node) {
|
---|
| 888 | if (IsConstant(node)) {
|
---|
| 889 | var constT = node as ConstantTreeNode;
|
---|
| 890 | return MakeConstant(Math.Pow(constT.Value, 1.0 / 3.0));
|
---|
| 891 | } else if (IsFactor(node)) {
|
---|
| 892 | var factNode = node as FactorVariableTreeNode;
|
---|
| 893 | return MakeFactor(factNode.Symbol, factNode.VariableName, factNode.Weights.Select(w => Math.Pow(w, 1.0 / 3.0)));
|
---|
| 894 | } else if (IsBinFactor(node)) {
|
---|
| 895 | var binFactor = node as BinaryFactorVariableTreeNode;
|
---|
| 896 | return MakeBinFactor(binFactor.Symbol, binFactor.VariableName, binFactor.VariableValue, Math.Sqrt(Math.Pow(binFactor.Weight, 1.0 / 3.0)));
|
---|
| 897 | } else if (IsCube(node)) {
|
---|
| 898 | return node.GetSubtree(0);
|
---|
| 899 | } else {
|
---|
| 900 | var cubeRootNode = cubeRootSymbol.CreateTreeNode();
|
---|
| 901 | cubeRootNode.AddSubtree(node);
|
---|
| 902 | return cubeRootNode;
|
---|
| 903 | }
|
---|
| 904 | }
|
---|
| 905 |
|
---|
[15145] | 906 | private static ISymbolicExpressionTreeNode MakeRoot(ISymbolicExpressionTreeNode a, ISymbolicExpressionTreeNode b) {
|
---|
[14843] | 907 | if (IsConstant(a) && IsConstant(b)) {
|
---|
| 908 | var constA = a as ConstantTreeNode;
|
---|
| 909 | var constB = b as ConstantTreeNode;
|
---|
| 910 | return MakeConstant(Math.Pow(constA.Value, 1.0 / Math.Round(constB.Value)));
|
---|
| 911 | } else if (IsFactor(a) && IsConstant(b)) {
|
---|
| 912 | var factNode = a as FactorVariableTreeNode;
|
---|
| 913 | var constNode = b as ConstantTreeNode;
|
---|
| 914 | return MakeFactor(factNode.Symbol, factNode.VariableName,
|
---|
| 915 | factNode.Weights.Select(w => Math.Pow(w, 1.0 / Math.Round(constNode.Value))));
|
---|
| 916 | } else if (IsBinFactor(a) && IsConstant(b)) {
|
---|
| 917 | var binFactor = a as BinaryFactorVariableTreeNode;
|
---|
| 918 | var constNode = b as ConstantTreeNode;
|
---|
| 919 | return MakeBinFactor(binFactor.Symbol, binFactor.VariableName, binFactor.VariableValue, Math.Pow(binFactor.Weight, 1.0 / Math.Round(constNode.Value)));
|
---|
| 920 | } else if (IsConstant(a) && IsFactor(b)) {
|
---|
| 921 | var constNode = a as ConstantTreeNode;
|
---|
| 922 | var factNode = b as FactorVariableTreeNode;
|
---|
| 923 | return MakeFactor(factNode.Symbol, factNode.VariableName, factNode.Weights.Select(w => Math.Pow(constNode.Value, 1.0 / Math.Round(w))));
|
---|
| 924 | } else if (IsConstant(a) && IsBinFactor(b)) {
|
---|
| 925 | var constNode = a as ConstantTreeNode;
|
---|
| 926 | var factNode = b as BinaryFactorVariableTreeNode;
|
---|
| 927 | return MakeBinFactor(factNode.Symbol, factNode.VariableName, factNode.VariableValue, Math.Pow(constNode.Value, 1.0 / Math.Round(factNode.Weight)));
|
---|
| 928 | } else if (IsFactor(a) && IsFactor(b) && AreSameTypeAndVariable(a, b)) {
|
---|
| 929 | var node0 = a as FactorVariableTreeNode;
|
---|
| 930 | var node1 = b as FactorVariableTreeNode;
|
---|
| 931 | return MakeFactor(node0.Symbol, node0.VariableName, node0.Weights.Zip(node1.Weights, (u, v) => Math.Pow(u, 1.0 / Math.Round(v))));
|
---|
| 932 | } else if (IsConstant(b)) {
|
---|
| 933 | var constB = b as ConstantTreeNode;
|
---|
| 934 | var constBValue = Math.Round(constB.Value);
|
---|
| 935 | if (constBValue.IsAlmost(1.0)) {
|
---|
| 936 | return a;
|
---|
| 937 | } else if (constBValue.IsAlmost(0.0)) {
|
---|
| 938 | return MakeConstant(1.0);
|
---|
| 939 | } else if (constBValue.IsAlmost(-1.0)) {
|
---|
| 940 | return MakeFraction(MakeConstant(1.0), a);
|
---|
| 941 | } else if (constBValue < 0) {
|
---|
| 942 | var rootNode = rootSymbol.CreateTreeNode();
|
---|
| 943 | rootNode.AddSubtree(a);
|
---|
| 944 | rootNode.AddSubtree(MakeConstant(-1.0 * constBValue));
|
---|
| 945 | return MakeFraction(MakeConstant(1.0), rootNode);
|
---|
| 946 | } else {
|
---|
| 947 | var rootNode = rootSymbol.CreateTreeNode();
|
---|
| 948 | rootNode.AddSubtree(a);
|
---|
| 949 | rootNode.AddSubtree(MakeConstant(constBValue));
|
---|
| 950 | return rootNode;
|
---|
| 951 | }
|
---|
| 952 | } else {
|
---|
| 953 | var rootNode = rootSymbol.CreateTreeNode();
|
---|
| 954 | rootNode.AddSubtree(a);
|
---|
| 955 | rootNode.AddSubtree(b);
|
---|
| 956 | return rootNode;
|
---|
| 957 | }
|
---|
| 958 | }
|
---|
| 959 |
|
---|
| 960 |
|
---|
[15145] | 961 | private static ISymbolicExpressionTreeNode MakePower(ISymbolicExpressionTreeNode a, ISymbolicExpressionTreeNode b) {
|
---|
[14843] | 962 | if (IsConstant(a) && IsConstant(b)) {
|
---|
| 963 | var constA = a as ConstantTreeNode;
|
---|
| 964 | var constB = b as ConstantTreeNode;
|
---|
| 965 | return MakeConstant(Math.Pow(constA.Value, Math.Round(constB.Value)));
|
---|
| 966 | } else if (IsFactor(a) && IsConstant(b)) {
|
---|
| 967 | var factNode = a as FactorVariableTreeNode;
|
---|
| 968 | var constNode = b as ConstantTreeNode;
|
---|
| 969 | return MakeFactor(factNode.Symbol, factNode.VariableName, factNode.Weights.Select(w => Math.Pow(w, Math.Round(constNode.Value))));
|
---|
| 970 | } else if (IsBinFactor(a) && IsConstant(b)) {
|
---|
| 971 | var binFactor = a as BinaryFactorVariableTreeNode;
|
---|
| 972 | var constNode = b as ConstantTreeNode;
|
---|
| 973 | return MakeBinFactor(binFactor.Symbol, binFactor.VariableName, binFactor.VariableValue, Math.Pow(binFactor.Weight, Math.Round(constNode.Value)));
|
---|
| 974 | } else if (IsConstant(a) && IsFactor(b)) {
|
---|
| 975 | var constNode = a as ConstantTreeNode;
|
---|
| 976 | var factNode = b as FactorVariableTreeNode;
|
---|
| 977 | return MakeFactor(factNode.Symbol, factNode.VariableName, factNode.Weights.Select(w => Math.Pow(constNode.Value, Math.Round(w))));
|
---|
| 978 | } else if (IsConstant(a) && IsBinFactor(b)) {
|
---|
| 979 | var constNode = a as ConstantTreeNode;
|
---|
| 980 | var factNode = b as BinaryFactorVariableTreeNode;
|
---|
| 981 | return MakeBinFactor(factNode.Symbol, factNode.VariableName, factNode.VariableValue, Math.Pow(constNode.Value, Math.Round(factNode.Weight)));
|
---|
| 982 | } else if (IsFactor(a) && IsFactor(b) && AreSameTypeAndVariable(a, b)) {
|
---|
| 983 | var node0 = a as FactorVariableTreeNode;
|
---|
| 984 | var node1 = b as FactorVariableTreeNode;
|
---|
| 985 | return MakeFactor(node0.Symbol, node0.VariableName, node0.Weights.Zip(node1.Weights, (u, v) => Math.Pow(u, Math.Round(v))));
|
---|
| 986 | } else if (IsConstant(b)) {
|
---|
| 987 | var constB = b as ConstantTreeNode;
|
---|
| 988 | double exponent = Math.Round(constB.Value);
|
---|
| 989 | if (exponent.IsAlmost(0.0)) {
|
---|
| 990 | return MakeConstant(1.0);
|
---|
| 991 | } else if (exponent.IsAlmost(1.0)) {
|
---|
| 992 | return a;
|
---|
| 993 | } else if (exponent.IsAlmost(-1.0)) {
|
---|
| 994 | return MakeFraction(MakeConstant(1.0), a);
|
---|
| 995 | } else if (exponent < 0) {
|
---|
| 996 | var powNode = powSymbol.CreateTreeNode();
|
---|
| 997 | powNode.AddSubtree(a);
|
---|
| 998 | powNode.AddSubtree(MakeConstant(-1.0 * exponent));
|
---|
| 999 | return MakeFraction(MakeConstant(1.0), powNode);
|
---|
| 1000 | } else {
|
---|
| 1001 | var powNode = powSymbol.CreateTreeNode();
|
---|
| 1002 | powNode.AddSubtree(a);
|
---|
| 1003 | powNode.AddSubtree(MakeConstant(exponent));
|
---|
| 1004 | return powNode;
|
---|
| 1005 | }
|
---|
| 1006 | } else {
|
---|
| 1007 | var powNode = powSymbol.CreateTreeNode();
|
---|
| 1008 | powNode.AddSubtree(a);
|
---|
| 1009 | powNode.AddSubtree(b);
|
---|
| 1010 | return powNode;
|
---|
| 1011 | }
|
---|
| 1012 | }
|
---|
| 1013 |
|
---|
| 1014 |
|
---|
| 1015 | // MakeFraction, MakeProduct and MakeSum take two already simplified trees and create a new simplified tree
|
---|
[15145] | 1016 | private static ISymbolicExpressionTreeNode MakeFraction(ISymbolicExpressionTreeNode a, ISymbolicExpressionTreeNode b) {
|
---|
[14843] | 1017 | if (IsConstant(a) && IsConstant(b)) {
|
---|
| 1018 | // fold constants
|
---|
| 1019 | return MakeConstant(((ConstantTreeNode)a).Value / ((ConstantTreeNode)b).Value);
|
---|
| 1020 | } else if ((IsConstant(a) && !((ConstantTreeNode)a).Value.IsAlmost(1.0))) {
|
---|
| 1021 | return MakeFraction(MakeConstant(1.0), MakeProduct(b, Invert(a)));
|
---|
| 1022 | } else if (IsVariableBase(a) && IsConstant(b)) {
|
---|
| 1023 | // merge constant values into variable weights
|
---|
| 1024 | var constB = ((ConstantTreeNode)b).Value;
|
---|
| 1025 | ((VariableTreeNodeBase)a).Weight /= constB;
|
---|
| 1026 | return a;
|
---|
| 1027 | } else if (IsFactor(a) && IsConstant(b)) {
|
---|
| 1028 | var factNode = a as FactorVariableTreeNode;
|
---|
| 1029 | var constNode = b as ConstantTreeNode;
|
---|
| 1030 | return MakeFactor(factNode.Symbol, factNode.VariableName, factNode.Weights.Select(w => w / constNode.Value));
|
---|
| 1031 | } else if (IsBinFactor(a) && IsConstant(b)) {
|
---|
| 1032 | var factNode = a as BinaryFactorVariableTreeNode;
|
---|
| 1033 | var constNode = b as ConstantTreeNode;
|
---|
| 1034 | return MakeBinFactor(factNode.Symbol, factNode.VariableName, factNode.VariableValue, factNode.Weight / constNode.Value);
|
---|
| 1035 | } else if (IsFactor(a) && IsFactor(b) && AreSameTypeAndVariable(a, b)) {
|
---|
| 1036 | var node0 = a as FactorVariableTreeNode;
|
---|
| 1037 | var node1 = b as FactorVariableTreeNode;
|
---|
| 1038 | return MakeFactor(node0.Symbol, node0.VariableName, node0.Weights.Zip(node1.Weights, (u, v) => u / v));
|
---|
| 1039 | } else if (IsFactor(a) && IsBinFactor(b) && ((IVariableTreeNode)a).VariableName == ((IVariableTreeNode)b).VariableName) {
|
---|
| 1040 | var node0 = a as FactorVariableTreeNode;
|
---|
| 1041 | var node1 = b as BinaryFactorVariableTreeNode;
|
---|
| 1042 | var varValues = node0.Symbol.GetVariableValues(node0.VariableName).ToArray();
|
---|
| 1043 | var wi = Array.IndexOf(varValues, node1.VariableValue);
|
---|
| 1044 | if (wi < 0) throw new ArgumentException();
|
---|
| 1045 | var newWeighs = new double[varValues.Length];
|
---|
| 1046 | node0.Weights.CopyTo(newWeighs, 0);
|
---|
| 1047 | for (int i = 0; i < newWeighs.Length; i++)
|
---|
| 1048 | if (wi == i) newWeighs[i] /= node1.Weight;
|
---|
| 1049 | else newWeighs[i] /= 0.0;
|
---|
| 1050 | return MakeFactor(node0.Symbol, node0.VariableName, newWeighs);
|
---|
| 1051 | } else if (IsFactor(a)) {
|
---|
| 1052 | return MakeFraction(MakeConstant(1.0), MakeProduct(b, Invert(a)));
|
---|
| 1053 | } else if (IsVariableBase(a) && IsVariableBase(b) && AreSameTypeAndVariable(a, b) && !IsBinFactor(b)) {
|
---|
| 1054 | // cancel variables (not allowed for bin factors because of division by zero)
|
---|
| 1055 | var aVar = a as VariableTreeNode;
|
---|
| 1056 | var bVar = b as VariableTreeNode;
|
---|
| 1057 | return MakeConstant(aVar.Weight / bVar.Weight);
|
---|
| 1058 | } else if (IsAddition(a) && IsConstant(b)) {
|
---|
| 1059 | return a.Subtrees
|
---|
| 1060 | .Select(x => GetSimplifiedTree(x))
|
---|
| 1061 | .Select(x => MakeFraction(x, GetSimplifiedTree(b)))
|
---|
| 1062 | .Aggregate((c, d) => MakeSum(c, d));
|
---|
| 1063 | } else if (IsMultiplication(a) && IsConstant(b)) {
|
---|
| 1064 | return MakeProduct(a, Invert(b));
|
---|
| 1065 | } else if (IsDivision(a) && IsConstant(b)) {
|
---|
| 1066 | // (a1 / a2) / c => (a1 / (a2 * c))
|
---|
| 1067 | return MakeFraction(a.GetSubtree(0), MakeProduct(a.GetSubtree(1), b));
|
---|
| 1068 | } else if (IsDivision(a) && IsDivision(b)) {
|
---|
| 1069 | // (a1 / a2) / (b1 / b2) =>
|
---|
| 1070 | return MakeFraction(MakeProduct(a.GetSubtree(0), b.GetSubtree(1)), MakeProduct(a.GetSubtree(1), b.GetSubtree(0)));
|
---|
| 1071 | } else if (IsDivision(a)) {
|
---|
| 1072 | // (a1 / a2) / b => (a1 / (a2 * b))
|
---|
| 1073 | return MakeFraction(a.GetSubtree(0), MakeProduct(a.GetSubtree(1), b));
|
---|
| 1074 | } else if (IsDivision(b)) {
|
---|
| 1075 | // a / (b1 / b2) => (a * b2) / b1
|
---|
| 1076 | return MakeFraction(MakeProduct(a, b.GetSubtree(1)), b.GetSubtree(0));
|
---|
[17072] | 1077 | } else if (IsAnalyticalQuotient(a)) {
|
---|
| 1078 | return MakeAnalyticalQuotient(a.GetSubtree(0), MakeProduct(a.GetSubtree(1), b));
|
---|
[14843] | 1079 | } else {
|
---|
| 1080 | var div = divSymbol.CreateTreeNode();
|
---|
| 1081 | div.AddSubtree(a);
|
---|
| 1082 | div.AddSubtree(b);
|
---|
| 1083 | return div;
|
---|
| 1084 | }
|
---|
| 1085 | }
|
---|
| 1086 |
|
---|
[15145] | 1087 | private static ISymbolicExpressionTreeNode MakeSum(ISymbolicExpressionTreeNode a, ISymbolicExpressionTreeNode b) {
|
---|
[14843] | 1088 | if (IsConstant(a) && IsConstant(b)) {
|
---|
| 1089 | // fold constants
|
---|
| 1090 | ((ConstantTreeNode)a).Value += ((ConstantTreeNode)b).Value;
|
---|
| 1091 | return a;
|
---|
| 1092 | } else if (IsConstant(a)) {
|
---|
| 1093 | // c + x => x + c
|
---|
| 1094 | // b is not constant => make sure constant is on the right
|
---|
| 1095 | return MakeSum(b, a);
|
---|
| 1096 | } else if (IsConstant(b) && ((ConstantTreeNode)b).Value.IsAlmost(0.0)) {
|
---|
| 1097 | // x + 0 => x
|
---|
| 1098 | return a;
|
---|
| 1099 | } else if (IsFactor(a) && IsConstant(b)) {
|
---|
| 1100 | var factNode = a as FactorVariableTreeNode;
|
---|
| 1101 | var constNode = b as ConstantTreeNode;
|
---|
| 1102 | return MakeFactor(factNode.Symbol, factNode.VariableName, factNode.Weights.Select((w) => w + constNode.Value));
|
---|
| 1103 | } else if (IsFactor(a) && IsFactor(b) && AreSameTypeAndVariable(a, b)) {
|
---|
| 1104 | var node0 = a as FactorVariableTreeNode;
|
---|
| 1105 | var node1 = b as FactorVariableTreeNode;
|
---|
| 1106 | return MakeFactor(node0.Symbol, node0.VariableName, node0.Weights.Zip(node1.Weights, (u, v) => u + v));
|
---|
| 1107 | } else if (IsBinFactor(a) && IsFactor(b)) {
|
---|
| 1108 | return MakeSum(b, a);
|
---|
| 1109 | } else if (IsFactor(a) && IsBinFactor(b) &&
|
---|
| 1110 | ((IVariableTreeNode)a).VariableName == ((IVariableTreeNode)b).VariableName) {
|
---|
| 1111 | var node0 = a as FactorVariableTreeNode;
|
---|
| 1112 | var node1 = b as BinaryFactorVariableTreeNode;
|
---|
| 1113 | var varValues = node0.Symbol.GetVariableValues(node0.VariableName).ToArray();
|
---|
| 1114 | var wi = Array.IndexOf(varValues, node1.VariableValue);
|
---|
| 1115 | if (wi < 0) throw new ArgumentException();
|
---|
| 1116 | var newWeighs = new double[varValues.Length];
|
---|
| 1117 | node0.Weights.CopyTo(newWeighs, 0);
|
---|
| 1118 | newWeighs[wi] += node1.Weight;
|
---|
| 1119 | return MakeFactor(node0.Symbol, node0.VariableName, newWeighs);
|
---|
| 1120 | } else if (IsAddition(a) && IsAddition(b)) {
|
---|
| 1121 | // merge additions
|
---|
| 1122 | var add = addSymbol.CreateTreeNode();
|
---|
| 1123 | // add all sub trees except for the last
|
---|
| 1124 | for (int i = 0; i < a.Subtrees.Count() - 1; i++) add.AddSubtree(a.GetSubtree(i));
|
---|
| 1125 | for (int i = 0; i < b.Subtrees.Count() - 1; i++) add.AddSubtree(b.GetSubtree(i));
|
---|
| 1126 | if (IsConstant(a.Subtrees.Last()) && IsConstant(b.Subtrees.Last())) {
|
---|
| 1127 | add.AddSubtree(MakeSum(a.Subtrees.Last(), b.Subtrees.Last()));
|
---|
| 1128 | } else if (IsConstant(a.Subtrees.Last())) {
|
---|
| 1129 | add.AddSubtree(b.Subtrees.Last());
|
---|
| 1130 | add.AddSubtree(a.Subtrees.Last());
|
---|
| 1131 | } else {
|
---|
| 1132 | add.AddSubtree(a.Subtrees.Last());
|
---|
| 1133 | add.AddSubtree(b.Subtrees.Last());
|
---|
| 1134 | }
|
---|
| 1135 | MergeVariablesInSum(add);
|
---|
| 1136 | if (add.Subtrees.Count() == 1) {
|
---|
| 1137 | return add.GetSubtree(0);
|
---|
| 1138 | } else {
|
---|
| 1139 | return add;
|
---|
| 1140 | }
|
---|
| 1141 | } else if (IsAddition(b)) {
|
---|
| 1142 | return MakeSum(b, a);
|
---|
| 1143 | } else if (IsAddition(a) && IsConstant(b)) {
|
---|
| 1144 | // a is an addition and b is a constant => append b to a and make sure the constants are merged
|
---|
| 1145 | var add = addSymbol.CreateTreeNode();
|
---|
| 1146 | // add all sub trees except for the last
|
---|
| 1147 | for (int i = 0; i < a.Subtrees.Count() - 1; i++) add.AddSubtree(a.GetSubtree(i));
|
---|
| 1148 | if (IsConstant(a.Subtrees.Last()))
|
---|
| 1149 | add.AddSubtree(MakeSum(a.Subtrees.Last(), b));
|
---|
| 1150 | else {
|
---|
| 1151 | add.AddSubtree(a.Subtrees.Last());
|
---|
| 1152 | add.AddSubtree(b);
|
---|
| 1153 | }
|
---|
| 1154 | return add;
|
---|
| 1155 | } else if (IsAddition(a)) {
|
---|
| 1156 | // a is already an addition => append b
|
---|
| 1157 | var add = addSymbol.CreateTreeNode();
|
---|
| 1158 | add.AddSubtree(b);
|
---|
| 1159 | foreach (var subtree in a.Subtrees) {
|
---|
| 1160 | add.AddSubtree(subtree);
|
---|
| 1161 | }
|
---|
| 1162 | MergeVariablesInSum(add);
|
---|
| 1163 | if (add.Subtrees.Count() == 1) {
|
---|
| 1164 | return add.GetSubtree(0);
|
---|
| 1165 | } else {
|
---|
| 1166 | return add;
|
---|
| 1167 | }
|
---|
| 1168 | } else {
|
---|
| 1169 | var add = addSymbol.CreateTreeNode();
|
---|
| 1170 | add.AddSubtree(a);
|
---|
| 1171 | add.AddSubtree(b);
|
---|
| 1172 | MergeVariablesInSum(add);
|
---|
| 1173 | if (add.Subtrees.Count() == 1) {
|
---|
| 1174 | return add.GetSubtree(0);
|
---|
| 1175 | } else {
|
---|
| 1176 | return add;
|
---|
| 1177 | }
|
---|
| 1178 | }
|
---|
| 1179 | }
|
---|
| 1180 |
|
---|
| 1181 | // makes sure variable symbols in sums are combined
|
---|
[15145] | 1182 | private static void MergeVariablesInSum(ISymbolicExpressionTreeNode sum) {
|
---|
[14843] | 1183 | var subtrees = new List<ISymbolicExpressionTreeNode>(sum.Subtrees);
|
---|
| 1184 | while (sum.Subtrees.Any()) sum.RemoveSubtree(0);
|
---|
| 1185 | var groupedVarNodes = from node in subtrees.OfType<IVariableTreeNode>()
|
---|
| 1186 | where node.SubtreeCount == 0
|
---|
| 1187 | group node by GroupId(node) into g
|
---|
| 1188 | select g;
|
---|
| 1189 | var constant = (from node in subtrees.OfType<ConstantTreeNode>()
|
---|
| 1190 | select node.Value).DefaultIfEmpty(0.0).Sum();
|
---|
| 1191 | var unchangedSubtrees = subtrees.Where(t => t.SubtreeCount > 0 || !(t is IVariableTreeNode) && !(t is ConstantTreeNode));
|
---|
| 1192 |
|
---|
| 1193 | foreach (var variableNodeGroup in groupedVarNodes) {
|
---|
| 1194 | var firstNode = variableNodeGroup.First();
|
---|
| 1195 | if (firstNode is VariableTreeNodeBase) {
|
---|
| 1196 | var representative = firstNode as VariableTreeNodeBase;
|
---|
| 1197 | var weightSum = variableNodeGroup.Cast<VariableTreeNodeBase>().Select(t => t.Weight).Sum();
|
---|
| 1198 | representative.Weight = weightSum;
|
---|
| 1199 | sum.AddSubtree(representative);
|
---|
| 1200 | } else if (firstNode is FactorVariableTreeNode) {
|
---|
| 1201 | var representative = firstNode as FactorVariableTreeNode;
|
---|
| 1202 | foreach (var node in variableNodeGroup.Skip(1).Cast<FactorVariableTreeNode>()) {
|
---|
| 1203 | for (int j = 0; j < representative.Weights.Length; j++) {
|
---|
| 1204 | representative.Weights[j] += node.Weights[j];
|
---|
| 1205 | }
|
---|
| 1206 | }
|
---|
| 1207 | sum.AddSubtree(representative);
|
---|
| 1208 | }
|
---|
| 1209 | }
|
---|
| 1210 | foreach (var unchangedSubtree in unchangedSubtrees)
|
---|
| 1211 | sum.AddSubtree(unchangedSubtree);
|
---|
| 1212 | if (!constant.IsAlmost(0.0)) {
|
---|
| 1213 | sum.AddSubtree(MakeConstant(constant));
|
---|
| 1214 | }
|
---|
| 1215 | }
|
---|
| 1216 |
|
---|
| 1217 | // nodes referencing variables can be grouped if they have
|
---|
[15145] | 1218 | private static string GroupId(IVariableTreeNode node) {
|
---|
[14843] | 1219 | var binaryFactorNode = node as BinaryFactorVariableTreeNode;
|
---|
| 1220 | var factorNode = node as FactorVariableTreeNode;
|
---|
| 1221 | var variableNode = node as VariableTreeNode;
|
---|
| 1222 | var laggedVarNode = node as LaggedVariableTreeNode;
|
---|
| 1223 | if (variableNode != null) {
|
---|
| 1224 | return "var " + variableNode.VariableName;
|
---|
| 1225 | } else if (binaryFactorNode != null) {
|
---|
| 1226 | return "binfactor " + binaryFactorNode.VariableName + " " + binaryFactorNode.VariableValue;
|
---|
| 1227 | } else if (factorNode != null) {
|
---|
| 1228 | return "factor " + factorNode.VariableName;
|
---|
| 1229 | } else if (laggedVarNode != null) {
|
---|
| 1230 | return "lagged " + laggedVarNode.VariableName + " " + laggedVarNode.Lag;
|
---|
| 1231 | } else {
|
---|
| 1232 | throw new NotSupportedException();
|
---|
| 1233 | }
|
---|
| 1234 | }
|
---|
| 1235 |
|
---|
| 1236 |
|
---|
[15145] | 1237 | private static ISymbolicExpressionTreeNode MakeProduct(ISymbolicExpressionTreeNode a, ISymbolicExpressionTreeNode b) {
|
---|
[14843] | 1238 | if (IsConstant(a) && IsConstant(b)) {
|
---|
| 1239 | // fold constants
|
---|
| 1240 | return MakeConstant(((ConstantTreeNode)a).Value * ((ConstantTreeNode)b).Value);
|
---|
| 1241 | } else if (IsConstant(a)) {
|
---|
| 1242 | // a * $ => $ * a
|
---|
| 1243 | return MakeProduct(b, a);
|
---|
| 1244 | } else if (IsFactor(a) && IsFactor(b) && AreSameTypeAndVariable(a, b)) {
|
---|
| 1245 | var node0 = a as FactorVariableTreeNode;
|
---|
| 1246 | var node1 = b as FactorVariableTreeNode;
|
---|
| 1247 | return MakeFactor(node0.Symbol, node0.VariableName, node0.Weights.Zip(node1.Weights, (u, v) => u * v));
|
---|
| 1248 | } else if (IsBinFactor(a) && IsBinFactor(b) && AreSameTypeAndVariable(a, b)) {
|
---|
| 1249 | var node0 = a as BinaryFactorVariableTreeNode;
|
---|
| 1250 | var node1 = b as BinaryFactorVariableTreeNode;
|
---|
| 1251 | return MakeBinFactor(node0.Symbol, node0.VariableName, node0.VariableValue, node0.Weight * node1.Weight);
|
---|
| 1252 | } else if (IsFactor(a) && IsConstant(b)) {
|
---|
| 1253 | var node0 = a as FactorVariableTreeNode;
|
---|
| 1254 | var node1 = b as ConstantTreeNode;
|
---|
| 1255 | return MakeFactor(node0.Symbol, node0.VariableName, node0.Weights.Select(w => w * node1.Value));
|
---|
| 1256 | } else if (IsBinFactor(a) && IsConstant(b)) {
|
---|
| 1257 | var node0 = a as BinaryFactorVariableTreeNode;
|
---|
| 1258 | var node1 = b as ConstantTreeNode;
|
---|
| 1259 | return MakeBinFactor(node0.Symbol, node0.VariableName, node0.VariableValue, node0.Weight * node1.Value);
|
---|
| 1260 | } else if (IsBinFactor(a) && IsFactor(b)) {
|
---|
| 1261 | return MakeProduct(b, a);
|
---|
| 1262 | } else if (IsFactor(a) && IsBinFactor(b) &&
|
---|
| 1263 | ((IVariableTreeNode)a).VariableName == ((IVariableTreeNode)b).VariableName) {
|
---|
| 1264 | var node0 = a as FactorVariableTreeNode;
|
---|
| 1265 | var node1 = b as BinaryFactorVariableTreeNode;
|
---|
| 1266 | var varValues = node0.Symbol.GetVariableValues(node0.VariableName).ToArray();
|
---|
| 1267 | var wi = Array.IndexOf(varValues, node1.VariableValue);
|
---|
| 1268 | if (wi < 0) throw new ArgumentException();
|
---|
| 1269 | return MakeBinFactor(node1.Symbol, node1.VariableName, node1.VariableValue, node1.Weight * node0.Weights[wi]);
|
---|
| 1270 | } else if (IsConstant(b) && ((ConstantTreeNode)b).Value.IsAlmost(1.0)) {
|
---|
| 1271 | // $ * 1.0 => $
|
---|
| 1272 | return a;
|
---|
[17066] | 1273 | } else if (IsConstant(b) && ((ConstantTreeNode)b).Value.IsAlmost(0.0)) {
|
---|
| 1274 | return MakeConstant(0);
|
---|
[14843] | 1275 | } else if (IsConstant(b) && IsVariableBase(a)) {
|
---|
| 1276 | // multiply constants into variables weights
|
---|
| 1277 | ((VariableTreeNodeBase)a).Weight *= ((ConstantTreeNode)b).Value;
|
---|
| 1278 | return a;
|
---|
| 1279 | } else if (IsConstant(b) && IsAddition(a) ||
|
---|
| 1280 | IsFactor(b) && IsAddition(a) ||
|
---|
| 1281 | IsBinFactor(b) && IsAddition(a)) {
|
---|
| 1282 | // multiply constants into additions
|
---|
| 1283 | return a.Subtrees.Select(x => MakeProduct(GetSimplifiedTree(x), GetSimplifiedTree(b))).Aggregate((c, d) => MakeSum(c, d));
|
---|
| 1284 | } else if (IsDivision(a) && IsDivision(b)) {
|
---|
| 1285 | // (a1 / a2) * (b1 / b2) => (a1 * b1) / (a2 * b2)
|
---|
| 1286 | return MakeFraction(MakeProduct(a.GetSubtree(0), b.GetSubtree(0)), MakeProduct(a.GetSubtree(1), b.GetSubtree(1)));
|
---|
| 1287 | } else if (IsDivision(a)) {
|
---|
| 1288 | // (a1 / a2) * b => (a1 * b) / a2
|
---|
| 1289 | return MakeFraction(MakeProduct(a.GetSubtree(0), b), a.GetSubtree(1));
|
---|
| 1290 | } else if (IsDivision(b)) {
|
---|
| 1291 | // a * (b1 / b2) => (b1 * a) / b2
|
---|
| 1292 | return MakeFraction(MakeProduct(b.GetSubtree(0), a), b.GetSubtree(1));
|
---|
| 1293 | } else if (IsMultiplication(a) && IsMultiplication(b)) {
|
---|
| 1294 | // merge multiplications (make sure constants are merged)
|
---|
| 1295 | var mul = mulSymbol.CreateTreeNode();
|
---|
| 1296 | for (int i = 0; i < a.Subtrees.Count(); i++) mul.AddSubtree(a.GetSubtree(i));
|
---|
| 1297 | for (int i = 0; i < b.Subtrees.Count(); i++) mul.AddSubtree(b.GetSubtree(i));
|
---|
| 1298 | MergeVariablesAndConstantsInProduct(mul);
|
---|
| 1299 | return mul;
|
---|
| 1300 | } else if (IsMultiplication(b)) {
|
---|
| 1301 | return MakeProduct(b, a);
|
---|
| 1302 | } else if (IsMultiplication(a)) {
|
---|
| 1303 | // a is already an multiplication => append b
|
---|
| 1304 | a.AddSubtree(GetSimplifiedTree(b));
|
---|
| 1305 | MergeVariablesAndConstantsInProduct(a);
|
---|
| 1306 | return a;
|
---|
[17072] | 1307 | } else if (IsAbsolute(a) && IsAbsolute(b)) {
|
---|
| 1308 | return MakeAbs(MakeProduct(a.GetSubtree(0), b.GetSubtree(0)));
|
---|
| 1309 | } else if (IsAbsolute(a) && IsConstant(b)) {
|
---|
| 1310 | var constNode = b as ConstantTreeNode;
|
---|
| 1311 | var posF = Math.Abs(constNode.Value);
|
---|
| 1312 | if (constNode.Value > 0) {
|
---|
| 1313 | return MakeAbs(MakeProduct(a.GetSubtree(0), MakeConstant(posF)));
|
---|
| 1314 | } else {
|
---|
| 1315 | var mul = mulSymbol.CreateTreeNode();
|
---|
| 1316 | mul.AddSubtree(MakeAbs(MakeProduct(a.GetSubtree(0), MakeConstant(posF))));
|
---|
| 1317 | mul.AddSubtree(MakeConstant(-1.0));
|
---|
| 1318 | return mul;
|
---|
| 1319 | }
|
---|
| 1320 | } else if (IsAnalyticalQuotient(a)) {
|
---|
| 1321 | return MakeAnalyticalQuotient(MakeProduct(a.GetSubtree(0), b), a.GetSubtree(1));
|
---|
[14843] | 1322 | } else {
|
---|
| 1323 | var mul = mulSymbol.CreateTreeNode();
|
---|
| 1324 | mul.AddSubtree(a);
|
---|
| 1325 | mul.AddSubtree(b);
|
---|
| 1326 | MergeVariablesAndConstantsInProduct(mul);
|
---|
| 1327 | return mul;
|
---|
| 1328 | }
|
---|
| 1329 | }
|
---|
| 1330 |
|
---|
| 1331 | #endregion
|
---|
| 1332 |
|
---|
| 1333 | #region helper functions
|
---|
| 1334 |
|
---|
[15145] | 1335 | private static bool ContainsVariableCondition(ISymbolicExpressionTreeNode node) {
|
---|
[14843] | 1336 | if (node.Symbol is VariableCondition) return true;
|
---|
| 1337 | foreach (var subtree in node.Subtrees)
|
---|
| 1338 | if (ContainsVariableCondition(subtree)) return true;
|
---|
| 1339 | return false;
|
---|
| 1340 | }
|
---|
| 1341 |
|
---|
[15145] | 1342 | private static ISymbolicExpressionTreeNode AddLagToDynamicNodes(ISymbolicExpressionTreeNode node, int lag) {
|
---|
[14843] | 1343 | var laggedTreeNode = node as ILaggedTreeNode;
|
---|
| 1344 | var variableNode = node as VariableTreeNode;
|
---|
| 1345 | var variableConditionNode = node as VariableConditionTreeNode;
|
---|
| 1346 | if (laggedTreeNode != null)
|
---|
| 1347 | laggedTreeNode.Lag += lag;
|
---|
| 1348 | else if (variableNode != null) {
|
---|
| 1349 | var laggedVariableNode = (LaggedVariableTreeNode)laggedVariableSymbol.CreateTreeNode();
|
---|
| 1350 | laggedVariableNode.Lag = lag;
|
---|
| 1351 | laggedVariableNode.VariableName = variableNode.VariableName;
|
---|
| 1352 | return laggedVariableNode;
|
---|
| 1353 | } else if (variableConditionNode != null) {
|
---|
| 1354 | throw new NotSupportedException("Removal of time lags around variable condition symbols is not allowed.");
|
---|
| 1355 | }
|
---|
| 1356 | var subtrees = new List<ISymbolicExpressionTreeNode>(node.Subtrees);
|
---|
| 1357 | while (node.SubtreeCount > 0) node.RemoveSubtree(0);
|
---|
| 1358 | foreach (var subtree in subtrees) {
|
---|
| 1359 | node.AddSubtree(AddLagToDynamicNodes(subtree, lag));
|
---|
| 1360 | }
|
---|
| 1361 | return node;
|
---|
| 1362 | }
|
---|
| 1363 |
|
---|
[15145] | 1364 | private static bool AreSameTypeAndVariable(ISymbolicExpressionTreeNode a, ISymbolicExpressionTreeNode b) {
|
---|
[14843] | 1365 | return GroupId((IVariableTreeNode)a) == GroupId((IVariableTreeNode)b);
|
---|
| 1366 | }
|
---|
| 1367 |
|
---|
| 1368 | // helper to combine the constant factors in products and to combine variables (powers of 2, 3...)
|
---|
[15145] | 1369 | private static void MergeVariablesAndConstantsInProduct(ISymbolicExpressionTreeNode prod) {
|
---|
[14843] | 1370 | var subtrees = new List<ISymbolicExpressionTreeNode>(prod.Subtrees);
|
---|
| 1371 | while (prod.Subtrees.Any()) prod.RemoveSubtree(0);
|
---|
| 1372 | var groupedVarNodes = from node in subtrees.OfType<IVariableTreeNode>()
|
---|
| 1373 | where node.SubtreeCount == 0
|
---|
| 1374 | group node by GroupId(node) into g
|
---|
| 1375 | orderby g.Count()
|
---|
| 1376 | select g;
|
---|
| 1377 | var constantProduct = (from node in subtrees.OfType<VariableTreeNodeBase>()
|
---|
| 1378 | select node.Weight)
|
---|
| 1379 | .Concat(from node in subtrees.OfType<ConstantTreeNode>()
|
---|
| 1380 | select node.Value)
|
---|
| 1381 | .DefaultIfEmpty(1.0)
|
---|
| 1382 | .Aggregate((c1, c2) => c1 * c2);
|
---|
| 1383 |
|
---|
| 1384 | var unchangedSubtrees = from tree in subtrees
|
---|
| 1385 | where tree.SubtreeCount > 0 || !(tree is IVariableTreeNode) && !(tree is ConstantTreeNode)
|
---|
| 1386 | select tree;
|
---|
| 1387 |
|
---|
| 1388 | foreach (var variableNodeGroup in groupedVarNodes) {
|
---|
| 1389 | var firstNode = variableNodeGroup.First();
|
---|
| 1390 | if (firstNode is VariableTreeNodeBase) {
|
---|
| 1391 | var representative = (VariableTreeNodeBase)firstNode;
|
---|
| 1392 | representative.Weight = 1.0;
|
---|
| 1393 | if (variableNodeGroup.Count() > 1) {
|
---|
| 1394 | var poly = mulSymbol.CreateTreeNode();
|
---|
| 1395 | for (int p = 0; p < variableNodeGroup.Count(); p++) {
|
---|
| 1396 | poly.AddSubtree((ISymbolicExpressionTreeNode)representative.Clone());
|
---|
| 1397 | }
|
---|
| 1398 | prod.AddSubtree(poly);
|
---|
| 1399 | } else {
|
---|
| 1400 | prod.AddSubtree(representative);
|
---|
| 1401 | }
|
---|
| 1402 | } else if (firstNode is FactorVariableTreeNode) {
|
---|
| 1403 | var representative = (FactorVariableTreeNode)firstNode;
|
---|
| 1404 | foreach (var node in variableNodeGroup.Skip(1).Cast<FactorVariableTreeNode>()) {
|
---|
| 1405 | for (int j = 0; j < representative.Weights.Length; j++) {
|
---|
| 1406 | representative.Weights[j] *= node.Weights[j];
|
---|
| 1407 | }
|
---|
| 1408 | }
|
---|
| 1409 | for (int j = 0; j < representative.Weights.Length; j++) {
|
---|
| 1410 | representative.Weights[j] *= constantProduct;
|
---|
| 1411 | }
|
---|
| 1412 | constantProduct = 1.0;
|
---|
| 1413 | // if the product already contains a factor it is not necessary to multiply a constant below
|
---|
| 1414 | prod.AddSubtree(representative);
|
---|
| 1415 | }
|
---|
| 1416 | }
|
---|
| 1417 |
|
---|
| 1418 | foreach (var unchangedSubtree in unchangedSubtrees)
|
---|
| 1419 | prod.AddSubtree(unchangedSubtree);
|
---|
| 1420 |
|
---|
| 1421 | if (!constantProduct.IsAlmost(1.0)) {
|
---|
| 1422 | prod.AddSubtree(MakeConstant(constantProduct));
|
---|
| 1423 | }
|
---|
| 1424 | }
|
---|
| 1425 |
|
---|
| 1426 |
|
---|
| 1427 | /// <summary>
|
---|
| 1428 | /// x => x * -1
|
---|
| 1429 | /// Is only used in cases where it is not necessary to create new tree nodes. Manipulates x directly.
|
---|
| 1430 | /// </summary>
|
---|
| 1431 | /// <param name="x"></param>
|
---|
| 1432 | /// <returns>-x</returns>
|
---|
[15145] | 1433 | private static ISymbolicExpressionTreeNode Negate(ISymbolicExpressionTreeNode x) {
|
---|
[14843] | 1434 | if (IsConstant(x)) {
|
---|
| 1435 | ((ConstantTreeNode)x).Value *= -1;
|
---|
| 1436 | } else if (IsVariableBase(x)) {
|
---|
| 1437 | var variableTree = (VariableTreeNodeBase)x;
|
---|
| 1438 | variableTree.Weight *= -1.0;
|
---|
| 1439 | } else if (IsFactor(x)) {
|
---|
| 1440 | var factorNode = (FactorVariableTreeNode)x;
|
---|
| 1441 | for (int i = 0; i < factorNode.Weights.Length; i++) factorNode.Weights[i] *= -1;
|
---|
| 1442 | } else if (IsBinFactor(x)) {
|
---|
| 1443 | var factorNode = (BinaryFactorVariableTreeNode)x;
|
---|
| 1444 | factorNode.Weight *= -1;
|
---|
| 1445 | } else if (IsAddition(x)) {
|
---|
| 1446 | // (x0 + x1 + .. + xn) * -1 => (-x0 + -x1 + .. + -xn)
|
---|
| 1447 | var subtrees = new List<ISymbolicExpressionTreeNode>(x.Subtrees);
|
---|
| 1448 | while (x.Subtrees.Any()) x.RemoveSubtree(0);
|
---|
| 1449 | foreach (var subtree in subtrees) {
|
---|
| 1450 | x.AddSubtree(Negate(subtree));
|
---|
| 1451 | }
|
---|
| 1452 | } else if (IsMultiplication(x) || IsDivision(x)) {
|
---|
| 1453 | // x0 * x1 * .. * xn * -1 => x0 * x1 * .. * -xn
|
---|
| 1454 | var lastSubTree = x.Subtrees.Last();
|
---|
| 1455 | x.RemoveSubtree(x.SubtreeCount - 1);
|
---|
| 1456 | x.AddSubtree(Negate(lastSubTree)); // last is maybe a constant, prefer to negate the constant
|
---|
| 1457 | } else {
|
---|
| 1458 | // any other function
|
---|
| 1459 | return MakeProduct(x, MakeConstant(-1));
|
---|
| 1460 | }
|
---|
| 1461 | return x;
|
---|
| 1462 | }
|
---|
| 1463 |
|
---|
| 1464 | /// <summary>
|
---|
| 1465 | /// x => 1/x
|
---|
| 1466 | /// Must create new tree nodes
|
---|
| 1467 | /// </summary>
|
---|
| 1468 | /// <param name="x"></param>
|
---|
| 1469 | /// <returns></returns>
|
---|
[15145] | 1470 | private static ISymbolicExpressionTreeNode Invert(ISymbolicExpressionTreeNode x) {
|
---|
[14843] | 1471 | if (IsConstant(x)) {
|
---|
| 1472 | return MakeConstant(1.0 / ((ConstantTreeNode)x).Value);
|
---|
| 1473 | } else if (IsFactor(x)) {
|
---|
| 1474 | var factorNode = (FactorVariableTreeNode)x;
|
---|
| 1475 | return MakeFactor(factorNode.Symbol, factorNode.VariableName, factorNode.Weights.Select(w => 1.0 / w));
|
---|
| 1476 | } else if (IsDivision(x)) {
|
---|
| 1477 | return MakeFraction(x.GetSubtree(1), x.GetSubtree(0));
|
---|
| 1478 | } else {
|
---|
| 1479 | // any other function
|
---|
| 1480 | return MakeFraction(MakeConstant(1), x);
|
---|
| 1481 | }
|
---|
| 1482 | }
|
---|
| 1483 |
|
---|
[15145] | 1484 | private static ISymbolicExpressionTreeNode MakeConstant(double value) {
|
---|
[14843] | 1485 | ConstantTreeNode constantTreeNode = (ConstantTreeNode)(constSymbol.CreateTreeNode());
|
---|
| 1486 | constantTreeNode.Value = value;
|
---|
| 1487 | return constantTreeNode;
|
---|
| 1488 | }
|
---|
| 1489 |
|
---|
[15145] | 1490 | private static ISymbolicExpressionTreeNode MakeFactor(FactorVariable sy, string variableName, IEnumerable<double> weights) {
|
---|
[14843] | 1491 | var tree = (FactorVariableTreeNode)sy.CreateTreeNode();
|
---|
| 1492 | tree.VariableName = variableName;
|
---|
| 1493 | tree.Weights = weights.ToArray();
|
---|
| 1494 | return tree;
|
---|
| 1495 | }
|
---|
[15145] | 1496 | private static ISymbolicExpressionTreeNode MakeBinFactor(BinaryFactorVariable sy, string variableName, string variableValue, double weight) {
|
---|
[14843] | 1497 | var tree = (BinaryFactorVariableTreeNode)sy.CreateTreeNode();
|
---|
| 1498 | tree.VariableName = variableName;
|
---|
| 1499 | tree.VariableValue = variableValue;
|
---|
| 1500 | tree.Weight = weight;
|
---|
| 1501 | return tree;
|
---|
| 1502 | }
|
---|
| 1503 |
|
---|
| 1504 |
|
---|
| 1505 | #endregion
|
---|
| 1506 | }
|
---|
| 1507 | }
|
---|