[14843] | 1 | #region License Information
|
---|
| 2 |
|
---|
| 3 | /* HeuristicLab
|
---|
[17180] | 4 | * Copyright (C) Heuristic and Evolutionary Algorithms Laboratory (HEAL)
|
---|
[14843] | 5 | *
|
---|
| 6 | * This file is part of HeuristicLab.
|
---|
| 7 | *
|
---|
| 8 | * HeuristicLab is free software: you can redistribute it and/or modify
|
---|
| 9 | * it under the terms of the GNU General Public License as published by
|
---|
| 10 | * the Free Software Foundation, either version 3 of the License, or
|
---|
| 11 | * (at your option) any later version.
|
---|
| 12 | *
|
---|
| 13 | * HeuristicLab is distributed in the hope that it will be useful,
|
---|
| 14 | * but WITHOUT ANY WARRANTY; without even the implied warranty of
|
---|
| 15 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
---|
| 16 | * GNU General Public License for more details.
|
---|
| 17 | *
|
---|
| 18 | * You should have received a copy of the GNU General Public License
|
---|
| 19 | * along with HeuristicLab. If not, see <http://www.gnu.org/licenses/>.
|
---|
| 20 | */
|
---|
| 21 |
|
---|
| 22 | #endregion
|
---|
| 23 |
|
---|
| 24 | using System;
|
---|
| 25 | using System.Collections.Generic;
|
---|
| 26 | using System.Linq;
|
---|
| 27 | using HeuristicLab.Common;
|
---|
| 28 | using HeuristicLab.Encodings.SymbolicExpressionTreeEncoding;
|
---|
| 29 |
|
---|
| 30 | namespace HeuristicLab.Problems.DataAnalysis.Symbolic {
|
---|
| 31 | /// <summary>
|
---|
| 32 | /// Simplifier for symbolic expressions
|
---|
| 33 | /// </summary>
|
---|
[17593] | 34 | public class VectorTreeSimplifier {
|
---|
[14949] | 35 | private static readonly Addition addSymbol = new Addition();
|
---|
| 36 | private static readonly Multiplication mulSymbol = new Multiplication();
|
---|
| 37 | private static readonly Division divSymbol = new Division();
|
---|
| 38 | private static readonly Constant constSymbol = new Constant();
|
---|
[16356] | 39 | private static readonly Absolute absSymbol = new Absolute();
|
---|
[14949] | 40 | private static readonly Logarithm logSymbol = new Logarithm();
|
---|
| 41 | private static readonly Exponential expSymbol = new Exponential();
|
---|
| 42 | private static readonly Root rootSymbol = new Root();
|
---|
| 43 | private static readonly Square sqrSymbol = new Square();
|
---|
| 44 | private static readonly SquareRoot sqrtSymbol = new SquareRoot();
|
---|
[16360] | 45 | private static readonly AnalyticQuotient aqSymbol = new AnalyticQuotient();
|
---|
[16356] | 46 | private static readonly Cube cubeSymbol = new Cube();
|
---|
| 47 | private static readonly CubeRoot cubeRootSymbol = new CubeRoot();
|
---|
[14949] | 48 | private static readonly Power powSymbol = new Power();
|
---|
| 49 | private static readonly Sine sineSymbol = new Sine();
|
---|
| 50 | private static readonly Cosine cosineSymbol = new Cosine();
|
---|
| 51 | private static readonly Tangent tanSymbol = new Tangent();
|
---|
| 52 | private static readonly IfThenElse ifThenElseSymbol = new IfThenElse();
|
---|
| 53 | private static readonly And andSymbol = new And();
|
---|
| 54 | private static readonly Or orSymbol = new Or();
|
---|
| 55 | private static readonly Not notSymbol = new Not();
|
---|
| 56 | private static readonly GreaterThan gtSymbol = new GreaterThan();
|
---|
| 57 | private static readonly LessThan ltSymbol = new LessThan();
|
---|
| 58 | private static readonly Integral integralSymbol = new Integral();
|
---|
| 59 | private static readonly LaggedVariable laggedVariableSymbol = new LaggedVariable();
|
---|
| 60 | private static readonly TimeLag timeLagSymbol = new TimeLag();
|
---|
[17593] | 61 | private static readonly Sum sumSymbol = new Sum();
|
---|
| 62 | private static readonly Mean meanSymbol = new Mean();
|
---|
| 63 | private static readonly Length lengthSymbol = new Length();
|
---|
[14843] | 64 |
|
---|
[17593] | 65 | private readonly SymbolicDataAnalysisExpressionTreeVectorInterpreter interpreter;
|
---|
| 66 | private readonly IDataAnalysisProblemData problemData;
|
---|
[14949] | 67 |
|
---|
[17593] | 68 | public VectorTreeSimplifier(SymbolicDataAnalysisExpressionTreeVectorInterpreter interpreter, IDataAnalysisProblemData problemData) {
|
---|
| 69 | this.interpreter = interpreter;
|
---|
| 70 | this.problemData = problemData;
|
---|
| 71 | }
|
---|
| 72 |
|
---|
| 73 | public ISymbolicExpressionTree Simplify(ISymbolicExpressionTree originalTree) {
|
---|
[14843] | 74 | var clone = (ISymbolicExpressionTreeNode)originalTree.Root.Clone();
|
---|
| 75 | // macro expand (initially no argument trees)
|
---|
| 76 | var macroExpandedTree = MacroExpand(clone, clone.GetSubtree(0), new List<ISymbolicExpressionTreeNode>());
|
---|
| 77 | ISymbolicExpressionTreeNode rootNode = (new ProgramRootSymbol()).CreateTreeNode();
|
---|
| 78 | rootNode.AddSubtree(GetSimplifiedTree(macroExpandedTree));
|
---|
| 79 |
|
---|
| 80 | #if DEBUG
|
---|
| 81 | // check that each node is only referenced once
|
---|
| 82 | var nodes = rootNode.IterateNodesPrefix().ToArray();
|
---|
[14949] | 83 | foreach (var n in nodes) if (nodes.Count(ni => ni == n) > 1) throw new InvalidOperationException();
|
---|
[14843] | 84 | #endif
|
---|
| 85 | return new SymbolicExpressionTree(rootNode);
|
---|
| 86 | }
|
---|
| 87 |
|
---|
| 88 | // the argumentTrees list contains already expanded trees used as arguments for invocations
|
---|
[14949] | 89 | private static ISymbolicExpressionTreeNode MacroExpand(ISymbolicExpressionTreeNode root, ISymbolicExpressionTreeNode node,
|
---|
[14843] | 90 | IList<ISymbolicExpressionTreeNode> argumentTrees) {
|
---|
| 91 | List<ISymbolicExpressionTreeNode> subtrees = new List<ISymbolicExpressionTreeNode>(node.Subtrees);
|
---|
| 92 | while (node.SubtreeCount > 0) node.RemoveSubtree(0);
|
---|
| 93 | if (node.Symbol is InvokeFunction) {
|
---|
| 94 | var invokeSym = node.Symbol as InvokeFunction;
|
---|
| 95 | var defunNode = FindFunctionDefinition(root, invokeSym.FunctionName);
|
---|
| 96 | var macroExpandedArguments = new List<ISymbolicExpressionTreeNode>();
|
---|
| 97 | foreach (var subtree in subtrees) {
|
---|
| 98 | macroExpandedArguments.Add(MacroExpand(root, subtree, argumentTrees));
|
---|
| 99 | }
|
---|
| 100 | return MacroExpand(root, defunNode, macroExpandedArguments);
|
---|
| 101 | } else if (node.Symbol is Argument) {
|
---|
| 102 | var argSym = node.Symbol as Argument;
|
---|
| 103 | // return the correct argument sub-tree (already macro-expanded)
|
---|
| 104 | return (SymbolicExpressionTreeNode)argumentTrees[argSym.ArgumentIndex].Clone();
|
---|
| 105 | } else {
|
---|
| 106 | // recursive application
|
---|
| 107 | foreach (var subtree in subtrees) {
|
---|
| 108 | node.AddSubtree(MacroExpand(root, subtree, argumentTrees));
|
---|
| 109 | }
|
---|
| 110 | return node;
|
---|
| 111 | }
|
---|
| 112 | }
|
---|
| 113 |
|
---|
[14949] | 114 | private static ISymbolicExpressionTreeNode FindFunctionDefinition(ISymbolicExpressionTreeNode root, string functionName) {
|
---|
[14843] | 115 | foreach (var subtree in root.Subtrees.OfType<DefunTreeNode>()) {
|
---|
| 116 | if (subtree.FunctionName == functionName) return subtree.GetSubtree(0);
|
---|
| 117 | }
|
---|
| 118 |
|
---|
| 119 | throw new ArgumentException("Definition of function " + functionName + " not found.");
|
---|
| 120 | }
|
---|
| 121 |
|
---|
| 122 | #region symbol predicates
|
---|
| 123 |
|
---|
| 124 | // arithmetic
|
---|
[14949] | 125 | private static bool IsDivision(ISymbolicExpressionTreeNode node) {
|
---|
[14843] | 126 | return node.Symbol is Division;
|
---|
| 127 | }
|
---|
| 128 |
|
---|
[14949] | 129 | private static bool IsMultiplication(ISymbolicExpressionTreeNode node) {
|
---|
[14843] | 130 | return node.Symbol is Multiplication;
|
---|
| 131 | }
|
---|
| 132 |
|
---|
[14949] | 133 | private static bool IsSubtraction(ISymbolicExpressionTreeNode node) {
|
---|
[14843] | 134 | return node.Symbol is Subtraction;
|
---|
| 135 | }
|
---|
| 136 |
|
---|
[14949] | 137 | private static bool IsAddition(ISymbolicExpressionTreeNode node) {
|
---|
[14843] | 138 | return node.Symbol is Addition;
|
---|
| 139 | }
|
---|
| 140 |
|
---|
[14949] | 141 | private static bool IsAverage(ISymbolicExpressionTreeNode node) {
|
---|
[14843] | 142 | return node.Symbol is Average;
|
---|
| 143 | }
|
---|
| 144 |
|
---|
[16356] | 145 | private static bool IsAbsolute(ISymbolicExpressionTreeNode node) {
|
---|
| 146 | return node.Symbol is Absolute;
|
---|
| 147 | }
|
---|
| 148 |
|
---|
[14843] | 149 | // exponential
|
---|
[14949] | 150 | private static bool IsLog(ISymbolicExpressionTreeNode node) {
|
---|
[14843] | 151 | return node.Symbol is Logarithm;
|
---|
| 152 | }
|
---|
| 153 |
|
---|
[14949] | 154 | private static bool IsExp(ISymbolicExpressionTreeNode node) {
|
---|
[14843] | 155 | return node.Symbol is Exponential;
|
---|
| 156 | }
|
---|
| 157 |
|
---|
[14949] | 158 | private static bool IsRoot(ISymbolicExpressionTreeNode node) {
|
---|
[14843] | 159 | return node.Symbol is Root;
|
---|
| 160 | }
|
---|
| 161 |
|
---|
[14949] | 162 | private static bool IsSquare(ISymbolicExpressionTreeNode node) {
|
---|
[14843] | 163 | return node.Symbol is Square;
|
---|
| 164 | }
|
---|
| 165 |
|
---|
[14949] | 166 | private static bool IsSquareRoot(ISymbolicExpressionTreeNode node) {
|
---|
[14843] | 167 | return node.Symbol is SquareRoot;
|
---|
| 168 | }
|
---|
| 169 |
|
---|
[16356] | 170 | private static bool IsCube(ISymbolicExpressionTreeNode node) {
|
---|
| 171 | return node.Symbol is Cube;
|
---|
| 172 | }
|
---|
| 173 |
|
---|
| 174 | private static bool IsCubeRoot(ISymbolicExpressionTreeNode node) {
|
---|
| 175 | return node.Symbol is CubeRoot;
|
---|
| 176 | }
|
---|
| 177 |
|
---|
[14949] | 178 | private static bool IsPower(ISymbolicExpressionTreeNode node) {
|
---|
[14843] | 179 | return node.Symbol is Power;
|
---|
| 180 | }
|
---|
| 181 |
|
---|
| 182 | // trigonometric
|
---|
[14949] | 183 | private static bool IsSine(ISymbolicExpressionTreeNode node) {
|
---|
[14843] | 184 | return node.Symbol is Sine;
|
---|
| 185 | }
|
---|
| 186 |
|
---|
[14949] | 187 | private static bool IsCosine(ISymbolicExpressionTreeNode node) {
|
---|
[14843] | 188 | return node.Symbol is Cosine;
|
---|
| 189 | }
|
---|
| 190 |
|
---|
[14949] | 191 | private static bool IsTangent(ISymbolicExpressionTreeNode node) {
|
---|
[14843] | 192 | return node.Symbol is Tangent;
|
---|
| 193 | }
|
---|
| 194 |
|
---|
[16356] | 195 | private static bool IsAnalyticalQuotient(ISymbolicExpressionTreeNode node) {
|
---|
[16360] | 196 | return node.Symbol is AnalyticQuotient;
|
---|
[16356] | 197 | }
|
---|
| 198 |
|
---|
[14843] | 199 | // boolean
|
---|
[14949] | 200 | private static bool IsIfThenElse(ISymbolicExpressionTreeNode node) {
|
---|
[14843] | 201 | return node.Symbol is IfThenElse;
|
---|
| 202 | }
|
---|
| 203 |
|
---|
[14949] | 204 | private static bool IsAnd(ISymbolicExpressionTreeNode node) {
|
---|
[14843] | 205 | return node.Symbol is And;
|
---|
| 206 | }
|
---|
| 207 |
|
---|
[14949] | 208 | private static bool IsOr(ISymbolicExpressionTreeNode node) {
|
---|
[14843] | 209 | return node.Symbol is Or;
|
---|
| 210 | }
|
---|
| 211 |
|
---|
[14949] | 212 | private static bool IsNot(ISymbolicExpressionTreeNode node) {
|
---|
[14843] | 213 | return node.Symbol is Not;
|
---|
| 214 | }
|
---|
| 215 |
|
---|
| 216 | // comparison
|
---|
[14949] | 217 | private static bool IsGreaterThan(ISymbolicExpressionTreeNode node) {
|
---|
[14843] | 218 | return node.Symbol is GreaterThan;
|
---|
| 219 | }
|
---|
| 220 |
|
---|
[14949] | 221 | private static bool IsLessThan(ISymbolicExpressionTreeNode node) {
|
---|
[14843] | 222 | return node.Symbol is LessThan;
|
---|
| 223 | }
|
---|
| 224 |
|
---|
[14949] | 225 | private static bool IsBoolean(ISymbolicExpressionTreeNode node) {
|
---|
[14843] | 226 | return
|
---|
| 227 | node.Symbol is GreaterThan ||
|
---|
| 228 | node.Symbol is LessThan ||
|
---|
| 229 | node.Symbol is And ||
|
---|
| 230 | node.Symbol is Or;
|
---|
| 231 | }
|
---|
| 232 |
|
---|
| 233 | // terminals
|
---|
[14949] | 234 | private static bool IsVariable(ISymbolicExpressionTreeNode node) {
|
---|
[14843] | 235 | return node.Symbol is Variable;
|
---|
| 236 | }
|
---|
| 237 |
|
---|
[14949] | 238 | private static bool IsVariableBase(ISymbolicExpressionTreeNode node) {
|
---|
[14843] | 239 | return node is VariableTreeNodeBase;
|
---|
| 240 | }
|
---|
| 241 |
|
---|
[14949] | 242 | private static bool IsFactor(ISymbolicExpressionTreeNode node) {
|
---|
[14843] | 243 | return node is FactorVariableTreeNode;
|
---|
| 244 | }
|
---|
| 245 |
|
---|
[14949] | 246 | private static bool IsBinFactor(ISymbolicExpressionTreeNode node) {
|
---|
[14843] | 247 | return node is BinaryFactorVariableTreeNode;
|
---|
| 248 | }
|
---|
| 249 |
|
---|
[14949] | 250 | private static bool IsConstant(ISymbolicExpressionTreeNode node) {
|
---|
[14843] | 251 | return node.Symbol is Constant;
|
---|
| 252 | }
|
---|
| 253 |
|
---|
| 254 | // dynamic
|
---|
[14949] | 255 | private static bool IsTimeLag(ISymbolicExpressionTreeNode node) {
|
---|
[14843] | 256 | return node.Symbol is TimeLag;
|
---|
| 257 | }
|
---|
| 258 |
|
---|
[14949] | 259 | private static bool IsIntegral(ISymbolicExpressionTreeNode node) {
|
---|
[14843] | 260 | return node.Symbol is Integral;
|
---|
| 261 | }
|
---|
| 262 |
|
---|
[17593] | 263 | private static bool IsSum(ISymbolicExpressionTreeNode node) {
|
---|
| 264 | return node.Symbol is Sum;
|
---|
| 265 | }
|
---|
| 266 |
|
---|
| 267 | private static bool IsMean(ISymbolicExpressionTreeNode node) {
|
---|
| 268 | return node.Symbol is Mean;
|
---|
| 269 | }
|
---|
[14843] | 270 | #endregion
|
---|
| 271 |
|
---|
[17593] | 272 | #region type predicates
|
---|
| 273 | public bool IsScalarNode(ISymbolicExpressionTreeNode node) {
|
---|
| 274 | var results = interpreter.EvaluateNode(node, problemData.Dataset, problemData.TrainingIndices);
|
---|
| 275 | return results.All(r => r.IsScalar);
|
---|
| 276 | }
|
---|
| 277 | public bool IsVectorNode(ISymbolicExpressionTreeNode node) {
|
---|
| 278 | var results = interpreter.EvaluateNode(node, problemData.Dataset, problemData.TrainingIndices);
|
---|
| 279 | return results.All(r => r.IsVector);
|
---|
| 280 | }
|
---|
| 281 | #endregion
|
---|
| 282 |
|
---|
[14843] | 283 | /// <summary>
|
---|
| 284 | /// Creates a new simplified tree
|
---|
| 285 | /// </summary>
|
---|
| 286 | /// <param name="original"></param>
|
---|
| 287 | /// <returns></returns>
|
---|
[17593] | 288 | public ISymbolicExpressionTreeNode GetSimplifiedTree(ISymbolicExpressionTreeNode original) {
|
---|
[14843] | 289 | if (IsConstant(original) || IsVariableBase(original)) {
|
---|
| 290 | return (ISymbolicExpressionTreeNode)original.Clone();
|
---|
[16356] | 291 | } else if (IsAbsolute(original)) {
|
---|
| 292 | return SimplifyAbsolute(original);
|
---|
[14843] | 293 | } else if (IsAddition(original)) {
|
---|
| 294 | return SimplifyAddition(original);
|
---|
| 295 | } else if (IsSubtraction(original)) {
|
---|
| 296 | return SimplifySubtraction(original);
|
---|
| 297 | } else if (IsMultiplication(original)) {
|
---|
| 298 | return SimplifyMultiplication(original);
|
---|
| 299 | } else if (IsDivision(original)) {
|
---|
| 300 | return SimplifyDivision(original);
|
---|
| 301 | } else if (IsAverage(original)) {
|
---|
| 302 | return SimplifyAverage(original);
|
---|
| 303 | } else if (IsLog(original)) {
|
---|
| 304 | return SimplifyLog(original);
|
---|
| 305 | } else if (IsExp(original)) {
|
---|
| 306 | return SimplifyExp(original);
|
---|
| 307 | } else if (IsSquare(original)) {
|
---|
| 308 | return SimplifySquare(original);
|
---|
| 309 | } else if (IsSquareRoot(original)) {
|
---|
| 310 | return SimplifySquareRoot(original);
|
---|
[16356] | 311 | } else if (IsCube(original)) {
|
---|
| 312 | return SimplifyCube(original);
|
---|
| 313 | } else if (IsCubeRoot(original)) {
|
---|
| 314 | return SimplifyCubeRoot(original);
|
---|
[14843] | 315 | } else if (IsPower(original)) {
|
---|
| 316 | return SimplifyPower(original);
|
---|
| 317 | } else if (IsRoot(original)) {
|
---|
| 318 | return SimplifyRoot(original);
|
---|
| 319 | } else if (IsSine(original)) {
|
---|
| 320 | return SimplifySine(original);
|
---|
| 321 | } else if (IsCosine(original)) {
|
---|
| 322 | return SimplifyCosine(original);
|
---|
| 323 | } else if (IsTangent(original)) {
|
---|
| 324 | return SimplifyTangent(original);
|
---|
[16356] | 325 | } else if (IsAnalyticalQuotient(original)) {
|
---|
| 326 | return SimplifyAnalyticalQuotient(original);
|
---|
[14843] | 327 | } else if (IsIfThenElse(original)) {
|
---|
| 328 | return SimplifyIfThenElse(original);
|
---|
| 329 | } else if (IsGreaterThan(original)) {
|
---|
| 330 | return SimplifyGreaterThan(original);
|
---|
| 331 | } else if (IsLessThan(original)) {
|
---|
| 332 | return SimplifyLessThan(original);
|
---|
| 333 | } else if (IsAnd(original)) {
|
---|
| 334 | return SimplifyAnd(original);
|
---|
| 335 | } else if (IsOr(original)) {
|
---|
| 336 | return SimplifyOr(original);
|
---|
| 337 | } else if (IsNot(original)) {
|
---|
| 338 | return SimplifyNot(original);
|
---|
| 339 | } else if (IsTimeLag(original)) {
|
---|
| 340 | return SimplifyTimeLag(original);
|
---|
| 341 | } else if (IsIntegral(original)) {
|
---|
| 342 | return SimplifyIntegral(original);
|
---|
[17593] | 343 | } else if (IsSum(original)) {
|
---|
| 344 | return SimplifySumAggregation(original);
|
---|
| 345 | } else if (IsMean(original)) {
|
---|
| 346 | return SimplifyMeanAggregation(original);
|
---|
[14843] | 347 | } else {
|
---|
| 348 | return SimplifyAny(original);
|
---|
| 349 | }
|
---|
| 350 | }
|
---|
| 351 |
|
---|
| 352 | #region specific simplification routines
|
---|
| 353 |
|
---|
[17593] | 354 | private ISymbolicExpressionTreeNode SimplifyAny(ISymbolicExpressionTreeNode original) {
|
---|
[14843] | 355 | // can't simplify this function but simplify all subtrees
|
---|
| 356 | List<ISymbolicExpressionTreeNode> subtrees = new List<ISymbolicExpressionTreeNode>(original.Subtrees);
|
---|
| 357 | while (original.Subtrees.Count() > 0) original.RemoveSubtree(0);
|
---|
| 358 | var clone = (SymbolicExpressionTreeNode)original.Clone();
|
---|
| 359 | List<ISymbolicExpressionTreeNode> simplifiedSubtrees = new List<ISymbolicExpressionTreeNode>();
|
---|
| 360 | foreach (var subtree in subtrees) {
|
---|
| 361 | simplifiedSubtrees.Add(GetSimplifiedTree(subtree));
|
---|
| 362 | original.AddSubtree(subtree);
|
---|
| 363 | }
|
---|
| 364 | foreach (var simplifiedSubtree in simplifiedSubtrees) {
|
---|
| 365 | clone.AddSubtree(simplifiedSubtree);
|
---|
| 366 | }
|
---|
| 367 | if (simplifiedSubtrees.TrueForAll(t => IsConstant(t))) {
|
---|
| 368 | SimplifyConstantExpression(clone);
|
---|
| 369 | }
|
---|
| 370 | return clone;
|
---|
| 371 | }
|
---|
| 372 |
|
---|
[17593] | 373 | private ISymbolicExpressionTreeNode SimplifyConstantExpression(ISymbolicExpressionTreeNode original) {
|
---|
[14843] | 374 | // not yet implemented
|
---|
| 375 | return original;
|
---|
| 376 | }
|
---|
| 377 |
|
---|
[17593] | 378 | private ISymbolicExpressionTreeNode SimplifyAverage(ISymbolicExpressionTreeNode original) {
|
---|
[14843] | 379 | if (original.Subtrees.Count() == 1) {
|
---|
| 380 | return GetSimplifiedTree(original.GetSubtree(0));
|
---|
| 381 | } else {
|
---|
| 382 | // simplify expressions x0..xn
|
---|
| 383 | // make sum(x0..xn) / n
|
---|
| 384 | var sum = original.Subtrees
|
---|
| 385 | .Select(GetSimplifiedTree)
|
---|
| 386 | .Aggregate(MakeSum);
|
---|
| 387 | return MakeFraction(sum, MakeConstant(original.Subtrees.Count()));
|
---|
| 388 | }
|
---|
| 389 | }
|
---|
| 390 |
|
---|
[17593] | 391 | private ISymbolicExpressionTreeNode SimplifyDivision(ISymbolicExpressionTreeNode original) {
|
---|
[14843] | 392 | if (original.Subtrees.Count() == 1) {
|
---|
| 393 | return Invert(GetSimplifiedTree(original.GetSubtree(0)));
|
---|
| 394 | } else {
|
---|
| 395 | // simplify expressions x0..xn
|
---|
| 396 | // make multiplication (x0 * 1/(x1 * x1 * .. * xn))
|
---|
| 397 | var first = original.GetSubtree(0);
|
---|
| 398 | var second = original.GetSubtree(1);
|
---|
| 399 | var remaining = original.Subtrees.Skip(2);
|
---|
| 400 | return
|
---|
| 401 | MakeProduct(GetSimplifiedTree(first),
|
---|
| 402 | Invert(remaining.Aggregate(GetSimplifiedTree(second), (a, b) => MakeProduct(a, GetSimplifiedTree(b)))));
|
---|
| 403 | }
|
---|
| 404 | }
|
---|
| 405 |
|
---|
[17593] | 406 | private ISymbolicExpressionTreeNode SimplifyMultiplication(ISymbolicExpressionTreeNode original) {
|
---|
[14843] | 407 | if (original.Subtrees.Count() == 1) {
|
---|
| 408 | return GetSimplifiedTree(original.GetSubtree(0));
|
---|
| 409 | } else {
|
---|
| 410 | return original.Subtrees
|
---|
| 411 | .Select(GetSimplifiedTree)
|
---|
| 412 | .Aggregate(MakeProduct);
|
---|
| 413 | }
|
---|
| 414 | }
|
---|
| 415 |
|
---|
[17593] | 416 | private ISymbolicExpressionTreeNode SimplifySubtraction(ISymbolicExpressionTreeNode original) {
|
---|
[14843] | 417 | if (original.Subtrees.Count() == 1) {
|
---|
| 418 | return Negate(GetSimplifiedTree(original.GetSubtree(0)));
|
---|
| 419 | } else {
|
---|
| 420 | // simplify expressions x0..xn
|
---|
| 421 | // make addition (x0,-x1..-xn)
|
---|
| 422 | var first = original.Subtrees.First();
|
---|
| 423 | var remaining = original.Subtrees.Skip(1);
|
---|
| 424 | return remaining.Aggregate(GetSimplifiedTree(first), (a, b) => MakeSum(a, Negate(GetSimplifiedTree(b))));
|
---|
| 425 | }
|
---|
| 426 | }
|
---|
| 427 |
|
---|
[17593] | 428 | private ISymbolicExpressionTreeNode SimplifyAddition(ISymbolicExpressionTreeNode original) {
|
---|
[14843] | 429 | if (original.Subtrees.Count() == 1) {
|
---|
| 430 | return GetSimplifiedTree(original.GetSubtree(0));
|
---|
| 431 | } else {
|
---|
| 432 | // simplify expression x0..xn
|
---|
| 433 | // make addition (x0..xn)
|
---|
| 434 | return original.Subtrees
|
---|
| 435 | .Select(GetSimplifiedTree)
|
---|
| 436 | .Aggregate(MakeSum);
|
---|
| 437 | }
|
---|
| 438 | }
|
---|
| 439 |
|
---|
[17593] | 440 | private ISymbolicExpressionTreeNode SimplifyAbsolute(ISymbolicExpressionTreeNode original) {
|
---|
[16356] | 441 | return MakeAbs(GetSimplifiedTree(original.GetSubtree(0)));
|
---|
| 442 | }
|
---|
| 443 |
|
---|
[17593] | 444 | private ISymbolicExpressionTreeNode SimplifyNot(ISymbolicExpressionTreeNode original) {
|
---|
[14843] | 445 | return MakeNot(GetSimplifiedTree(original.GetSubtree(0)));
|
---|
| 446 | }
|
---|
| 447 |
|
---|
[17593] | 448 | private ISymbolicExpressionTreeNode SimplifyOr(ISymbolicExpressionTreeNode original) {
|
---|
[14843] | 449 | return original.Subtrees
|
---|
| 450 | .Select(GetSimplifiedTree)
|
---|
| 451 | .Aggregate(MakeOr);
|
---|
| 452 | }
|
---|
| 453 |
|
---|
[17593] | 454 | private ISymbolicExpressionTreeNode SimplifyAnd(ISymbolicExpressionTreeNode original) {
|
---|
[14843] | 455 | return original.Subtrees
|
---|
| 456 | .Select(GetSimplifiedTree)
|
---|
| 457 | .Aggregate(MakeAnd);
|
---|
| 458 | }
|
---|
| 459 |
|
---|
[17593] | 460 | private ISymbolicExpressionTreeNode SimplifyLessThan(ISymbolicExpressionTreeNode original) {
|
---|
[14843] | 461 | return MakeLessThan(GetSimplifiedTree(original.GetSubtree(0)), GetSimplifiedTree(original.GetSubtree(1)));
|
---|
| 462 | }
|
---|
| 463 |
|
---|
[17593] | 464 | private ISymbolicExpressionTreeNode SimplifyGreaterThan(ISymbolicExpressionTreeNode original) {
|
---|
[14843] | 465 | return MakeGreaterThan(GetSimplifiedTree(original.GetSubtree(0)), GetSimplifiedTree(original.GetSubtree(1)));
|
---|
| 466 | }
|
---|
| 467 |
|
---|
[17593] | 468 | private ISymbolicExpressionTreeNode SimplifyIfThenElse(ISymbolicExpressionTreeNode original) {
|
---|
[14843] | 469 | return MakeIfThenElse(GetSimplifiedTree(original.GetSubtree(0)), GetSimplifiedTree(original.GetSubtree(1)),
|
---|
| 470 | GetSimplifiedTree(original.GetSubtree(2)));
|
---|
| 471 | }
|
---|
| 472 |
|
---|
[17593] | 473 | private ISymbolicExpressionTreeNode SimplifyTangent(ISymbolicExpressionTreeNode original) {
|
---|
[14843] | 474 | return MakeTangent(GetSimplifiedTree(original.GetSubtree(0)));
|
---|
| 475 | }
|
---|
| 476 |
|
---|
[17593] | 477 | private ISymbolicExpressionTreeNode SimplifyCosine(ISymbolicExpressionTreeNode original) {
|
---|
[14843] | 478 | return MakeCosine(GetSimplifiedTree(original.GetSubtree(0)));
|
---|
| 479 | }
|
---|
| 480 |
|
---|
[17593] | 481 | private ISymbolicExpressionTreeNode SimplifySine(ISymbolicExpressionTreeNode original) {
|
---|
[14843] | 482 | return MakeSine(GetSimplifiedTree(original.GetSubtree(0)));
|
---|
| 483 | }
|
---|
| 484 |
|
---|
[17593] | 485 | private ISymbolicExpressionTreeNode SimplifyExp(ISymbolicExpressionTreeNode original) {
|
---|
[14843] | 486 | return MakeExp(GetSimplifiedTree(original.GetSubtree(0)));
|
---|
| 487 | }
|
---|
| 488 |
|
---|
[17593] | 489 | private ISymbolicExpressionTreeNode SimplifySquare(ISymbolicExpressionTreeNode original) {
|
---|
[14843] | 490 | return MakeSquare(GetSimplifiedTree(original.GetSubtree(0)));
|
---|
| 491 | }
|
---|
| 492 |
|
---|
[17593] | 493 | private ISymbolicExpressionTreeNode SimplifySquareRoot(ISymbolicExpressionTreeNode original) {
|
---|
[14843] | 494 | return MakeSquareRoot(GetSimplifiedTree(original.GetSubtree(0)));
|
---|
| 495 | }
|
---|
[17593] | 496 | private ISymbolicExpressionTreeNode SimplifyCube(ISymbolicExpressionTreeNode original) {
|
---|
[16356] | 497 | return MakeCube(GetSimplifiedTree(original.GetSubtree(0)));
|
---|
| 498 | }
|
---|
[14843] | 499 |
|
---|
[17593] | 500 | private ISymbolicExpressionTreeNode SimplifyCubeRoot(ISymbolicExpressionTreeNode original) {
|
---|
[16356] | 501 | return MakeCubeRoot(GetSimplifiedTree(original.GetSubtree(0)));
|
---|
| 502 | }
|
---|
| 503 |
|
---|
[17593] | 504 | private ISymbolicExpressionTreeNode SimplifyLog(ISymbolicExpressionTreeNode original) {
|
---|
[14843] | 505 | return MakeLog(GetSimplifiedTree(original.GetSubtree(0)));
|
---|
| 506 | }
|
---|
| 507 |
|
---|
[17593] | 508 | private ISymbolicExpressionTreeNode SimplifyRoot(ISymbolicExpressionTreeNode original) {
|
---|
[14843] | 509 | return MakeRoot(GetSimplifiedTree(original.GetSubtree(0)), GetSimplifiedTree(original.GetSubtree(1)));
|
---|
| 510 | }
|
---|
| 511 |
|
---|
[17593] | 512 | private ISymbolicExpressionTreeNode SimplifyPower(ISymbolicExpressionTreeNode original) {
|
---|
[14843] | 513 | return MakePower(GetSimplifiedTree(original.GetSubtree(0)), GetSimplifiedTree(original.GetSubtree(1)));
|
---|
| 514 | }
|
---|
| 515 |
|
---|
[17593] | 516 | private ISymbolicExpressionTreeNode SimplifyAnalyticalQuotient(ISymbolicExpressionTreeNode original) {
|
---|
[16356] | 517 | return MakeAnalyticalQuotient(GetSimplifiedTree(original.GetSubtree(0)), GetSimplifiedTree(original.GetSubtree(1)));
|
---|
| 518 | }
|
---|
| 519 |
|
---|
[17593] | 520 | private ISymbolicExpressionTreeNode SimplifyTimeLag(ISymbolicExpressionTreeNode original) {
|
---|
[14843] | 521 | var laggedTreeNode = original as ILaggedTreeNode;
|
---|
| 522 | var simplifiedSubtree = GetSimplifiedTree(original.GetSubtree(0));
|
---|
| 523 | if (!ContainsVariableCondition(simplifiedSubtree)) {
|
---|
| 524 | return AddLagToDynamicNodes(simplifiedSubtree, laggedTreeNode.Lag);
|
---|
| 525 | } else {
|
---|
| 526 | return MakeTimeLag(simplifiedSubtree, laggedTreeNode.Lag);
|
---|
| 527 | }
|
---|
| 528 | }
|
---|
| 529 |
|
---|
[17593] | 530 | private ISymbolicExpressionTreeNode SimplifyIntegral(ISymbolicExpressionTreeNode original) {
|
---|
[14843] | 531 | var laggedTreeNode = original as ILaggedTreeNode;
|
---|
| 532 | var simplifiedSubtree = GetSimplifiedTree(original.GetSubtree(0));
|
---|
| 533 | if (IsConstant(simplifiedSubtree)) {
|
---|
| 534 | return GetSimplifiedTree(MakeProduct(simplifiedSubtree, MakeConstant(-laggedTreeNode.Lag)));
|
---|
| 535 | } else {
|
---|
| 536 | return MakeIntegral(simplifiedSubtree, laggedTreeNode.Lag);
|
---|
| 537 | }
|
---|
| 538 | }
|
---|
| 539 |
|
---|
[17593] | 540 | private ISymbolicExpressionTreeNode SimplifySumAggregation(ISymbolicExpressionTreeNode original) {
|
---|
| 541 | return MakeSumAggregation(GetSimplifiedTree(original.GetSubtree(0)));
|
---|
| 542 | }
|
---|
| 543 |
|
---|
| 544 | private ISymbolicExpressionTreeNode SimplifyMeanAggregation(ISymbolicExpressionTreeNode original) {
|
---|
| 545 | return MakeMeanAggregation(GetSimplifiedTree(original.GetSubtree(0)));
|
---|
| 546 | }
|
---|
| 547 |
|
---|
[14843] | 548 | #endregion
|
---|
| 549 |
|
---|
| 550 | #region low level tree restructuring
|
---|
| 551 |
|
---|
[17593] | 552 | private ISymbolicExpressionTreeNode MakeTimeLag(ISymbolicExpressionTreeNode subtree, int lag) {
|
---|
[14843] | 553 | if (lag == 0) return subtree;
|
---|
| 554 | if (IsConstant(subtree)) return subtree;
|
---|
| 555 | var lagNode = (LaggedTreeNode)timeLagSymbol.CreateTreeNode();
|
---|
| 556 | lagNode.Lag = lag;
|
---|
| 557 | lagNode.AddSubtree(subtree);
|
---|
| 558 | return lagNode;
|
---|
| 559 | }
|
---|
| 560 |
|
---|
[17593] | 561 | private ISymbolicExpressionTreeNode MakeIntegral(ISymbolicExpressionTreeNode subtree, int lag) {
|
---|
[14843] | 562 | if (lag == 0) return subtree;
|
---|
| 563 | else if (lag == -1 || lag == 1) {
|
---|
| 564 | return MakeSum(subtree, AddLagToDynamicNodes((ISymbolicExpressionTreeNode)subtree.Clone(), lag));
|
---|
| 565 | } else {
|
---|
| 566 | var node = (LaggedTreeNode)integralSymbol.CreateTreeNode();
|
---|
| 567 | node.Lag = lag;
|
---|
| 568 | node.AddSubtree(subtree);
|
---|
| 569 | return node;
|
---|
| 570 | }
|
---|
| 571 | }
|
---|
| 572 |
|
---|
[17593] | 573 | private ISymbolicExpressionTreeNode MakeNot(ISymbolicExpressionTreeNode t) {
|
---|
[14843] | 574 | if (IsConstant(t)) {
|
---|
| 575 | var constNode = t as ConstantTreeNode;
|
---|
| 576 | if (constNode.Value > 0) return MakeConstant(-1.0);
|
---|
| 577 | else return MakeConstant(1.0);
|
---|
| 578 | } else if (IsNot(t)) {
|
---|
| 579 | return t.GetSubtree(0);
|
---|
| 580 | } else if (!IsBoolean(t)) {
|
---|
| 581 | var gtNode = gtSymbol.CreateTreeNode();
|
---|
| 582 | gtNode.AddSubtree(t);
|
---|
| 583 | gtNode.AddSubtree(MakeConstant(0.0));
|
---|
| 584 | var notNode = notSymbol.CreateTreeNode();
|
---|
| 585 | notNode.AddSubtree(gtNode);
|
---|
| 586 | return notNode;
|
---|
| 587 | } else {
|
---|
| 588 | var notNode = notSymbol.CreateTreeNode();
|
---|
| 589 | notNode.AddSubtree(t);
|
---|
| 590 | return notNode;
|
---|
| 591 | }
|
---|
| 592 | }
|
---|
| 593 |
|
---|
[17593] | 594 | private ISymbolicExpressionTreeNode MakeOr(ISymbolicExpressionTreeNode a, ISymbolicExpressionTreeNode b) {
|
---|
[14843] | 595 | if (IsConstant(a) && IsConstant(b)) {
|
---|
| 596 | var constA = a as ConstantTreeNode;
|
---|
| 597 | var constB = b as ConstantTreeNode;
|
---|
| 598 | if (constA.Value > 0.0 || constB.Value > 0.0) {
|
---|
| 599 | return MakeConstant(1.0);
|
---|
| 600 | } else {
|
---|
| 601 | return MakeConstant(-1.0);
|
---|
| 602 | }
|
---|
| 603 | } else if (IsConstant(a)) {
|
---|
| 604 | return MakeOr(b, a);
|
---|
| 605 | } else if (IsConstant(b)) {
|
---|
| 606 | var constT = b as ConstantTreeNode;
|
---|
| 607 | if (constT.Value > 0.0) {
|
---|
| 608 | // boolean expression is necessarily true
|
---|
| 609 | return MakeConstant(1.0);
|
---|
| 610 | } else {
|
---|
| 611 | // the constant value has no effect on the result of the boolean condition so we can drop the constant term
|
---|
| 612 | var orNode = orSymbol.CreateTreeNode();
|
---|
| 613 | orNode.AddSubtree(a);
|
---|
| 614 | return orNode;
|
---|
| 615 | }
|
---|
| 616 | } else {
|
---|
| 617 | var orNode = orSymbol.CreateTreeNode();
|
---|
| 618 | orNode.AddSubtree(a);
|
---|
| 619 | orNode.AddSubtree(b);
|
---|
| 620 | return orNode;
|
---|
| 621 | }
|
---|
| 622 | }
|
---|
| 623 |
|
---|
[17593] | 624 | private ISymbolicExpressionTreeNode MakeAnd(ISymbolicExpressionTreeNode a, ISymbolicExpressionTreeNode b) {
|
---|
[14843] | 625 | if (IsConstant(a) && IsConstant(b)) {
|
---|
| 626 | var constA = a as ConstantTreeNode;
|
---|
| 627 | var constB = b as ConstantTreeNode;
|
---|
| 628 | if (constA.Value > 0.0 && constB.Value > 0.0) {
|
---|
| 629 | return MakeConstant(1.0);
|
---|
| 630 | } else {
|
---|
| 631 | return MakeConstant(-1.0);
|
---|
| 632 | }
|
---|
| 633 | } else if (IsConstant(a)) {
|
---|
| 634 | return MakeAnd(b, a);
|
---|
| 635 | } else if (IsConstant(b)) {
|
---|
| 636 | var constB = b as ConstantTreeNode;
|
---|
| 637 | if (constB.Value > 0.0) {
|
---|
| 638 | // the constant value has no effect on the result of the boolean condition so we can drop the constant term
|
---|
| 639 | var andNode = andSymbol.CreateTreeNode();
|
---|
| 640 | andNode.AddSubtree(a);
|
---|
| 641 | return andNode;
|
---|
| 642 | } else {
|
---|
| 643 | // boolean expression is necessarily false
|
---|
| 644 | return MakeConstant(-1.0);
|
---|
| 645 | }
|
---|
| 646 | } else {
|
---|
| 647 | var andNode = andSymbol.CreateTreeNode();
|
---|
| 648 | andNode.AddSubtree(a);
|
---|
| 649 | andNode.AddSubtree(b);
|
---|
| 650 | return andNode;
|
---|
| 651 | }
|
---|
| 652 | }
|
---|
| 653 |
|
---|
[17593] | 654 | private ISymbolicExpressionTreeNode MakeLessThan(ISymbolicExpressionTreeNode leftSide,
|
---|
[14843] | 655 | ISymbolicExpressionTreeNode rightSide) {
|
---|
| 656 | if (IsConstant(leftSide) && IsConstant(rightSide)) {
|
---|
| 657 | var lsConst = leftSide as ConstantTreeNode;
|
---|
| 658 | var rsConst = rightSide as ConstantTreeNode;
|
---|
| 659 | if (lsConst.Value < rsConst.Value) return MakeConstant(1.0);
|
---|
| 660 | else return MakeConstant(-1.0);
|
---|
| 661 | } else {
|
---|
| 662 | var ltNode = ltSymbol.CreateTreeNode();
|
---|
| 663 | ltNode.AddSubtree(leftSide);
|
---|
| 664 | ltNode.AddSubtree(rightSide);
|
---|
| 665 | return ltNode;
|
---|
| 666 | }
|
---|
| 667 | }
|
---|
| 668 |
|
---|
[17593] | 669 | private ISymbolicExpressionTreeNode MakeGreaterThan(ISymbolicExpressionTreeNode leftSide,
|
---|
[14843] | 670 | ISymbolicExpressionTreeNode rightSide) {
|
---|
| 671 | if (IsConstant(leftSide) && IsConstant(rightSide)) {
|
---|
| 672 | var lsConst = leftSide as ConstantTreeNode;
|
---|
| 673 | var rsConst = rightSide as ConstantTreeNode;
|
---|
| 674 | if (lsConst.Value > rsConst.Value) return MakeConstant(1.0);
|
---|
| 675 | else return MakeConstant(-1.0);
|
---|
| 676 | } else {
|
---|
| 677 | var gtNode = gtSymbol.CreateTreeNode();
|
---|
| 678 | gtNode.AddSubtree(leftSide);
|
---|
| 679 | gtNode.AddSubtree(rightSide);
|
---|
| 680 | return gtNode;
|
---|
| 681 | }
|
---|
| 682 | }
|
---|
| 683 |
|
---|
[17593] | 684 | private ISymbolicExpressionTreeNode MakeIfThenElse(ISymbolicExpressionTreeNode condition,
|
---|
[14843] | 685 | ISymbolicExpressionTreeNode trueBranch, ISymbolicExpressionTreeNode falseBranch) {
|
---|
| 686 | if (IsConstant(condition)) {
|
---|
| 687 | var constT = condition as ConstantTreeNode;
|
---|
| 688 | if (constT.Value > 0.0) return trueBranch;
|
---|
| 689 | else return falseBranch;
|
---|
| 690 | } else {
|
---|
| 691 | var ifNode = ifThenElseSymbol.CreateTreeNode();
|
---|
| 692 | if (IsBoolean(condition)) {
|
---|
| 693 | ifNode.AddSubtree(condition);
|
---|
| 694 | } else {
|
---|
| 695 | var gtNode = gtSymbol.CreateTreeNode();
|
---|
| 696 | gtNode.AddSubtree(condition);
|
---|
| 697 | gtNode.AddSubtree(MakeConstant(0.0));
|
---|
| 698 | ifNode.AddSubtree(gtNode);
|
---|
| 699 | }
|
---|
| 700 | ifNode.AddSubtree(trueBranch);
|
---|
| 701 | ifNode.AddSubtree(falseBranch);
|
---|
| 702 | return ifNode;
|
---|
| 703 | }
|
---|
| 704 | }
|
---|
| 705 |
|
---|
[17593] | 706 | private ISymbolicExpressionTreeNode MakeSine(ISymbolicExpressionTreeNode node) {
|
---|
[14843] | 707 | if (IsConstant(node)) {
|
---|
| 708 | var constT = node as ConstantTreeNode;
|
---|
| 709 | return MakeConstant(Math.Sin(constT.Value));
|
---|
| 710 | } else if (IsFactor(node)) {
|
---|
| 711 | var factor = node as FactorVariableTreeNode;
|
---|
| 712 | return MakeFactor(factor.Symbol, factor.VariableName, factor.Weights.Select(Math.Sin));
|
---|
| 713 | } else if (IsBinFactor(node)) {
|
---|
| 714 | var binFactor = node as BinaryFactorVariableTreeNode;
|
---|
| 715 | return MakeBinFactor(binFactor.Symbol, binFactor.VariableName, binFactor.VariableValue, Math.Sin(binFactor.Weight));
|
---|
| 716 | } else {
|
---|
| 717 | var sineNode = sineSymbol.CreateTreeNode();
|
---|
| 718 | sineNode.AddSubtree(node);
|
---|
| 719 | return sineNode;
|
---|
| 720 | }
|
---|
| 721 | }
|
---|
| 722 |
|
---|
[17593] | 723 | private ISymbolicExpressionTreeNode MakeTangent(ISymbolicExpressionTreeNode node) {
|
---|
[14843] | 724 | if (IsConstant(node)) {
|
---|
| 725 | var constT = node as ConstantTreeNode;
|
---|
| 726 | return MakeConstant(Math.Tan(constT.Value));
|
---|
| 727 | } else if (IsFactor(node)) {
|
---|
| 728 | var factor = node as FactorVariableTreeNode;
|
---|
| 729 | return MakeFactor(factor.Symbol, factor.VariableName, factor.Weights.Select(Math.Tan));
|
---|
| 730 | } else if (IsBinFactor(node)) {
|
---|
| 731 | var binFactor = node as BinaryFactorVariableTreeNode;
|
---|
| 732 | return MakeBinFactor(binFactor.Symbol, binFactor.VariableName, binFactor.VariableValue, Math.Tan(binFactor.Weight));
|
---|
| 733 | } else {
|
---|
| 734 | var tanNode = tanSymbol.CreateTreeNode();
|
---|
| 735 | tanNode.AddSubtree(node);
|
---|
| 736 | return tanNode;
|
---|
| 737 | }
|
---|
| 738 | }
|
---|
| 739 |
|
---|
[17593] | 740 | private ISymbolicExpressionTreeNode MakeCosine(ISymbolicExpressionTreeNode node) {
|
---|
[14843] | 741 | if (IsConstant(node)) {
|
---|
| 742 | var constT = node as ConstantTreeNode;
|
---|
| 743 | return MakeConstant(Math.Cos(constT.Value));
|
---|
| 744 | } else if (IsFactor(node)) {
|
---|
| 745 | var factor = node as FactorVariableTreeNode;
|
---|
| 746 | return MakeFactor(factor.Symbol, factor.VariableName, factor.Weights.Select(Math.Cos));
|
---|
| 747 | } else if (IsBinFactor(node)) {
|
---|
| 748 | var binFactor = node as BinaryFactorVariableTreeNode;
|
---|
| 749 | // cos(0) = 1 see similar case for Exp(binfactor)
|
---|
| 750 | return MakeSum(MakeBinFactor(binFactor.Symbol, binFactor.VariableName, binFactor.VariableValue, Math.Cos(binFactor.Weight) - 1),
|
---|
| 751 | MakeConstant(1.0));
|
---|
| 752 | } else {
|
---|
| 753 | var cosNode = cosineSymbol.CreateTreeNode();
|
---|
| 754 | cosNode.AddSubtree(node);
|
---|
| 755 | return cosNode;
|
---|
| 756 | }
|
---|
| 757 | }
|
---|
| 758 |
|
---|
[17593] | 759 | private ISymbolicExpressionTreeNode MakeExp(ISymbolicExpressionTreeNode node) {
|
---|
[14843] | 760 | if (IsConstant(node)) {
|
---|
| 761 | var constT = node as ConstantTreeNode;
|
---|
| 762 | return MakeConstant(Math.Exp(constT.Value));
|
---|
| 763 | } else if (IsFactor(node)) {
|
---|
| 764 | var factNode = node as FactorVariableTreeNode;
|
---|
| 765 | return MakeFactor(factNode.Symbol, factNode.VariableName, factNode.Weights.Select(w => Math.Exp(w)));
|
---|
| 766 | } else if (IsBinFactor(node)) {
|
---|
| 767 | // exp( binfactor w val=a) = if(val=a) exp(w) else exp(0) = binfactor( (exp(w) - 1) val a) + 1
|
---|
| 768 | var binFactor = node as BinaryFactorVariableTreeNode;
|
---|
| 769 | return
|
---|
| 770 | MakeSum(MakeBinFactor(binFactor.Symbol, binFactor.VariableName, binFactor.VariableValue, Math.Exp(binFactor.Weight) - 1), MakeConstant(1.0));
|
---|
| 771 | } else if (IsLog(node)) {
|
---|
| 772 | return node.GetSubtree(0);
|
---|
| 773 | } else if (IsAddition(node)) {
|
---|
| 774 | return node.Subtrees.Select(s => MakeExp(s)).Aggregate((s, t) => MakeProduct(s, t));
|
---|
| 775 | } else if (IsSubtraction(node)) {
|
---|
| 776 | return node.Subtrees.Select(s => MakeExp(s)).Aggregate((s, t) => MakeProduct(s, Negate(t)));
|
---|
| 777 | } else {
|
---|
| 778 | var expNode = expSymbol.CreateTreeNode();
|
---|
| 779 | expNode.AddSubtree(node);
|
---|
| 780 | return expNode;
|
---|
| 781 | }
|
---|
| 782 | }
|
---|
[17593] | 783 | private ISymbolicExpressionTreeNode MakeLog(ISymbolicExpressionTreeNode node) {
|
---|
[14843] | 784 | if (IsConstant(node)) {
|
---|
| 785 | var constT = node as ConstantTreeNode;
|
---|
| 786 | return MakeConstant(Math.Log(constT.Value));
|
---|
| 787 | } else if (IsFactor(node)) {
|
---|
| 788 | var factNode = node as FactorVariableTreeNode;
|
---|
| 789 | return MakeFactor(factNode.Symbol, factNode.VariableName, factNode.Weights.Select(w => Math.Log(w)));
|
---|
| 790 | } else if (IsExp(node)) {
|
---|
| 791 | return node.GetSubtree(0);
|
---|
| 792 | } else if (IsSquareRoot(node)) {
|
---|
| 793 | return MakeFraction(MakeLog(node.GetSubtree(0)), MakeConstant(2.0));
|
---|
| 794 | } else {
|
---|
| 795 | var logNode = logSymbol.CreateTreeNode();
|
---|
| 796 | logNode.AddSubtree(node);
|
---|
| 797 | return logNode;
|
---|
| 798 | }
|
---|
| 799 | }
|
---|
| 800 |
|
---|
[17593] | 801 | private ISymbolicExpressionTreeNode MakeSquare(ISymbolicExpressionTreeNode node) {
|
---|
[14843] | 802 | if (IsConstant(node)) {
|
---|
| 803 | var constT = node as ConstantTreeNode;
|
---|
| 804 | return MakeConstant(constT.Value * constT.Value);
|
---|
| 805 | } else if (IsFactor(node)) {
|
---|
| 806 | var factNode = node as FactorVariableTreeNode;
|
---|
| 807 | return MakeFactor(factNode.Symbol, factNode.VariableName, factNode.Weights.Select(w => w * w));
|
---|
| 808 | } else if (IsBinFactor(node)) {
|
---|
| 809 | var binFactor = node as BinaryFactorVariableTreeNode;
|
---|
| 810 | return MakeBinFactor(binFactor.Symbol, binFactor.VariableName, binFactor.VariableValue, binFactor.Weight * binFactor.Weight);
|
---|
| 811 | } else if (IsSquareRoot(node)) {
|
---|
| 812 | return node.GetSubtree(0);
|
---|
[16356] | 813 | } else if (IsMultiplication(node)) {
|
---|
| 814 | // sqr( x * y ) = sqr(x) * sqr(y)
|
---|
| 815 | var mulNode = mulSymbol.CreateTreeNode();
|
---|
| 816 | foreach (var subtree in node.Subtrees) {
|
---|
| 817 | mulNode.AddSubtree(MakeSquare(subtree));
|
---|
| 818 | }
|
---|
| 819 | return mulNode;
|
---|
| 820 | } else if (IsAbsolute(node)) {
|
---|
| 821 | return MakeSquare(node.GetSubtree(0)); // sqr(abs(x)) = sqr(x)
|
---|
| 822 | } else if (IsExp(node)) {
|
---|
| 823 | return MakeExp(MakeProduct(node.GetSubtree(0), MakeConstant(2.0))); // sqr(exp(x)) = exp(2x)
|
---|
| 824 | } else if (IsCube(node)) {
|
---|
| 825 | return MakePower(node.GetSubtree(0), MakeConstant(6));
|
---|
[14843] | 826 | } else {
|
---|
| 827 | var sqrNode = sqrSymbol.CreateTreeNode();
|
---|
| 828 | sqrNode.AddSubtree(node);
|
---|
| 829 | return sqrNode;
|
---|
| 830 | }
|
---|
| 831 | }
|
---|
| 832 |
|
---|
[17593] | 833 | private ISymbolicExpressionTreeNode MakeCube(ISymbolicExpressionTreeNode node) {
|
---|
[16356] | 834 | if (IsConstant(node)) {
|
---|
| 835 | var constT = node as ConstantTreeNode;
|
---|
| 836 | return MakeConstant(constT.Value * constT.Value * constT.Value);
|
---|
| 837 | } else if (IsFactor(node)) {
|
---|
| 838 | var factNode = node as FactorVariableTreeNode;
|
---|
| 839 | return MakeFactor(factNode.Symbol, factNode.VariableName, factNode.Weights.Select(w => w * w * w));
|
---|
| 840 | } else if (IsBinFactor(node)) {
|
---|
| 841 | var binFactor = node as BinaryFactorVariableTreeNode;
|
---|
| 842 | return MakeBinFactor(binFactor.Symbol, binFactor.VariableName, binFactor.VariableValue, binFactor.Weight * binFactor.Weight * binFactor.Weight);
|
---|
| 843 | } else if (IsCubeRoot(node)) {
|
---|
| 844 | 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
|
---|
| 845 | } else if (IsExp(node)) {
|
---|
| 846 | return MakeExp(MakeProduct(node.GetSubtree(0), MakeConstant(3)));
|
---|
| 847 | } else if (IsSquare(node)) {
|
---|
| 848 | return MakePower(node.GetSubtree(0), MakeConstant(6));
|
---|
| 849 | } else {
|
---|
| 850 | var cubeNode = cubeSymbol.CreateTreeNode();
|
---|
| 851 | cubeNode.AddSubtree(node);
|
---|
| 852 | return cubeNode;
|
---|
| 853 | }
|
---|
| 854 | }
|
---|
| 855 |
|
---|
[17593] | 856 | private ISymbolicExpressionTreeNode MakeAbs(ISymbolicExpressionTreeNode node) {
|
---|
[16356] | 857 | if (IsConstant(node)) {
|
---|
| 858 | var constT = node as ConstantTreeNode;
|
---|
| 859 | return MakeConstant(Math.Abs(constT.Value));
|
---|
| 860 | } else if (IsFactor(node)) {
|
---|
| 861 | var factNode = node as FactorVariableTreeNode;
|
---|
| 862 | return MakeFactor(factNode.Symbol, factNode.VariableName, factNode.Weights.Select(w => Math.Abs(w)));
|
---|
| 863 | } else if (IsBinFactor(node)) {
|
---|
| 864 | var binFactor = node as BinaryFactorVariableTreeNode;
|
---|
| 865 | return MakeBinFactor(binFactor.Symbol, binFactor.VariableName, binFactor.VariableValue, Math.Abs(binFactor.Weight));
|
---|
| 866 | } else if (IsSquare(node) || IsExp(node) || IsSquareRoot(node) || IsCubeRoot(node)) {
|
---|
| 867 | return node; // abs(sqr(x)) = sqr(x), abs(exp(x)) = exp(x) ...
|
---|
| 868 | } else if (IsMultiplication(node)) {
|
---|
| 869 | var mul = mulSymbol.CreateTreeNode();
|
---|
| 870 | foreach (var st in node.Subtrees) {
|
---|
| 871 | mul.AddSubtree(MakeAbs(st));
|
---|
| 872 | }
|
---|
| 873 | return mul;
|
---|
| 874 | } else if (IsDivision(node)) {
|
---|
| 875 | var div = divSymbol.CreateTreeNode();
|
---|
| 876 | foreach (var st in node.Subtrees) {
|
---|
| 877 | div.AddSubtree(MakeAbs(st));
|
---|
| 878 | }
|
---|
| 879 | return div;
|
---|
| 880 | } else {
|
---|
| 881 | var absNode = absSymbol.CreateTreeNode();
|
---|
| 882 | absNode.AddSubtree(node);
|
---|
| 883 | return absNode;
|
---|
| 884 | }
|
---|
| 885 | }
|
---|
| 886 |
|
---|
| 887 | // constant folding only
|
---|
[17593] | 888 | private ISymbolicExpressionTreeNode MakeAnalyticalQuotient(ISymbolicExpressionTreeNode a, ISymbolicExpressionTreeNode b) {
|
---|
[16356] | 889 | if (IsConstant(b)) {
|
---|
| 890 | var c = b as ConstantTreeNode;
|
---|
| 891 | return MakeFraction(a, MakeConstant(Math.Sqrt(1.0 + c.Value * c.Value)));
|
---|
| 892 | } else if (IsFactor(b)) {
|
---|
| 893 | var factNode = b as FactorVariableTreeNode;
|
---|
| 894 | return MakeFraction(a, MakeFactor(factNode.Symbol, factNode.VariableName, factNode.Weights.Select(w => Math.Sqrt(1.0 + w * w))));
|
---|
| 895 | } else if (IsBinFactor(b)) {
|
---|
| 896 | var binFactor = b as BinaryFactorVariableTreeNode;
|
---|
| 897 | return MakeFraction(a, MakeBinFactor(binFactor.Symbol, binFactor.VariableName, binFactor.VariableValue, Math.Sqrt(1.0 + binFactor.Weight * binFactor.Weight)));
|
---|
| 898 | } else {
|
---|
| 899 | var aqNode = aqSymbol.CreateTreeNode();
|
---|
| 900 | aqNode.AddSubtree(a);
|
---|
| 901 | aqNode.AddSubtree(b);
|
---|
| 902 | return aqNode;
|
---|
| 903 | }
|
---|
| 904 | }
|
---|
| 905 |
|
---|
[17593] | 906 | private ISymbolicExpressionTreeNode MakeSquareRoot(ISymbolicExpressionTreeNode node) {
|
---|
[14843] | 907 | if (IsConstant(node)) {
|
---|
| 908 | var constT = node as ConstantTreeNode;
|
---|
| 909 | return MakeConstant(Math.Sqrt(constT.Value));
|
---|
| 910 | } else if (IsFactor(node)) {
|
---|
| 911 | var factNode = node as FactorVariableTreeNode;
|
---|
| 912 | return MakeFactor(factNode.Symbol, factNode.VariableName, factNode.Weights.Select(w => Math.Sqrt(w)));
|
---|
| 913 | } else if (IsBinFactor(node)) {
|
---|
| 914 | var binFactor = node as BinaryFactorVariableTreeNode;
|
---|
| 915 | return MakeBinFactor(binFactor.Symbol, binFactor.VariableName, binFactor.VariableValue, Math.Sqrt(binFactor.Weight));
|
---|
| 916 | } else if (IsSquare(node)) {
|
---|
[16356] | 917 | 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] | 918 | } else {
|
---|
| 919 | var sqrtNode = sqrtSymbol.CreateTreeNode();
|
---|
| 920 | sqrtNode.AddSubtree(node);
|
---|
| 921 | return sqrtNode;
|
---|
| 922 | }
|
---|
| 923 | }
|
---|
| 924 |
|
---|
[17593] | 925 | private ISymbolicExpressionTreeNode MakeCubeRoot(ISymbolicExpressionTreeNode node) {
|
---|
[16356] | 926 | if (IsConstant(node)) {
|
---|
| 927 | var constT = node as ConstantTreeNode;
|
---|
| 928 | return MakeConstant(Math.Pow(constT.Value, 1.0 / 3.0));
|
---|
| 929 | } else if (IsFactor(node)) {
|
---|
| 930 | var factNode = node as FactorVariableTreeNode;
|
---|
| 931 | return MakeFactor(factNode.Symbol, factNode.VariableName, factNode.Weights.Select(w => Math.Pow(w, 1.0 / 3.0)));
|
---|
| 932 | } else if (IsBinFactor(node)) {
|
---|
| 933 | var binFactor = node as BinaryFactorVariableTreeNode;
|
---|
| 934 | return MakeBinFactor(binFactor.Symbol, binFactor.VariableName, binFactor.VariableValue, Math.Sqrt(Math.Pow(binFactor.Weight, 1.0 / 3.0)));
|
---|
| 935 | } else if (IsCube(node)) {
|
---|
| 936 | return node.GetSubtree(0);
|
---|
| 937 | } else {
|
---|
| 938 | var cubeRootNode = cubeRootSymbol.CreateTreeNode();
|
---|
| 939 | cubeRootNode.AddSubtree(node);
|
---|
| 940 | return cubeRootNode;
|
---|
| 941 | }
|
---|
| 942 | }
|
---|
| 943 |
|
---|
[17593] | 944 | private ISymbolicExpressionTreeNode MakeRoot(ISymbolicExpressionTreeNode a, ISymbolicExpressionTreeNode b) {
|
---|
[14843] | 945 | if (IsConstant(a) && IsConstant(b)) {
|
---|
| 946 | var constA = a as ConstantTreeNode;
|
---|
| 947 | var constB = b as ConstantTreeNode;
|
---|
| 948 | return MakeConstant(Math.Pow(constA.Value, 1.0 / Math.Round(constB.Value)));
|
---|
| 949 | } else if (IsFactor(a) && IsConstant(b)) {
|
---|
| 950 | var factNode = a as FactorVariableTreeNode;
|
---|
| 951 | var constNode = b as ConstantTreeNode;
|
---|
| 952 | return MakeFactor(factNode.Symbol, factNode.VariableName,
|
---|
| 953 | factNode.Weights.Select(w => Math.Pow(w, 1.0 / Math.Round(constNode.Value))));
|
---|
| 954 | } else if (IsBinFactor(a) && IsConstant(b)) {
|
---|
| 955 | var binFactor = a as BinaryFactorVariableTreeNode;
|
---|
| 956 | var constNode = b as ConstantTreeNode;
|
---|
| 957 | return MakeBinFactor(binFactor.Symbol, binFactor.VariableName, binFactor.VariableValue, Math.Pow(binFactor.Weight, 1.0 / Math.Round(constNode.Value)));
|
---|
| 958 | } else if (IsConstant(a) && IsFactor(b)) {
|
---|
| 959 | var constNode = a as ConstantTreeNode;
|
---|
| 960 | var factNode = b as FactorVariableTreeNode;
|
---|
| 961 | return MakeFactor(factNode.Symbol, factNode.VariableName, factNode.Weights.Select(w => Math.Pow(constNode.Value, 1.0 / Math.Round(w))));
|
---|
| 962 | } else if (IsConstant(a) && IsBinFactor(b)) {
|
---|
| 963 | var constNode = a as ConstantTreeNode;
|
---|
| 964 | var factNode = b as BinaryFactorVariableTreeNode;
|
---|
| 965 | return MakeBinFactor(factNode.Symbol, factNode.VariableName, factNode.VariableValue, Math.Pow(constNode.Value, 1.0 / Math.Round(factNode.Weight)));
|
---|
| 966 | } else if (IsFactor(a) && IsFactor(b) && AreSameTypeAndVariable(a, b)) {
|
---|
| 967 | var node0 = a as FactorVariableTreeNode;
|
---|
| 968 | var node1 = b as FactorVariableTreeNode;
|
---|
| 969 | return MakeFactor(node0.Symbol, node0.VariableName, node0.Weights.Zip(node1.Weights, (u, v) => Math.Pow(u, 1.0 / Math.Round(v))));
|
---|
| 970 | } else if (IsConstant(b)) {
|
---|
| 971 | var constB = b as ConstantTreeNode;
|
---|
| 972 | var constBValue = Math.Round(constB.Value);
|
---|
| 973 | if (constBValue.IsAlmost(1.0)) {
|
---|
| 974 | return a;
|
---|
| 975 | } else if (constBValue.IsAlmost(0.0)) {
|
---|
| 976 | return MakeConstant(1.0);
|
---|
| 977 | } else if (constBValue.IsAlmost(-1.0)) {
|
---|
| 978 | return MakeFraction(MakeConstant(1.0), a);
|
---|
| 979 | } else if (constBValue < 0) {
|
---|
| 980 | var rootNode = rootSymbol.CreateTreeNode();
|
---|
| 981 | rootNode.AddSubtree(a);
|
---|
| 982 | rootNode.AddSubtree(MakeConstant(-1.0 * constBValue));
|
---|
| 983 | return MakeFraction(MakeConstant(1.0), rootNode);
|
---|
| 984 | } else {
|
---|
| 985 | var rootNode = rootSymbol.CreateTreeNode();
|
---|
| 986 | rootNode.AddSubtree(a);
|
---|
| 987 | rootNode.AddSubtree(MakeConstant(constBValue));
|
---|
| 988 | return rootNode;
|
---|
| 989 | }
|
---|
| 990 | } else {
|
---|
| 991 | var rootNode = rootSymbol.CreateTreeNode();
|
---|
| 992 | rootNode.AddSubtree(a);
|
---|
| 993 | rootNode.AddSubtree(b);
|
---|
| 994 | return rootNode;
|
---|
| 995 | }
|
---|
| 996 | }
|
---|
| 997 |
|
---|
| 998 |
|
---|
[17593] | 999 | private ISymbolicExpressionTreeNode MakePower(ISymbolicExpressionTreeNode a, ISymbolicExpressionTreeNode b) {
|
---|
[14843] | 1000 | if (IsConstant(a) && IsConstant(b)) {
|
---|
| 1001 | var constA = a as ConstantTreeNode;
|
---|
| 1002 | var constB = b as ConstantTreeNode;
|
---|
| 1003 | return MakeConstant(Math.Pow(constA.Value, Math.Round(constB.Value)));
|
---|
| 1004 | } else if (IsFactor(a) && IsConstant(b)) {
|
---|
| 1005 | var factNode = a as FactorVariableTreeNode;
|
---|
| 1006 | var constNode = b as ConstantTreeNode;
|
---|
| 1007 | return MakeFactor(factNode.Symbol, factNode.VariableName, factNode.Weights.Select(w => Math.Pow(w, Math.Round(constNode.Value))));
|
---|
| 1008 | } else if (IsBinFactor(a) && IsConstant(b)) {
|
---|
| 1009 | var binFactor = a as BinaryFactorVariableTreeNode;
|
---|
| 1010 | var constNode = b as ConstantTreeNode;
|
---|
| 1011 | return MakeBinFactor(binFactor.Symbol, binFactor.VariableName, binFactor.VariableValue, Math.Pow(binFactor.Weight, Math.Round(constNode.Value)));
|
---|
| 1012 | } else if (IsConstant(a) && IsFactor(b)) {
|
---|
| 1013 | var constNode = a as ConstantTreeNode;
|
---|
| 1014 | var factNode = b as FactorVariableTreeNode;
|
---|
| 1015 | return MakeFactor(factNode.Symbol, factNode.VariableName, factNode.Weights.Select(w => Math.Pow(constNode.Value, Math.Round(w))));
|
---|
| 1016 | } else if (IsConstant(a) && IsBinFactor(b)) {
|
---|
| 1017 | var constNode = a as ConstantTreeNode;
|
---|
| 1018 | var factNode = b as BinaryFactorVariableTreeNode;
|
---|
| 1019 | return MakeBinFactor(factNode.Symbol, factNode.VariableName, factNode.VariableValue, Math.Pow(constNode.Value, Math.Round(factNode.Weight)));
|
---|
| 1020 | } else if (IsFactor(a) && IsFactor(b) && AreSameTypeAndVariable(a, b)) {
|
---|
| 1021 | var node0 = a as FactorVariableTreeNode;
|
---|
| 1022 | var node1 = b as FactorVariableTreeNode;
|
---|
| 1023 | return MakeFactor(node0.Symbol, node0.VariableName, node0.Weights.Zip(node1.Weights, (u, v) => Math.Pow(u, Math.Round(v))));
|
---|
| 1024 | } else if (IsConstant(b)) {
|
---|
| 1025 | var constB = b as ConstantTreeNode;
|
---|
| 1026 | double exponent = Math.Round(constB.Value);
|
---|
| 1027 | if (exponent.IsAlmost(0.0)) {
|
---|
| 1028 | return MakeConstant(1.0);
|
---|
| 1029 | } else if (exponent.IsAlmost(1.0)) {
|
---|
| 1030 | return a;
|
---|
| 1031 | } else if (exponent.IsAlmost(-1.0)) {
|
---|
| 1032 | return MakeFraction(MakeConstant(1.0), a);
|
---|
| 1033 | } else if (exponent < 0) {
|
---|
| 1034 | var powNode = powSymbol.CreateTreeNode();
|
---|
| 1035 | powNode.AddSubtree(a);
|
---|
| 1036 | powNode.AddSubtree(MakeConstant(-1.0 * exponent));
|
---|
| 1037 | return MakeFraction(MakeConstant(1.0), powNode);
|
---|
| 1038 | } else {
|
---|
| 1039 | var powNode = powSymbol.CreateTreeNode();
|
---|
| 1040 | powNode.AddSubtree(a);
|
---|
| 1041 | powNode.AddSubtree(MakeConstant(exponent));
|
---|
| 1042 | return powNode;
|
---|
| 1043 | }
|
---|
| 1044 | } else {
|
---|
| 1045 | var powNode = powSymbol.CreateTreeNode();
|
---|
| 1046 | powNode.AddSubtree(a);
|
---|
| 1047 | powNode.AddSubtree(b);
|
---|
| 1048 | return powNode;
|
---|
| 1049 | }
|
---|
| 1050 | }
|
---|
| 1051 |
|
---|
| 1052 |
|
---|
| 1053 | // MakeFraction, MakeProduct and MakeSum take two already simplified trees and create a new simplified tree
|
---|
[17593] | 1054 | private ISymbolicExpressionTreeNode MakeFraction(ISymbolicExpressionTreeNode a, ISymbolicExpressionTreeNode b) {
|
---|
[14843] | 1055 | if (IsConstant(a) && IsConstant(b)) {
|
---|
| 1056 | // fold constants
|
---|
| 1057 | return MakeConstant(((ConstantTreeNode)a).Value / ((ConstantTreeNode)b).Value);
|
---|
| 1058 | } else if ((IsConstant(a) && !((ConstantTreeNode)a).Value.IsAlmost(1.0))) {
|
---|
| 1059 | return MakeFraction(MakeConstant(1.0), MakeProduct(b, Invert(a)));
|
---|
| 1060 | } else if (IsVariableBase(a) && IsConstant(b)) {
|
---|
| 1061 | // merge constant values into variable weights
|
---|
| 1062 | var constB = ((ConstantTreeNode)b).Value;
|
---|
| 1063 | ((VariableTreeNodeBase)a).Weight /= constB;
|
---|
| 1064 | return a;
|
---|
| 1065 | } else if (IsFactor(a) && IsConstant(b)) {
|
---|
| 1066 | var factNode = a as FactorVariableTreeNode;
|
---|
| 1067 | var constNode = b as ConstantTreeNode;
|
---|
| 1068 | return MakeFactor(factNode.Symbol, factNode.VariableName, factNode.Weights.Select(w => w / constNode.Value));
|
---|
| 1069 | } else if (IsBinFactor(a) && IsConstant(b)) {
|
---|
| 1070 | var factNode = a as BinaryFactorVariableTreeNode;
|
---|
| 1071 | var constNode = b as ConstantTreeNode;
|
---|
| 1072 | return MakeBinFactor(factNode.Symbol, factNode.VariableName, factNode.VariableValue, factNode.Weight / constNode.Value);
|
---|
| 1073 | } else if (IsFactor(a) && IsFactor(b) && AreSameTypeAndVariable(a, b)) {
|
---|
| 1074 | var node0 = a as FactorVariableTreeNode;
|
---|
| 1075 | var node1 = b as FactorVariableTreeNode;
|
---|
| 1076 | return MakeFactor(node0.Symbol, node0.VariableName, node0.Weights.Zip(node1.Weights, (u, v) => u / v));
|
---|
| 1077 | } else if (IsFactor(a) && IsBinFactor(b) && ((IVariableTreeNode)a).VariableName == ((IVariableTreeNode)b).VariableName) {
|
---|
| 1078 | var node0 = a as FactorVariableTreeNode;
|
---|
| 1079 | var node1 = b as BinaryFactorVariableTreeNode;
|
---|
| 1080 | var varValues = node0.Symbol.GetVariableValues(node0.VariableName).ToArray();
|
---|
| 1081 | var wi = Array.IndexOf(varValues, node1.VariableValue);
|
---|
| 1082 | if (wi < 0) throw new ArgumentException();
|
---|
| 1083 | var newWeighs = new double[varValues.Length];
|
---|
| 1084 | node0.Weights.CopyTo(newWeighs, 0);
|
---|
| 1085 | for (int i = 0; i < newWeighs.Length; i++)
|
---|
| 1086 | if (wi == i) newWeighs[i] /= node1.Weight;
|
---|
| 1087 | else newWeighs[i] /= 0.0;
|
---|
| 1088 | return MakeFactor(node0.Symbol, node0.VariableName, newWeighs);
|
---|
| 1089 | } else if (IsFactor(a)) {
|
---|
| 1090 | return MakeFraction(MakeConstant(1.0), MakeProduct(b, Invert(a)));
|
---|
| 1091 | } else if (IsVariableBase(a) && IsVariableBase(b) && AreSameTypeAndVariable(a, b) && !IsBinFactor(b)) {
|
---|
| 1092 | // cancel variables (not allowed for bin factors because of division by zero)
|
---|
| 1093 | var aVar = a as VariableTreeNode;
|
---|
| 1094 | var bVar = b as VariableTreeNode;
|
---|
| 1095 | return MakeConstant(aVar.Weight / bVar.Weight);
|
---|
| 1096 | } else if (IsAddition(a) && IsConstant(b)) {
|
---|
| 1097 | return a.Subtrees
|
---|
| 1098 | .Select(x => GetSimplifiedTree(x))
|
---|
| 1099 | .Select(x => MakeFraction(x, GetSimplifiedTree(b)))
|
---|
| 1100 | .Aggregate((c, d) => MakeSum(c, d));
|
---|
| 1101 | } else if (IsMultiplication(a) && IsConstant(b)) {
|
---|
| 1102 | return MakeProduct(a, Invert(b));
|
---|
| 1103 | } else if (IsDivision(a) && IsConstant(b)) {
|
---|
| 1104 | // (a1 / a2) / c => (a1 / (a2 * c))
|
---|
| 1105 | return MakeFraction(a.GetSubtree(0), MakeProduct(a.GetSubtree(1), b));
|
---|
| 1106 | } else if (IsDivision(a) && IsDivision(b)) {
|
---|
| 1107 | // (a1 / a2) / (b1 / b2) =>
|
---|
| 1108 | return MakeFraction(MakeProduct(a.GetSubtree(0), b.GetSubtree(1)), MakeProduct(a.GetSubtree(1), b.GetSubtree(0)));
|
---|
| 1109 | } else if (IsDivision(a)) {
|
---|
| 1110 | // (a1 / a2) / b => (a1 / (a2 * b))
|
---|
| 1111 | return MakeFraction(a.GetSubtree(0), MakeProduct(a.GetSubtree(1), b));
|
---|
| 1112 | } else if (IsDivision(b)) {
|
---|
| 1113 | // a / (b1 / b2) => (a * b2) / b1
|
---|
| 1114 | return MakeFraction(MakeProduct(a, b.GetSubtree(1)), b.GetSubtree(0));
|
---|
[16356] | 1115 | } else if (IsAnalyticalQuotient(a)) {
|
---|
| 1116 | return MakeAnalyticalQuotient(a.GetSubtree(0), MakeProduct(a.GetSubtree(1), b));
|
---|
[14843] | 1117 | } else {
|
---|
| 1118 | var div = divSymbol.CreateTreeNode();
|
---|
| 1119 | div.AddSubtree(a);
|
---|
| 1120 | div.AddSubtree(b);
|
---|
| 1121 | return div;
|
---|
| 1122 | }
|
---|
| 1123 | }
|
---|
| 1124 |
|
---|
[17593] | 1125 | private ISymbolicExpressionTreeNode MakeSum(ISymbolicExpressionTreeNode a, ISymbolicExpressionTreeNode b) {
|
---|
[14843] | 1126 | if (IsConstant(a) && IsConstant(b)) {
|
---|
| 1127 | // fold constants
|
---|
| 1128 | ((ConstantTreeNode)a).Value += ((ConstantTreeNode)b).Value;
|
---|
| 1129 | return a;
|
---|
| 1130 | } else if (IsConstant(a)) {
|
---|
| 1131 | // c + x => x + c
|
---|
| 1132 | // b is not constant => make sure constant is on the right
|
---|
| 1133 | return MakeSum(b, a);
|
---|
| 1134 | } else if (IsConstant(b) && ((ConstantTreeNode)b).Value.IsAlmost(0.0)) {
|
---|
| 1135 | // x + 0 => x
|
---|
| 1136 | return a;
|
---|
| 1137 | } else if (IsFactor(a) && IsConstant(b)) {
|
---|
| 1138 | var factNode = a as FactorVariableTreeNode;
|
---|
| 1139 | var constNode = b as ConstantTreeNode;
|
---|
| 1140 | return MakeFactor(factNode.Symbol, factNode.VariableName, factNode.Weights.Select((w) => w + constNode.Value));
|
---|
| 1141 | } else if (IsFactor(a) && IsFactor(b) && AreSameTypeAndVariable(a, b)) {
|
---|
| 1142 | var node0 = a as FactorVariableTreeNode;
|
---|
| 1143 | var node1 = b as FactorVariableTreeNode;
|
---|
| 1144 | return MakeFactor(node0.Symbol, node0.VariableName, node0.Weights.Zip(node1.Weights, (u, v) => u + v));
|
---|
| 1145 | } else if (IsBinFactor(a) && IsFactor(b)) {
|
---|
| 1146 | return MakeSum(b, a);
|
---|
| 1147 | } else if (IsFactor(a) && IsBinFactor(b) &&
|
---|
| 1148 | ((IVariableTreeNode)a).VariableName == ((IVariableTreeNode)b).VariableName) {
|
---|
| 1149 | var node0 = a as FactorVariableTreeNode;
|
---|
| 1150 | var node1 = b as BinaryFactorVariableTreeNode;
|
---|
| 1151 | var varValues = node0.Symbol.GetVariableValues(node0.VariableName).ToArray();
|
---|
| 1152 | var wi = Array.IndexOf(varValues, node1.VariableValue);
|
---|
| 1153 | if (wi < 0) throw new ArgumentException();
|
---|
| 1154 | var newWeighs = new double[varValues.Length];
|
---|
| 1155 | node0.Weights.CopyTo(newWeighs, 0);
|
---|
| 1156 | newWeighs[wi] += node1.Weight;
|
---|
| 1157 | return MakeFactor(node0.Symbol, node0.VariableName, newWeighs);
|
---|
| 1158 | } else if (IsAddition(a) && IsAddition(b)) {
|
---|
| 1159 | // merge additions
|
---|
| 1160 | var add = addSymbol.CreateTreeNode();
|
---|
| 1161 | // add all sub trees except for the last
|
---|
| 1162 | for (int i = 0; i < a.Subtrees.Count() - 1; i++) add.AddSubtree(a.GetSubtree(i));
|
---|
| 1163 | for (int i = 0; i < b.Subtrees.Count() - 1; i++) add.AddSubtree(b.GetSubtree(i));
|
---|
| 1164 | if (IsConstant(a.Subtrees.Last()) && IsConstant(b.Subtrees.Last())) {
|
---|
| 1165 | add.AddSubtree(MakeSum(a.Subtrees.Last(), b.Subtrees.Last()));
|
---|
| 1166 | } else if (IsConstant(a.Subtrees.Last())) {
|
---|
| 1167 | add.AddSubtree(b.Subtrees.Last());
|
---|
| 1168 | add.AddSubtree(a.Subtrees.Last());
|
---|
| 1169 | } else {
|
---|
| 1170 | add.AddSubtree(a.Subtrees.Last());
|
---|
| 1171 | add.AddSubtree(b.Subtrees.Last());
|
---|
| 1172 | }
|
---|
| 1173 | MergeVariablesInSum(add);
|
---|
| 1174 | if (add.Subtrees.Count() == 1) {
|
---|
| 1175 | return add.GetSubtree(0);
|
---|
| 1176 | } else {
|
---|
| 1177 | return add;
|
---|
| 1178 | }
|
---|
| 1179 | } else if (IsAddition(b)) {
|
---|
| 1180 | return MakeSum(b, a);
|
---|
| 1181 | } else if (IsAddition(a) && IsConstant(b)) {
|
---|
| 1182 | // a is an addition and b is a constant => append b to a and make sure the constants are merged
|
---|
| 1183 | var add = addSymbol.CreateTreeNode();
|
---|
| 1184 | // add all sub trees except for the last
|
---|
| 1185 | for (int i = 0; i < a.Subtrees.Count() - 1; i++) add.AddSubtree(a.GetSubtree(i));
|
---|
| 1186 | if (IsConstant(a.Subtrees.Last()))
|
---|
| 1187 | add.AddSubtree(MakeSum(a.Subtrees.Last(), b));
|
---|
| 1188 | else {
|
---|
| 1189 | add.AddSubtree(a.Subtrees.Last());
|
---|
| 1190 | add.AddSubtree(b);
|
---|
| 1191 | }
|
---|
| 1192 | return add;
|
---|
| 1193 | } else if (IsAddition(a)) {
|
---|
| 1194 | // a is already an addition => append b
|
---|
| 1195 | var add = addSymbol.CreateTreeNode();
|
---|
| 1196 | add.AddSubtree(b);
|
---|
| 1197 | foreach (var subtree in a.Subtrees) {
|
---|
| 1198 | add.AddSubtree(subtree);
|
---|
| 1199 | }
|
---|
| 1200 | MergeVariablesInSum(add);
|
---|
| 1201 | if (add.Subtrees.Count() == 1) {
|
---|
| 1202 | return add.GetSubtree(0);
|
---|
| 1203 | } else {
|
---|
| 1204 | return add;
|
---|
| 1205 | }
|
---|
| 1206 | } else {
|
---|
| 1207 | var add = addSymbol.CreateTreeNode();
|
---|
| 1208 | add.AddSubtree(a);
|
---|
| 1209 | add.AddSubtree(b);
|
---|
| 1210 | MergeVariablesInSum(add);
|
---|
| 1211 | if (add.Subtrees.Count() == 1) {
|
---|
| 1212 | return add.GetSubtree(0);
|
---|
| 1213 | } else {
|
---|
| 1214 | return add;
|
---|
| 1215 | }
|
---|
| 1216 | }
|
---|
| 1217 | }
|
---|
| 1218 |
|
---|
| 1219 | // makes sure variable symbols in sums are combined
|
---|
[17593] | 1220 | private void MergeVariablesInSum(ISymbolicExpressionTreeNode sum) {
|
---|
[14843] | 1221 | var subtrees = new List<ISymbolicExpressionTreeNode>(sum.Subtrees);
|
---|
| 1222 | while (sum.Subtrees.Any()) sum.RemoveSubtree(0);
|
---|
| 1223 | var groupedVarNodes = from node in subtrees.OfType<IVariableTreeNode>()
|
---|
| 1224 | where node.SubtreeCount == 0
|
---|
| 1225 | group node by GroupId(node) into g
|
---|
| 1226 | select g;
|
---|
| 1227 | var constant = (from node in subtrees.OfType<ConstantTreeNode>()
|
---|
| 1228 | select node.Value).DefaultIfEmpty(0.0).Sum();
|
---|
| 1229 | var unchangedSubtrees = subtrees.Where(t => t.SubtreeCount > 0 || !(t is IVariableTreeNode) && !(t is ConstantTreeNode));
|
---|
| 1230 |
|
---|
| 1231 | foreach (var variableNodeGroup in groupedVarNodes) {
|
---|
| 1232 | var firstNode = variableNodeGroup.First();
|
---|
| 1233 | if (firstNode is VariableTreeNodeBase) {
|
---|
| 1234 | var representative = firstNode as VariableTreeNodeBase;
|
---|
| 1235 | var weightSum = variableNodeGroup.Cast<VariableTreeNodeBase>().Select(t => t.Weight).Sum();
|
---|
| 1236 | representative.Weight = weightSum;
|
---|
| 1237 | sum.AddSubtree(representative);
|
---|
| 1238 | } else if (firstNode is FactorVariableTreeNode) {
|
---|
| 1239 | var representative = firstNode as FactorVariableTreeNode;
|
---|
| 1240 | foreach (var node in variableNodeGroup.Skip(1).Cast<FactorVariableTreeNode>()) {
|
---|
| 1241 | for (int j = 0; j < representative.Weights.Length; j++) {
|
---|
| 1242 | representative.Weights[j] += node.Weights[j];
|
---|
| 1243 | }
|
---|
| 1244 | }
|
---|
| 1245 | sum.AddSubtree(representative);
|
---|
| 1246 | }
|
---|
| 1247 | }
|
---|
| 1248 | foreach (var unchangedSubtree in unchangedSubtrees)
|
---|
| 1249 | sum.AddSubtree(unchangedSubtree);
|
---|
| 1250 | if (!constant.IsAlmost(0.0)) {
|
---|
| 1251 | sum.AddSubtree(MakeConstant(constant));
|
---|
| 1252 | }
|
---|
| 1253 | }
|
---|
| 1254 |
|
---|
| 1255 | // nodes referencing variables can be grouped if they have
|
---|
[17593] | 1256 | private string GroupId(IVariableTreeNode node) {
|
---|
[14843] | 1257 | var binaryFactorNode = node as BinaryFactorVariableTreeNode;
|
---|
| 1258 | var factorNode = node as FactorVariableTreeNode;
|
---|
| 1259 | var variableNode = node as VariableTreeNode;
|
---|
| 1260 | var laggedVarNode = node as LaggedVariableTreeNode;
|
---|
| 1261 | if (variableNode != null) {
|
---|
| 1262 | return "var " + variableNode.VariableName;
|
---|
| 1263 | } else if (binaryFactorNode != null) {
|
---|
| 1264 | return "binfactor " + binaryFactorNode.VariableName + " " + binaryFactorNode.VariableValue;
|
---|
| 1265 | } else if (factorNode != null) {
|
---|
| 1266 | return "factor " + factorNode.VariableName;
|
---|
| 1267 | } else if (laggedVarNode != null) {
|
---|
| 1268 | return "lagged " + laggedVarNode.VariableName + " " + laggedVarNode.Lag;
|
---|
| 1269 | } else {
|
---|
| 1270 | throw new NotSupportedException();
|
---|
| 1271 | }
|
---|
| 1272 | }
|
---|
| 1273 |
|
---|
| 1274 |
|
---|
[17593] | 1275 | private ISymbolicExpressionTreeNode MakeProduct(ISymbolicExpressionTreeNode a, ISymbolicExpressionTreeNode b) {
|
---|
[14843] | 1276 | if (IsConstant(a) && IsConstant(b)) {
|
---|
| 1277 | // fold constants
|
---|
| 1278 | return MakeConstant(((ConstantTreeNode)a).Value * ((ConstantTreeNode)b).Value);
|
---|
| 1279 | } else if (IsConstant(a)) {
|
---|
| 1280 | // a * $ => $ * a
|
---|
| 1281 | return MakeProduct(b, a);
|
---|
| 1282 | } else if (IsFactor(a) && IsFactor(b) && AreSameTypeAndVariable(a, b)) {
|
---|
| 1283 | var node0 = a as FactorVariableTreeNode;
|
---|
| 1284 | var node1 = b as FactorVariableTreeNode;
|
---|
| 1285 | return MakeFactor(node0.Symbol, node0.VariableName, node0.Weights.Zip(node1.Weights, (u, v) => u * v));
|
---|
| 1286 | } else if (IsBinFactor(a) && IsBinFactor(b) && AreSameTypeAndVariable(a, b)) {
|
---|
| 1287 | var node0 = a as BinaryFactorVariableTreeNode;
|
---|
| 1288 | var node1 = b as BinaryFactorVariableTreeNode;
|
---|
| 1289 | return MakeBinFactor(node0.Symbol, node0.VariableName, node0.VariableValue, node0.Weight * node1.Weight);
|
---|
| 1290 | } else if (IsFactor(a) && IsConstant(b)) {
|
---|
| 1291 | var node0 = a as FactorVariableTreeNode;
|
---|
| 1292 | var node1 = b as ConstantTreeNode;
|
---|
| 1293 | return MakeFactor(node0.Symbol, node0.VariableName, node0.Weights.Select(w => w * node1.Value));
|
---|
| 1294 | } else if (IsBinFactor(a) && IsConstant(b)) {
|
---|
| 1295 | var node0 = a as BinaryFactorVariableTreeNode;
|
---|
| 1296 | var node1 = b as ConstantTreeNode;
|
---|
| 1297 | return MakeBinFactor(node0.Symbol, node0.VariableName, node0.VariableValue, node0.Weight * node1.Value);
|
---|
| 1298 | } else if (IsBinFactor(a) && IsFactor(b)) {
|
---|
| 1299 | return MakeProduct(b, a);
|
---|
| 1300 | } else if (IsFactor(a) && IsBinFactor(b) &&
|
---|
| 1301 | ((IVariableTreeNode)a).VariableName == ((IVariableTreeNode)b).VariableName) {
|
---|
| 1302 | var node0 = a as FactorVariableTreeNode;
|
---|
| 1303 | var node1 = b as BinaryFactorVariableTreeNode;
|
---|
| 1304 | var varValues = node0.Symbol.GetVariableValues(node0.VariableName).ToArray();
|
---|
| 1305 | var wi = Array.IndexOf(varValues, node1.VariableValue);
|
---|
| 1306 | if (wi < 0) throw new ArgumentException();
|
---|
| 1307 | return MakeBinFactor(node1.Symbol, node1.VariableName, node1.VariableValue, node1.Weight * node0.Weights[wi]);
|
---|
| 1308 | } else if (IsConstant(b) && ((ConstantTreeNode)b).Value.IsAlmost(1.0)) {
|
---|
| 1309 | // $ * 1.0 => $
|
---|
| 1310 | return a;
|
---|
[16206] | 1311 | } else if (IsConstant(b) && ((ConstantTreeNode)b).Value.IsAlmost(0.0)) {
|
---|
| 1312 | return MakeConstant(0);
|
---|
[14843] | 1313 | } else if (IsConstant(b) && IsVariableBase(a)) {
|
---|
| 1314 | // multiply constants into variables weights
|
---|
| 1315 | ((VariableTreeNodeBase)a).Weight *= ((ConstantTreeNode)b).Value;
|
---|
| 1316 | return a;
|
---|
| 1317 | } else if (IsConstant(b) && IsAddition(a) ||
|
---|
| 1318 | IsFactor(b) && IsAddition(a) ||
|
---|
| 1319 | IsBinFactor(b) && IsAddition(a)) {
|
---|
| 1320 | // multiply constants into additions
|
---|
| 1321 | return a.Subtrees.Select(x => MakeProduct(GetSimplifiedTree(x), GetSimplifiedTree(b))).Aggregate((c, d) => MakeSum(c, d));
|
---|
| 1322 | } else if (IsDivision(a) && IsDivision(b)) {
|
---|
| 1323 | // (a1 / a2) * (b1 / b2) => (a1 * b1) / (a2 * b2)
|
---|
| 1324 | return MakeFraction(MakeProduct(a.GetSubtree(0), b.GetSubtree(0)), MakeProduct(a.GetSubtree(1), b.GetSubtree(1)));
|
---|
| 1325 | } else if (IsDivision(a)) {
|
---|
| 1326 | // (a1 / a2) * b => (a1 * b) / a2
|
---|
| 1327 | return MakeFraction(MakeProduct(a.GetSubtree(0), b), a.GetSubtree(1));
|
---|
| 1328 | } else if (IsDivision(b)) {
|
---|
| 1329 | // a * (b1 / b2) => (b1 * a) / b2
|
---|
| 1330 | return MakeFraction(MakeProduct(b.GetSubtree(0), a), b.GetSubtree(1));
|
---|
| 1331 | } else if (IsMultiplication(a) && IsMultiplication(b)) {
|
---|
| 1332 | // merge multiplications (make sure constants are merged)
|
---|
| 1333 | var mul = mulSymbol.CreateTreeNode();
|
---|
| 1334 | for (int i = 0; i < a.Subtrees.Count(); i++) mul.AddSubtree(a.GetSubtree(i));
|
---|
| 1335 | for (int i = 0; i < b.Subtrees.Count(); i++) mul.AddSubtree(b.GetSubtree(i));
|
---|
| 1336 | MergeVariablesAndConstantsInProduct(mul);
|
---|
| 1337 | return mul;
|
---|
| 1338 | } else if (IsMultiplication(b)) {
|
---|
| 1339 | return MakeProduct(b, a);
|
---|
| 1340 | } else if (IsMultiplication(a)) {
|
---|
| 1341 | // a is already an multiplication => append b
|
---|
| 1342 | a.AddSubtree(GetSimplifiedTree(b));
|
---|
| 1343 | MergeVariablesAndConstantsInProduct(a);
|
---|
| 1344 | return a;
|
---|
[16356] | 1345 | } else if (IsAbsolute(a) && IsAbsolute(b)) {
|
---|
| 1346 | return MakeAbs(MakeProduct(a.GetSubtree(0), b.GetSubtree(0)));
|
---|
| 1347 | } else if (IsAbsolute(a) && IsConstant(b)) {
|
---|
| 1348 | var constNode = b as ConstantTreeNode;
|
---|
| 1349 | var posF = Math.Abs(constNode.Value);
|
---|
| 1350 | if (constNode.Value > 0) {
|
---|
| 1351 | return MakeAbs(MakeProduct(a.GetSubtree(0), MakeConstant(posF)));
|
---|
| 1352 | } else {
|
---|
| 1353 | var mul = mulSymbol.CreateTreeNode();
|
---|
| 1354 | mul.AddSubtree(MakeAbs(MakeProduct(a.GetSubtree(0), MakeConstant(posF))));
|
---|
| 1355 | mul.AddSubtree(MakeConstant(-1.0));
|
---|
| 1356 | return mul;
|
---|
| 1357 | }
|
---|
| 1358 | } else if (IsAnalyticalQuotient(a)) {
|
---|
| 1359 | return MakeAnalyticalQuotient(MakeProduct(a.GetSubtree(0), b), a.GetSubtree(1));
|
---|
[14843] | 1360 | } else {
|
---|
| 1361 | var mul = mulSymbol.CreateTreeNode();
|
---|
| 1362 | mul.AddSubtree(a);
|
---|
| 1363 | mul.AddSubtree(b);
|
---|
| 1364 | MergeVariablesAndConstantsInProduct(mul);
|
---|
| 1365 | return mul;
|
---|
| 1366 | }
|
---|
| 1367 | }
|
---|
| 1368 |
|
---|
[17593] | 1369 | ISymbolicExpressionTreeNode MakeSumAggregation(ISymbolicExpressionTreeNode node) {
|
---|
| 1370 | if (IsConstant(node)) { // assumes scalar constant
|
---|
| 1371 | return node;
|
---|
[17596] | 1372 | } else if (IsAddition(node) || IsSubtraction(node)) {
|
---|
[17593] | 1373 | var terms = node.Subtrees;
|
---|
[17596] | 1374 | if (IsSubtraction(node)) {
|
---|
| 1375 | if (terms.Count() == 1) {
|
---|
| 1376 | terms = terms.Select(Negate);
|
---|
| 1377 | } else {
|
---|
| 1378 | var first = terms.First().ToEnumerable();
|
---|
| 1379 | var remaining = terms.Skip(1).Select(Negate);
|
---|
| 1380 | terms = first.Concat(remaining).ToList();
|
---|
| 1381 | }
|
---|
| 1382 | }
|
---|
| 1383 |
|
---|
[17593] | 1384 | var scalarTerms = terms.Where(IsScalarNode).ToList();
|
---|
| 1385 | var remainingTerms = terms.Except(scalarTerms).ToList();
|
---|
| 1386 |
|
---|
| 1387 | if (scalarTerms.Any() && remainingTerms.Any()) {
|
---|
| 1388 | var scalarNode = scalarTerms.Aggregate(MakeSum);
|
---|
| 1389 | var vectorNode = remainingTerms.Aggregate(MakeSum);
|
---|
| 1390 |
|
---|
| 1391 | var lengthNode = lengthSymbol.CreateTreeNode();
|
---|
| 1392 | lengthNode.AddSubtree((ISymbolicExpressionTreeNode)vectorNode.Clone());
|
---|
| 1393 | var scalarMulNode = mulSymbol.CreateTreeNode();
|
---|
| 1394 | scalarMulNode.AddSubtree(scalarNode);
|
---|
| 1395 | scalarMulNode.AddSubtree(lengthNode);
|
---|
| 1396 |
|
---|
| 1397 | var sumNode = sumSymbol.CreateTreeNode();
|
---|
| 1398 | sumNode.AddSubtree(vectorNode);
|
---|
| 1399 |
|
---|
| 1400 | return MakeSum(scalarMulNode, sumNode);
|
---|
| 1401 | } else if (scalarTerms.Any()) {
|
---|
| 1402 | var scalarNode = scalarTerms.Aggregate(MakeSum);
|
---|
| 1403 | return scalarNode;
|
---|
| 1404 | } else if (remainingTerms.Any()) {
|
---|
| 1405 | var vectorNode = remainingTerms.Aggregate(MakeSum);
|
---|
| 1406 | var sumNode = sumSymbol.CreateTreeNode();
|
---|
| 1407 | sumNode.AddSubtree(vectorNode);
|
---|
| 1408 | return sumNode;
|
---|
| 1409 | } else
|
---|
| 1410 | throw new InvalidOperationException("Addition does not contain any terms to simplify.");
|
---|
[17596] | 1411 | } else if (IsMultiplication(node) || IsDivision(node)) {
|
---|
[17593] | 1412 | var factors = node.Subtrees;
|
---|
[17596] | 1413 | if (IsDivision(node)) {
|
---|
| 1414 | if (factors.Count() == 1) {
|
---|
| 1415 | factors = factors.Select(Invert);
|
---|
| 1416 | } else {
|
---|
| 1417 | var first = factors.First().ToEnumerable();
|
---|
| 1418 | var remaining = factors.Skip(1).Select(Invert);
|
---|
| 1419 | factors = first.Concat(remaining).ToList();
|
---|
| 1420 | }
|
---|
| 1421 | }
|
---|
| 1422 |
|
---|
[17593] | 1423 | var scalarFactors = factors.Where(IsScalarNode).ToList();
|
---|
| 1424 | var remainingFactors = factors.Except(scalarFactors).ToList();
|
---|
| 1425 |
|
---|
| 1426 | if (scalarFactors.Any() && remainingFactors.Any()) {
|
---|
| 1427 | var scalarNode = scalarFactors.Aggregate(MakeProduct);
|
---|
| 1428 | var vectorNode = remainingFactors.Aggregate(MakeProduct);
|
---|
| 1429 |
|
---|
| 1430 | var sumNode = sumSymbol.CreateTreeNode();
|
---|
| 1431 | sumNode.AddSubtree(vectorNode);
|
---|
| 1432 |
|
---|
| 1433 | return MakeProduct(scalarNode, sumNode);
|
---|
| 1434 | } else if (scalarFactors.Any()) {
|
---|
| 1435 | var scalarNode = scalarFactors.Aggregate(MakeProduct);
|
---|
| 1436 | return scalarNode;
|
---|
| 1437 | } else if (remainingFactors.Any()) {
|
---|
| 1438 | var vectorNode = remainingFactors.Aggregate(MakeProduct);
|
---|
| 1439 | var sumNode = sumSymbol.CreateTreeNode();
|
---|
| 1440 | sumNode.AddSubtree(vectorNode);
|
---|
| 1441 | return sumNode;
|
---|
| 1442 | } else
|
---|
| 1443 | throw new InvalidOperationException("Multiplication does not contain any terms to simplify.");
|
---|
| 1444 | } else {
|
---|
| 1445 | var sumNode = sumSymbol.CreateTreeNode();
|
---|
| 1446 | sumNode.AddSubtree(node);
|
---|
| 1447 | return sumNode;
|
---|
| 1448 | }
|
---|
| 1449 | }
|
---|
| 1450 |
|
---|
| 1451 | ISymbolicExpressionTreeNode MakeMeanAggregation(ISymbolicExpressionTreeNode node) {
|
---|
| 1452 | if (IsConstant(node)) { // assumes scalar constant
|
---|
| 1453 | return node;
|
---|
[17596] | 1454 | } else if (IsAddition(node) || IsSubtraction(node)) {
|
---|
[17593] | 1455 | var terms = node.Subtrees;
|
---|
[17596] | 1456 | if (IsSubtraction(node)) {
|
---|
| 1457 | if (terms.Count() == 1) {
|
---|
| 1458 | terms = terms.Select(Negate);
|
---|
| 1459 | } else {
|
---|
| 1460 | var first = terms.First().ToEnumerable();
|
---|
| 1461 | var remaining = terms.Skip(1).Select(Negate);
|
---|
| 1462 | terms = first.Concat(remaining).ToList();
|
---|
| 1463 | }
|
---|
| 1464 | }
|
---|
| 1465 |
|
---|
[17593] | 1466 | var scalarTerms = terms.Where(IsScalarNode).ToList();
|
---|
| 1467 | var remainingTerms = terms.Except(scalarTerms).ToList();
|
---|
| 1468 |
|
---|
| 1469 | if (scalarTerms.Any() && remainingTerms.Any()) {
|
---|
| 1470 | var scalarNode = scalarTerms.Aggregate(MakeSum);
|
---|
| 1471 | var vectorNode = remainingTerms.Aggregate(MakeSum);
|
---|
| 1472 |
|
---|
| 1473 | var meanNode = meanSymbol.CreateTreeNode();
|
---|
| 1474 | meanNode.AddSubtree(vectorNode);
|
---|
| 1475 |
|
---|
| 1476 | return MakeSum(scalarNode, meanNode);
|
---|
| 1477 | } else if (scalarTerms.Any()) {
|
---|
| 1478 | var scalarNode = scalarTerms.Aggregate(MakeSum);
|
---|
| 1479 | return scalarNode;
|
---|
| 1480 | } else if (remainingTerms.Any()) {
|
---|
| 1481 | var vectorNode = remainingTerms.Aggregate(MakeSum);
|
---|
| 1482 | var meanNode = meanSymbol.CreateTreeNode();
|
---|
| 1483 | meanNode.AddSubtree(vectorNode);
|
---|
| 1484 | return meanNode;
|
---|
| 1485 | } else
|
---|
| 1486 | throw new InvalidOperationException("Addition does not contain any terms to simplify.");
|
---|
[17596] | 1487 | } else if (IsMultiplication(node) || IsDivision(node)) {
|
---|
[17593] | 1488 | var factors = node.Subtrees;
|
---|
[17596] | 1489 | if (IsDivision(node)) {
|
---|
| 1490 | if (factors.Count() == 1) {
|
---|
| 1491 | factors = factors.Select(Invert);
|
---|
| 1492 | } else {
|
---|
| 1493 | var first = factors.First().ToEnumerable();
|
---|
| 1494 | var remaining = factors.Skip(1).Select(Invert);
|
---|
| 1495 | factors = first.Concat(remaining).ToList();
|
---|
| 1496 | }
|
---|
| 1497 | }
|
---|
| 1498 |
|
---|
[17593] | 1499 | var scalarFactors = factors.Where(IsScalarNode).ToList();
|
---|
| 1500 | var remainingFactors = factors.Except(scalarFactors).ToList();
|
---|
| 1501 |
|
---|
| 1502 | if (scalarFactors.Any() && remainingFactors.Any()) {
|
---|
| 1503 | var scalarNode = scalarFactors.Aggregate(MakeProduct);
|
---|
| 1504 | var vectorNode = remainingFactors.Aggregate(MakeProduct);
|
---|
| 1505 |
|
---|
| 1506 | var meanNode = meanSymbol.CreateTreeNode();
|
---|
| 1507 | meanNode.AddSubtree(vectorNode);
|
---|
| 1508 |
|
---|
| 1509 | return MakeProduct(scalarNode, meanNode);
|
---|
| 1510 | } else if (scalarFactors.Any()) {
|
---|
| 1511 | var scalarNode = scalarFactors.Aggregate(MakeProduct);
|
---|
| 1512 | return scalarNode;
|
---|
| 1513 | } else if (remainingFactors.Any()) {
|
---|
| 1514 | var vectorNode = remainingFactors.Aggregate(MakeProduct);
|
---|
| 1515 | var meanNode = meanSymbol.CreateTreeNode();
|
---|
| 1516 | meanNode.AddSubtree(vectorNode);
|
---|
| 1517 | return meanNode;
|
---|
| 1518 | } else
|
---|
| 1519 | throw new InvalidOperationException("Multiplication does not contain any terms to simplify.");
|
---|
| 1520 | } else {
|
---|
| 1521 | var meanNode = meanSymbol.CreateTreeNode();
|
---|
| 1522 | meanNode.AddSubtree(node);
|
---|
| 1523 | return meanNode;
|
---|
| 1524 | }
|
---|
| 1525 | }
|
---|
| 1526 |
|
---|
[14843] | 1527 | #endregion
|
---|
| 1528 |
|
---|
| 1529 | #region helper functions
|
---|
| 1530 |
|
---|
[17593] | 1531 | private bool ContainsVariableCondition(ISymbolicExpressionTreeNode node) {
|
---|
[14843] | 1532 | if (node.Symbol is VariableCondition) return true;
|
---|
| 1533 | foreach (var subtree in node.Subtrees)
|
---|
| 1534 | if (ContainsVariableCondition(subtree)) return true;
|
---|
| 1535 | return false;
|
---|
| 1536 | }
|
---|
| 1537 |
|
---|
[17593] | 1538 | private ISymbolicExpressionTreeNode AddLagToDynamicNodes(ISymbolicExpressionTreeNode node, int lag) {
|
---|
[14843] | 1539 | var laggedTreeNode = node as ILaggedTreeNode;
|
---|
| 1540 | var variableNode = node as VariableTreeNode;
|
---|
| 1541 | var variableConditionNode = node as VariableConditionTreeNode;
|
---|
| 1542 | if (laggedTreeNode != null)
|
---|
| 1543 | laggedTreeNode.Lag += lag;
|
---|
| 1544 | else if (variableNode != null) {
|
---|
| 1545 | var laggedVariableNode = (LaggedVariableTreeNode)laggedVariableSymbol.CreateTreeNode();
|
---|
| 1546 | laggedVariableNode.Lag = lag;
|
---|
| 1547 | laggedVariableNode.VariableName = variableNode.VariableName;
|
---|
| 1548 | return laggedVariableNode;
|
---|
| 1549 | } else if (variableConditionNode != null) {
|
---|
| 1550 | throw new NotSupportedException("Removal of time lags around variable condition symbols is not allowed.");
|
---|
| 1551 | }
|
---|
| 1552 | var subtrees = new List<ISymbolicExpressionTreeNode>(node.Subtrees);
|
---|
| 1553 | while (node.SubtreeCount > 0) node.RemoveSubtree(0);
|
---|
| 1554 | foreach (var subtree in subtrees) {
|
---|
| 1555 | node.AddSubtree(AddLagToDynamicNodes(subtree, lag));
|
---|
| 1556 | }
|
---|
| 1557 | return node;
|
---|
| 1558 | }
|
---|
| 1559 |
|
---|
[17593] | 1560 | private bool AreSameTypeAndVariable(ISymbolicExpressionTreeNode a, ISymbolicExpressionTreeNode b) {
|
---|
[14843] | 1561 | return GroupId((IVariableTreeNode)a) == GroupId((IVariableTreeNode)b);
|
---|
| 1562 | }
|
---|
| 1563 |
|
---|
| 1564 | // helper to combine the constant factors in products and to combine variables (powers of 2, 3...)
|
---|
[17593] | 1565 | private void MergeVariablesAndConstantsInProduct(ISymbolicExpressionTreeNode prod) {
|
---|
[14843] | 1566 | var subtrees = new List<ISymbolicExpressionTreeNode>(prod.Subtrees);
|
---|
| 1567 | while (prod.Subtrees.Any()) prod.RemoveSubtree(0);
|
---|
| 1568 | var groupedVarNodes = from node in subtrees.OfType<IVariableTreeNode>()
|
---|
| 1569 | where node.SubtreeCount == 0
|
---|
| 1570 | group node by GroupId(node) into g
|
---|
| 1571 | orderby g.Count()
|
---|
| 1572 | select g;
|
---|
| 1573 | var constantProduct = (from node in subtrees.OfType<VariableTreeNodeBase>()
|
---|
| 1574 | select node.Weight)
|
---|
| 1575 | .Concat(from node in subtrees.OfType<ConstantTreeNode>()
|
---|
| 1576 | select node.Value)
|
---|
| 1577 | .DefaultIfEmpty(1.0)
|
---|
| 1578 | .Aggregate((c1, c2) => c1 * c2);
|
---|
| 1579 |
|
---|
| 1580 | var unchangedSubtrees = from tree in subtrees
|
---|
| 1581 | where tree.SubtreeCount > 0 || !(tree is IVariableTreeNode) && !(tree is ConstantTreeNode)
|
---|
| 1582 | select tree;
|
---|
| 1583 |
|
---|
| 1584 | foreach (var variableNodeGroup in groupedVarNodes) {
|
---|
| 1585 | var firstNode = variableNodeGroup.First();
|
---|
| 1586 | if (firstNode is VariableTreeNodeBase) {
|
---|
| 1587 | var representative = (VariableTreeNodeBase)firstNode;
|
---|
| 1588 | representative.Weight = 1.0;
|
---|
| 1589 | if (variableNodeGroup.Count() > 1) {
|
---|
| 1590 | var poly = mulSymbol.CreateTreeNode();
|
---|
| 1591 | for (int p = 0; p < variableNodeGroup.Count(); p++) {
|
---|
| 1592 | poly.AddSubtree((ISymbolicExpressionTreeNode)representative.Clone());
|
---|
| 1593 | }
|
---|
| 1594 | prod.AddSubtree(poly);
|
---|
| 1595 | } else {
|
---|
| 1596 | prod.AddSubtree(representative);
|
---|
| 1597 | }
|
---|
| 1598 | } else if (firstNode is FactorVariableTreeNode) {
|
---|
| 1599 | var representative = (FactorVariableTreeNode)firstNode;
|
---|
| 1600 | foreach (var node in variableNodeGroup.Skip(1).Cast<FactorVariableTreeNode>()) {
|
---|
| 1601 | for (int j = 0; j < representative.Weights.Length; j++) {
|
---|
| 1602 | representative.Weights[j] *= node.Weights[j];
|
---|
| 1603 | }
|
---|
| 1604 | }
|
---|
| 1605 | for (int j = 0; j < representative.Weights.Length; j++) {
|
---|
| 1606 | representative.Weights[j] *= constantProduct;
|
---|
| 1607 | }
|
---|
| 1608 | constantProduct = 1.0;
|
---|
| 1609 | // if the product already contains a factor it is not necessary to multiply a constant below
|
---|
| 1610 | prod.AddSubtree(representative);
|
---|
| 1611 | }
|
---|
| 1612 | }
|
---|
| 1613 |
|
---|
| 1614 | foreach (var unchangedSubtree in unchangedSubtrees)
|
---|
| 1615 | prod.AddSubtree(unchangedSubtree);
|
---|
| 1616 |
|
---|
| 1617 | if (!constantProduct.IsAlmost(1.0)) {
|
---|
| 1618 | prod.AddSubtree(MakeConstant(constantProduct));
|
---|
| 1619 | }
|
---|
| 1620 | }
|
---|
| 1621 |
|
---|
| 1622 |
|
---|
| 1623 | /// <summary>
|
---|
| 1624 | /// x => x * -1
|
---|
| 1625 | /// Is only used in cases where it is not necessary to create new tree nodes. Manipulates x directly.
|
---|
| 1626 | /// </summary>
|
---|
| 1627 | /// <param name="x"></param>
|
---|
| 1628 | /// <returns>-x</returns>
|
---|
[17593] | 1629 | private ISymbolicExpressionTreeNode Negate(ISymbolicExpressionTreeNode x) {
|
---|
[14843] | 1630 | if (IsConstant(x)) {
|
---|
| 1631 | ((ConstantTreeNode)x).Value *= -1;
|
---|
| 1632 | } else if (IsVariableBase(x)) {
|
---|
| 1633 | var variableTree = (VariableTreeNodeBase)x;
|
---|
| 1634 | variableTree.Weight *= -1.0;
|
---|
| 1635 | } else if (IsFactor(x)) {
|
---|
| 1636 | var factorNode = (FactorVariableTreeNode)x;
|
---|
| 1637 | for (int i = 0; i < factorNode.Weights.Length; i++) factorNode.Weights[i] *= -1;
|
---|
| 1638 | } else if (IsBinFactor(x)) {
|
---|
| 1639 | var factorNode = (BinaryFactorVariableTreeNode)x;
|
---|
| 1640 | factorNode.Weight *= -1;
|
---|
| 1641 | } else if (IsAddition(x)) {
|
---|
| 1642 | // (x0 + x1 + .. + xn) * -1 => (-x0 + -x1 + .. + -xn)
|
---|
| 1643 | var subtrees = new List<ISymbolicExpressionTreeNode>(x.Subtrees);
|
---|
| 1644 | while (x.Subtrees.Any()) x.RemoveSubtree(0);
|
---|
| 1645 | foreach (var subtree in subtrees) {
|
---|
| 1646 | x.AddSubtree(Negate(subtree));
|
---|
| 1647 | }
|
---|
| 1648 | } else if (IsMultiplication(x) || IsDivision(x)) {
|
---|
| 1649 | // x0 * x1 * .. * xn * -1 => x0 * x1 * .. * -xn
|
---|
| 1650 | var lastSubTree = x.Subtrees.Last();
|
---|
| 1651 | x.RemoveSubtree(x.SubtreeCount - 1);
|
---|
| 1652 | x.AddSubtree(Negate(lastSubTree)); // last is maybe a constant, prefer to negate the constant
|
---|
| 1653 | } else {
|
---|
| 1654 | // any other function
|
---|
| 1655 | return MakeProduct(x, MakeConstant(-1));
|
---|
| 1656 | }
|
---|
| 1657 | return x;
|
---|
| 1658 | }
|
---|
| 1659 |
|
---|
| 1660 | /// <summary>
|
---|
| 1661 | /// x => 1/x
|
---|
| 1662 | /// Must create new tree nodes
|
---|
| 1663 | /// </summary>
|
---|
| 1664 | /// <param name="x"></param>
|
---|
| 1665 | /// <returns></returns>
|
---|
[17593] | 1666 | private ISymbolicExpressionTreeNode Invert(ISymbolicExpressionTreeNode x) {
|
---|
[14843] | 1667 | if (IsConstant(x)) {
|
---|
| 1668 | return MakeConstant(1.0 / ((ConstantTreeNode)x).Value);
|
---|
| 1669 | } else if (IsFactor(x)) {
|
---|
| 1670 | var factorNode = (FactorVariableTreeNode)x;
|
---|
| 1671 | return MakeFactor(factorNode.Symbol, factorNode.VariableName, factorNode.Weights.Select(w => 1.0 / w));
|
---|
| 1672 | } else if (IsDivision(x)) {
|
---|
| 1673 | return MakeFraction(x.GetSubtree(1), x.GetSubtree(0));
|
---|
| 1674 | } else {
|
---|
| 1675 | // any other function
|
---|
| 1676 | return MakeFraction(MakeConstant(1), x);
|
---|
| 1677 | }
|
---|
| 1678 | }
|
---|
| 1679 |
|
---|
[17593] | 1680 | private ISymbolicExpressionTreeNode MakeConstant(double value) {
|
---|
[14843] | 1681 | ConstantTreeNode constantTreeNode = (ConstantTreeNode)(constSymbol.CreateTreeNode());
|
---|
| 1682 | constantTreeNode.Value = value;
|
---|
| 1683 | return constantTreeNode;
|
---|
| 1684 | }
|
---|
| 1685 |
|
---|
[17593] | 1686 | private ISymbolicExpressionTreeNode MakeFactor(FactorVariable sy, string variableName, IEnumerable<double> weights) {
|
---|
[14843] | 1687 | var tree = (FactorVariableTreeNode)sy.CreateTreeNode();
|
---|
| 1688 | tree.VariableName = variableName;
|
---|
| 1689 | tree.Weights = weights.ToArray();
|
---|
| 1690 | return tree;
|
---|
| 1691 | }
|
---|
[17593] | 1692 | private ISymbolicExpressionTreeNode MakeBinFactor(BinaryFactorVariable sy, string variableName, string variableValue, double weight) {
|
---|
[14843] | 1693 | var tree = (BinaryFactorVariableTreeNode)sy.CreateTreeNode();
|
---|
| 1694 | tree.VariableName = variableName;
|
---|
| 1695 | tree.VariableValue = variableValue;
|
---|
| 1696 | tree.Weight = weight;
|
---|
| 1697 | return tree;
|
---|
| 1698 | }
|
---|
| 1699 |
|
---|
| 1700 |
|
---|
| 1701 | #endregion
|
---|
| 1702 | }
|
---|
| 1703 | }
|
---|