[14024] | 1 | #region License Information
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| 2 | /* HeuristicLab
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[17180] | 3 | * Copyright (C) Heuristic and Evolutionary Algorithms Laboratory (HEAL)
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[14024] | 4 | *
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| 5 | * This file is part of HeuristicLab.
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| 6 | *
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| 7 | * HeuristicLab is free software: you can redistribute it and/or modify
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| 8 | * it under the terms of the GNU General Public License as published by
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| 9 | * the Free Software Foundation, either version 3 of the License, or
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| 10 | * (at your option) any later version.
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| 11 | *
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| 12 | * HeuristicLab is distributed in the hope that it will be useful,
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| 13 | * but WITHOUT ANY WARRANTY; without even the implied warranty of
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| 14 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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| 15 | * GNU General Public License for more details.
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| 16 | *
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| 17 | * You should have received a copy of the GNU General Public License
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| 18 | * along with HeuristicLab. If not, see <http://www.gnu.org/licenses/>.
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| 19 | */
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| 20 | #endregion
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| 21 |
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| 22 | using System;
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| 23 | using System.Collections.Generic;
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| 24 | using System.Globalization;
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| 25 | using System.Linq;
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| 26 | using System.Text;
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| 27 | using HeuristicLab.Collections;
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[14350] | 28 | using HeuristicLab.Common;
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[14024] | 29 | using HeuristicLab.Encodings.SymbolicExpressionTreeEncoding;
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| 30 |
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| 31 | namespace HeuristicLab.Problems.DataAnalysis.Symbolic {
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| 32 | /// <summary>
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| 33 | /// Parses mathematical expressions in infix form. E.g. x1 * (3.0 * x2 + x3)
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| 34 | /// Identifier format (functions or variables): '_' | letter { '_' | letter | digit }
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[14826] | 35 | /// Variables names and variable values can be set under quotes "" or '' because variable names might contain spaces.
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| 36 | /// Variable = ident | " ident " | ' ident '
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[14024] | 37 | /// It is also possible to use functions e.g. log("x1") or real-valued constants e.g. 3.1415 .
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| 38 | /// Variable names are case sensitive. Function names are not case sensitive.
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[14826] | 39 | ///
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| 40 | ///
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| 41 | /// S = Expr EOF
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[18175] | 42 | /// Expr = Term { '+' Term | '-' Term }
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[14826] | 43 | /// Term = Fact { '*' Fact | '/' Fact }
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[16356] | 44 | /// Fact = SimpleFact [ '^' SimpleFact ]
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| 45 | /// SimpleFact = '(' Expr ')'
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| 46 | /// | '{' Expr '}'
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| 47 | /// | 'LAG' '(' varId ',' ['+' | '-' ] number ')
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| 48 | /// | funcId '(' ArgList ')'
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| 49 | /// | VarExpr
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| 50 | /// | number
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[18175] | 51 | /// | ['+' | '-'] SimpleFact
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[14826] | 52 | /// ArgList = Expr { ',' Expr }
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| 53 | /// VarExpr = varId OptFactorPart
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[18175] | 54 | /// OptFactorPart = [ ('=' varVal | '[' ['+' | '-' ] number {',' ['+' | '-' ] number } ']' ) ]
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[14826] | 55 | /// varId = ident | ' ident ' | " ident "
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| 56 | /// varVal = ident | ' ident ' | " ident "
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| 57 | /// ident = '_' | letter { '_' | letter | digit }
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[14024] | 58 | /// </summary>
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[14026] | 59 | public sealed class InfixExpressionParser {
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[18093] | 60 | private enum TokenType { Operator, Identifier, Number, LeftPar, RightPar, LeftBracket, RightBracket, LeftAngleBracket, RightAngleBracket, Comma, Eq, End, NA };
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[14024] | 61 | private class Token {
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| 62 | internal double doubleVal;
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| 63 | internal string strVal;
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| 64 | internal TokenType TokenType;
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| 65 | }
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| 66 |
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[17902] | 67 | private class SymbolComparer : IEqualityComparer<ISymbol>, IComparer<ISymbol> {
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[14024] | 68 | public int Compare(ISymbol x, ISymbol y) {
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| 69 | return x.Name.CompareTo(y.Name);
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| 70 | }
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| 71 |
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| 72 | public bool Equals(ISymbol x, ISymbol y) {
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[17902] | 73 | return x.GetType() == y.GetType();
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[14024] | 74 | }
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| 75 |
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| 76 | public int GetHashCode(ISymbol obj) {
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[17902] | 77 | return obj.GetType().GetHashCode();
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[14024] | 78 | }
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| 79 | }
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| 80 | // format name <-> symbol
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| 81 | // the lookup table is also used in the corresponding formatter
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| 82 | internal static readonly BidirectionalLookup<string, ISymbol>
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[17902] | 83 | knownSymbols = new BidirectionalLookup<string, ISymbol>(StringComparer.InvariantCulture, new SymbolComparer());
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[14024] | 84 |
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[18100] | 85 | private Number number = new Number();
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[18175] | 86 | private Constant minusOne = new Constant() { Value = -1 };
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[14024] | 87 | private Variable variable = new Variable();
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[14826] | 88 | private BinaryFactorVariable binaryFactorVar = new BinaryFactorVariable();
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| 89 | private FactorVariable factorVar = new FactorVariable();
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[14024] | 90 |
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| 91 | private ProgramRootSymbol programRootSymbol = new ProgramRootSymbol();
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| 92 | private StartSymbol startSymbol = new StartSymbol();
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| 93 |
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| 94 | static InfixExpressionParser() {
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| 95 | // populate bidirectional lookup
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| 96 | var dict = new Dictionary<string, ISymbol>
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| 97 | {
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| 98 | { "+", new Addition()},
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| 99 | { "/", new Division()},
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| 100 | { "*", new Multiplication()},
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| 101 | { "-", new Subtraction()},
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[16356] | 102 | { "^", new Power() },
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| 103 | { "ABS", new Absolute() },
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[14024] | 104 | { "EXP", new Exponential()},
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| 105 | { "LOG", new Logarithm()},
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[16359] | 106 | { "POW", new Power() },
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[14024] | 107 | { "ROOT", new Root()},
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| 108 | { "SQR", new Square() },
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| 109 | { "SQRT", new SquareRoot() },
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[16356] | 110 | { "CUBE", new Cube() },
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| 111 | { "CUBEROOT", new CubeRoot() },
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[14024] | 112 | { "SIN",new Sine()},
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| 113 | { "COS", new Cosine()},
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| 114 | { "TAN", new Tangent()},
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[16656] | 115 | { "TANH", new HyperbolicTangent()},
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[14024] | 116 | { "AIRYA", new AiryA()},
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| 117 | { "AIRYB", new AiryB()},
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| 118 | { "BESSEL", new Bessel()},
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| 119 | { "COSINT", new CosineIntegral()},
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| 120 | { "SININT", new SineIntegral()},
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| 121 | { "HYPCOSINT", new HyperbolicCosineIntegral()},
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| 122 | { "HYPSININT", new HyperbolicSineIntegral()},
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| 123 | { "FRESNELSININT", new FresnelSineIntegral()},
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| 124 | { "FRESNELCOSINT", new FresnelCosineIntegral()},
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| 125 | { "NORM", new Norm()},
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| 126 | { "ERF", new Erf()},
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| 127 | { "GAMMA", new Gamma()},
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| 128 | { "PSI", new Psi()},
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| 129 | { "DAWSON", new Dawson()},
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| 130 | { "EXPINT", new ExponentialIntegralEi()},
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[16360] | 131 | { "AQ", new AnalyticQuotient() },
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[14024] | 132 | { "MEAN", new Average()},
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| 133 | { "IF", new IfThenElse()},
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[14347] | 134 | { "GT", new GreaterThan()},
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| 135 | { "LT", new LessThan()},
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[14024] | 136 | { "AND", new And()},
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| 137 | { "OR", new Or()},
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| 138 | { "NOT", new Not()},
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| 139 | { "XOR", new Xor()},
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| 140 | { "DIFF", new Derivative()},
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[14350] | 141 | { "LAG", new LaggedVariable() },
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[14024] | 142 | };
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| 143 |
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| 144 |
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| 145 | foreach (var kvp in dict) {
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| 146 | knownSymbols.Add(kvp.Key, kvp.Value);
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| 147 | }
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| 148 | }
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| 149 |
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| 150 | public ISymbolicExpressionTree Parse(string str) {
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| 151 | ISymbolicExpressionTreeNode root = programRootSymbol.CreateTreeNode();
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| 152 | ISymbolicExpressionTreeNode start = startSymbol.CreateTreeNode();
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| 153 | var allTokens = GetAllTokens(str).ToArray();
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| 154 | ISymbolicExpressionTreeNode mainBranch = ParseS(new Queue<Token>(allTokens));
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| 155 |
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| 156 | // only a main branch was given => insert the main branch into the default tree template
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| 157 | root.AddSubtree(start);
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| 158 | start.AddSubtree(mainBranch);
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| 159 | return new SymbolicExpressionTree(root);
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| 160 | }
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| 161 |
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| 162 | private IEnumerable<Token> GetAllTokens(string str) {
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| 163 | int pos = 0;
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| 164 | while (true) {
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[18175] | 165 | while (pos < str.Length && char.IsWhiteSpace(str[pos])) pos++;
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[14024] | 166 | if (pos >= str.Length) {
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| 167 | yield return new Token { TokenType = TokenType.End, strVal = "" };
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| 168 | yield break;
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| 169 | }
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| 170 | if (char.IsDigit(str[pos])) {
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[18175] | 171 | // read number (=> read until white space or other symbol)
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[14024] | 172 | var sb = new StringBuilder();
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| 173 | sb.Append(str[pos]);
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| 174 | pos++;
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| 175 | while (pos < str.Length && !char.IsWhiteSpace(str[pos])
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[14319] | 176 | && (str[pos] != '+' || str[pos - 1] == 'e' || str[pos - 1] == 'E') // continue reading exponents
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[14024] | 177 | && (str[pos] != '-' || str[pos - 1] == 'e' || str[pos - 1] == 'E')
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[14319] | 178 | && str[pos] != '*'
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[14024] | 179 | && str[pos] != '/'
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[16356] | 180 | && str[pos] != '^'
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[14347] | 181 | && str[pos] != ')'
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[14826] | 182 | && str[pos] != ']'
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[16356] | 183 | && str[pos] != '}'
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[18100] | 184 | && str[pos] != ','
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| 185 | && str[pos] != '>') {
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[14024] | 186 | sb.Append(str[pos]);
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| 187 | pos++;
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| 188 | }
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| 189 | double dblVal;
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| 190 | if (double.TryParse(sb.ToString(), NumberStyles.Float, CultureInfo.InvariantCulture, out dblVal))
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| 191 | yield return new Token { TokenType = TokenType.Number, strVal = sb.ToString(), doubleVal = dblVal };
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| 192 | else yield return new Token { TokenType = TokenType.NA, strVal = sb.ToString() };
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| 193 | } else if (char.IsLetter(str[pos]) || str[pos] == '_') {
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| 194 | // read ident
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| 195 | var sb = new StringBuilder();
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| 196 | sb.Append(str[pos]);
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| 197 | pos++;
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| 198 | while (pos < str.Length &&
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| 199 | (char.IsLetter(str[pos]) || str[pos] == '_' || char.IsDigit(str[pos]))) {
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| 200 | sb.Append(str[pos]);
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| 201 | pos++;
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| 202 | }
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| 203 | yield return new Token { TokenType = TokenType.Identifier, strVal = sb.ToString() };
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| 204 | } else if (str[pos] == '"') {
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| 205 | // read to next "
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| 206 | pos++;
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| 207 | var sb = new StringBuilder();
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| 208 | while (pos < str.Length && str[pos] != '"') {
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| 209 | sb.Append(str[pos]);
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| 210 | pos++;
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| 211 | }
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| 212 | if (pos < str.Length && str[pos] == '"') {
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| 213 | pos++; // skip "
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| 214 | yield return new Token { TokenType = TokenType.Identifier, strVal = sb.ToString() };
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| 215 | } else
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| 216 | yield return new Token { TokenType = TokenType.NA };
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| 217 |
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| 218 | } else if (str[pos] == '\'') {
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| 219 | // read to next '
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| 220 | pos++;
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| 221 | var sb = new StringBuilder();
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| 222 | while (pos < str.Length && str[pos] != '\'') {
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| 223 | sb.Append(str[pos]);
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| 224 | pos++;
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| 225 | }
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| 226 | if (pos < str.Length && str[pos] == '\'') {
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| 227 | pos++; // skip '
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| 228 | yield return new Token { TokenType = TokenType.Identifier, strVal = sb.ToString() };
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| 229 | } else
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| 230 | yield return new Token { TokenType = TokenType.NA };
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| 231 | } else if (str[pos] == '+') {
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| 232 | pos++;
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| 233 | yield return new Token { TokenType = TokenType.Operator, strVal = "+" };
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| 234 | } else if (str[pos] == '-') {
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| 235 | pos++;
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| 236 | yield return new Token { TokenType = TokenType.Operator, strVal = "-" };
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| 237 | } else if (str[pos] == '/') {
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| 238 | pos++;
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| 239 | yield return new Token { TokenType = TokenType.Operator, strVal = "/" };
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| 240 | } else if (str[pos] == '*') {
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| 241 | pos++;
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| 242 | yield return new Token { TokenType = TokenType.Operator, strVal = "*" };
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[16356] | 243 | } else if (str[pos] == '^') {
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| 244 | pos++;
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| 245 | yield return new Token { TokenType = TokenType.Operator, strVal = "^" };
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[14024] | 246 | } else if (str[pos] == '(') {
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| 247 | pos++;
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| 248 | yield return new Token { TokenType = TokenType.LeftPar, strVal = "(" };
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| 249 | } else if (str[pos] == ')') {
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| 250 | pos++;
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| 251 | yield return new Token { TokenType = TokenType.RightPar, strVal = ")" };
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[14826] | 252 | } else if (str[pos] == '[') {
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| 253 | pos++;
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| 254 | yield return new Token { TokenType = TokenType.LeftBracket, strVal = "[" };
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| 255 | } else if (str[pos] == ']') {
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| 256 | pos++;
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| 257 | yield return new Token { TokenType = TokenType.RightBracket, strVal = "]" };
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[16356] | 258 | } else if (str[pos] == '{') {
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| 259 | pos++;
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| 260 | yield return new Token { TokenType = TokenType.LeftPar, strVal = "{" };
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| 261 | } else if (str[pos] == '}') {
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| 262 | pos++;
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| 263 | yield return new Token { TokenType = TokenType.RightPar, strVal = "}" };
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[14826] | 264 | } else if (str[pos] == '=') {
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| 265 | pos++;
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| 266 | yield return new Token { TokenType = TokenType.Eq, strVal = "=" };
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[14347] | 267 | } else if (str[pos] == ',') {
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| 268 | pos++;
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| 269 | yield return new Token { TokenType = TokenType.Comma, strVal = "," };
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[18093] | 270 | } else if (str[pos] == '<') {
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| 271 | pos++;
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[18175] | 272 | yield return new Token { TokenType = TokenType.LeftAngleBracket, strVal = "<" };
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[18093] | 273 | } else if (str[pos] == '>') {
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| 274 | pos++;
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[18175] | 275 | yield return new Token { TokenType = TokenType.RightAngleBracket, strVal = ">" };
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[14319] | 276 | } else {
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| 277 | throw new ArgumentException("Invalid character: " + str[pos]);
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[14024] | 278 | }
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| 279 | }
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| 280 | }
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[14826] | 281 | /// S = Expr EOF
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[14024] | 282 | private ISymbolicExpressionTreeNode ParseS(Queue<Token> tokens) {
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| 283 | var expr = ParseExpr(tokens);
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| 284 |
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| 285 | var endTok = tokens.Dequeue();
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| 286 | if (endTok.TokenType != TokenType.End)
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| 287 | throw new ArgumentException(string.Format("Expected end of expression (got {0})", endTok.strVal));
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| 288 |
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| 289 | return expr;
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| 290 | }
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[14826] | 291 |
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[18175] | 292 | /// Expr = Term { '+' Term | '-' Term }
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[14024] | 293 | private ISymbolicExpressionTreeNode ParseExpr(Queue<Token> tokens) {
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[18175] | 294 | // build tree from bottom to top and left to right
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| 295 | // a + b - c => ((a + b) - c)
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| 296 | // a - b - c => ((a - b) - c)
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| 297 | // and then flatten as far as possible
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| 298 | var left = ParseTerm(tokens);
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| 299 |
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[14024] | 300 | var next = tokens.Peek();
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| 301 | while (next.strVal == "+" || next.strVal == "-") {
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| 302 | switch (next.strVal) {
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| 303 | case "+": {
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| 304 | tokens.Dequeue();
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[18175] | 305 | var right = ParseTerm(tokens);
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| 306 | var op = GetSymbol("+").CreateTreeNode();
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| 307 | op.AddSubtree(left);
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| 308 | op.AddSubtree(right);
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| 309 | left = op;
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[14024] | 310 | break;
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| 311 | }
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| 312 | case "-": {
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| 313 | tokens.Dequeue();
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[18175] | 314 | var right = ParseTerm(tokens);
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| 315 | var op = GetSymbol("-").CreateTreeNode();
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| 316 | op.AddSubtree(left);
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| 317 | op.AddSubtree(right);
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| 318 | left = op;
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[14024] | 319 | break;
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| 320 | }
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| 321 | }
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| 322 | next = tokens.Peek();
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| 323 | }
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| 324 |
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[18175] | 325 | FoldLeftRecursive(left);
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| 326 | return left;
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[14024] | 327 | }
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| 328 |
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| 329 | private ISymbol GetSymbol(string tok) {
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| 330 | var symb = knownSymbols.GetByFirst(tok).FirstOrDefault();
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| 331 | if (symb == null) throw new ArgumentException(string.Format("Unknown token {0} found.", tok));
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| 332 | return symb;
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| 333 | }
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| 334 |
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[14826] | 335 | /// Term = Fact { '*' Fact | '/' Fact }
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[14024] | 336 | private ISymbolicExpressionTreeNode ParseTerm(Queue<Token> tokens) {
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[18175] | 337 | // build tree from bottom to top and left to right
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| 338 | // a / b * c => ((a / b) * c)
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| 339 | // a / b / c => ((a / b) / c)
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| 340 | // and then flatten as far as possible
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[14024] | 341 |
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[18175] | 342 | var left = ParseFact(tokens);
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| 343 |
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[14024] | 344 | var next = tokens.Peek();
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| 345 | while (next.strVal == "*" || next.strVal == "/") {
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| 346 | switch (next.strVal) {
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| 347 | case "*": {
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| 348 | tokens.Dequeue();
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[18175] | 349 | var right = ParseFact(tokens);
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| 350 |
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| 351 | var op = GetSymbol("*").CreateTreeNode();
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| 352 | op.AddSubtree(left);
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| 353 | op.AddSubtree(right);
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| 354 | left = op;
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[14024] | 355 | break;
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| 356 | }
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| 357 | case "/": {
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| 358 | tokens.Dequeue();
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[18175] | 359 | var right = ParseFact(tokens);
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| 360 | var op = GetSymbol("/").CreateTreeNode();
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| 361 | op.AddSubtree(left);
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| 362 | op.AddSubtree(right);
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| 363 | left = op;
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[14024] | 364 | break;
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| 365 | }
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| 366 | }
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| 367 |
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| 368 | next = tokens.Peek();
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| 369 | }
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[18175] | 370 | // remove all nodes where the child op is the same as the parent op
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| 371 | // (a * b) * c) => (a * b * c)
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| 372 | // (a / b) / c) => (a / b / c)
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| 373 |
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| 374 | FoldLeftRecursive(left);
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| 375 | return left;
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| 376 | }
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| 377 |
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| 378 | private void FoldLeftRecursive(ISymbolicExpressionTreeNode parent) {
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| 379 | if (parent.SubtreeCount > 1) {
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| 380 | var child = parent.GetSubtree(0);
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| 381 | FoldLeftRecursive(child);
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| 382 | if (parent.Symbol == child.Symbol && IsAssociative(parent.Symbol)) {
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| 383 | parent.RemoveSubtree(0);
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| 384 | for (int i = 0; i < child.SubtreeCount; i++) {
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| 385 | parent.InsertSubtree(i, child.GetSubtree(i));
|
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| 386 | }
|
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| 387 | }
|
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[14024] | 388 | }
|
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| 389 | }
|
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| 390 |
|
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[16356] | 391 | // Fact = SimpleFact ['^' SimpleFact]
|
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| 392 | private ISymbolicExpressionTreeNode ParseFact(Queue<Token> tokens) {
|
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| 393 | var expr = ParseSimpleFact(tokens);
|
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| 394 | var next = tokens.Peek();
|
---|
| 395 | if (next.TokenType == TokenType.Operator && next.strVal == "^") {
|
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| 396 | tokens.Dequeue(); // skip;
|
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| 397 |
|
---|
| 398 | var p = GetSymbol("^").CreateTreeNode();
|
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| 399 | p.AddSubtree(expr);
|
---|
| 400 | p.AddSubtree(ParseSimpleFact(tokens));
|
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| 401 | expr = p;
|
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| 402 | }
|
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| 403 | return expr;
|
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| 404 | }
|
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| 405 |
|
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| 406 |
|
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| 407 | /// SimpleFact = '(' Expr ')'
|
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| 408 | /// | '{' Expr '}'
|
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| 409 | /// | 'LAG' '(' varId ',' ['+' | '-' ] number ')'
|
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| 410 | /// | funcId '(' ArgList ')
|
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| 411 | /// | VarExpr
|
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[18175] | 412 | /// | '<' 'num' [ '=' [ '+' | '-' ] number ] '>'
|
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[16356] | 413 | /// | number
|
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[18175] | 414 | /// | ['+' | '-' ] SimpleFact
|
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[14826] | 415 | /// ArgList = Expr { ',' Expr }
|
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| 416 | /// VarExpr = varId OptFactorPart
|
---|
| 417 | /// OptFactorPart = [ ('=' varVal | '[' ['+' | '-' ] number {',' ['+' | '-' ] number } ']' ) ]
|
---|
| 418 | /// varId = ident | ' ident ' | " ident "
|
---|
| 419 | /// varVal = ident | ' ident ' | " ident "
|
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| 420 | /// ident = '_' | letter { '_' | letter | digit }
|
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[16356] | 421 | private ISymbolicExpressionTreeNode ParseSimpleFact(Queue<Token> tokens) {
|
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[14024] | 422 | var next = tokens.Peek();
|
---|
| 423 | if (next.TokenType == TokenType.LeftPar) {
|
---|
[16356] | 424 | var initPar = tokens.Dequeue(); // match par type
|
---|
[14024] | 425 | var expr = ParseExpr(tokens);
|
---|
| 426 | var rPar = tokens.Dequeue();
|
---|
| 427 | if (rPar.TokenType != TokenType.RightPar)
|
---|
[16356] | 428 | throw new ArgumentException("expected closing parenthesis");
|
---|
| 429 | if (initPar.strVal == "(" && rPar.strVal == "}")
|
---|
| 430 | throw new ArgumentException("expected closing )");
|
---|
| 431 | if (initPar.strVal == "{" && rPar.strVal == ")")
|
---|
| 432 | throw new ArgumentException("expected closing }");
|
---|
[14024] | 433 | return expr;
|
---|
| 434 | } else if (next.TokenType == TokenType.Identifier) {
|
---|
| 435 | var idTok = tokens.Dequeue();
|
---|
| 436 | if (tokens.Peek().TokenType == TokenType.LeftPar) {
|
---|
[14826] | 437 | // function identifier or LAG
|
---|
[18175] | 438 | return ParseFunctionOrLaggedVariable(tokens, idTok);
|
---|
| 439 | } else {
|
---|
| 440 | return ParseVariable(tokens, idTok);
|
---|
| 441 | }
|
---|
| 442 | } else if (next.TokenType == TokenType.LeftAngleBracket) {
|
---|
| 443 | // '<' 'num' [ '=' ['+'|'-'] number ] '>'
|
---|
| 444 | return ParseNumber(tokens);
|
---|
| 445 | } else if (next.TokenType == TokenType.Operator && (next.strVal == "-" || next.strVal == "+")) {
|
---|
| 446 | // ['+' | '-' ] SimpleFact
|
---|
| 447 | if (tokens.Dequeue().strVal == "-") {
|
---|
| 448 | var arg = ParseSimpleFact(tokens);
|
---|
| 449 | if (arg is NumberTreeNode numNode) {
|
---|
| 450 | numNode.Value *= -1;
|
---|
| 451 | return numNode;
|
---|
| 452 | } else if (arg is ConstantTreeNode constNode) {
|
---|
| 453 | var constSy = new Constant { Value = -constNode.Value };
|
---|
| 454 | return constSy.CreateTreeNode();
|
---|
| 455 | } else if (arg is VariableTreeNode varNode) {
|
---|
| 456 | varNode.Weight *= -1;
|
---|
| 457 | return varNode;
|
---|
[14350] | 458 | } else {
|
---|
[18175] | 459 | var mul = GetSymbol("*").CreateTreeNode();
|
---|
| 460 | var neg = minusOne.CreateTreeNode();
|
---|
| 461 | mul.AddSubtree(neg);
|
---|
| 462 | mul.AddSubtree(arg);
|
---|
| 463 | return mul;
|
---|
[14350] | 464 | }
|
---|
[18175] | 465 | } else {
|
---|
| 466 | return ParseSimpleFact(tokens);
|
---|
| 467 | }
|
---|
| 468 | } else if (next.TokenType == TokenType.Number) {
|
---|
| 469 | // number
|
---|
| 470 | var numTok = tokens.Dequeue();
|
---|
| 471 | var constSy = new Constant { Value = numTok.doubleVal };
|
---|
| 472 | return constSy.CreateTreeNode();
|
---|
| 473 | } else {
|
---|
| 474 | throw new ArgumentException(string.Format("unexpected token in expression {0}", next.strVal));
|
---|
| 475 | }
|
---|
| 476 | }
|
---|
[14347] | 477 |
|
---|
[18175] | 478 | private ISymbolicExpressionTreeNode ParseNumber(Queue<Token> tokens) {
|
---|
| 479 | // we distinguish parameters and constants. The values of parameters can be changed.
|
---|
| 480 | // a parameter is written as '<' 'num' [ '=' ['+'|'-'] number ] '>' with an optional initialization
|
---|
| 481 | Token numberTok = null;
|
---|
| 482 | var leftAngleBracket = tokens.Dequeue();
|
---|
| 483 | if (leftAngleBracket.TokenType != TokenType.LeftAngleBracket)
|
---|
| 484 | throw new ArgumentException("opening bracket < expected");
|
---|
[14024] | 485 |
|
---|
[18175] | 486 | var idTok = tokens.Dequeue();
|
---|
| 487 | if (idTok.TokenType != TokenType.Identifier || idTok.strVal.ToLower() != "num")
|
---|
| 488 | throw new ArgumentException("string 'num' expected");
|
---|
[16356] | 489 |
|
---|
[18175] | 490 | var numNode = (NumberTreeNode)number.CreateTreeNode();
|
---|
[14826] | 491 |
|
---|
[18175] | 492 | if (tokens.Peek().TokenType == TokenType.Eq) {
|
---|
| 493 | tokens.Dequeue(); // skip "="
|
---|
| 494 | var next = tokens.Peek();
|
---|
| 495 | if (next.strVal != "+" && next.strVal != "-" && next.TokenType != TokenType.Number)
|
---|
| 496 | throw new ArgumentException("Expected '+', '-' or number.");
|
---|
| 497 |
|
---|
| 498 | var sign = 1.0;
|
---|
| 499 | if (next.strVal == "+" || next.strVal == "-") {
|
---|
| 500 | if (tokens.Dequeue().strVal == "-") sign = -1.0;
|
---|
[14024] | 501 | }
|
---|
[18175] | 502 | if (tokens.Peek().TokenType != TokenType.Number) {
|
---|
| 503 | throw new ArgumentException("Expected number.");
|
---|
| 504 | }
|
---|
| 505 | numberTok = tokens.Dequeue();
|
---|
| 506 | numNode.Value = sign * numberTok.doubleVal;
|
---|
| 507 | }
|
---|
[18093] | 508 |
|
---|
[18175] | 509 | var rightAngleBracket = tokens.Dequeue();
|
---|
| 510 | if (rightAngleBracket.TokenType != TokenType.RightAngleBracket)
|
---|
| 511 | throw new ArgumentException("closing bracket > expected");
|
---|
[18100] | 512 |
|
---|
[18175] | 513 | return numNode;
|
---|
| 514 | }
|
---|
[18100] | 515 |
|
---|
[18175] | 516 | private ISymbolicExpressionTreeNode ParseVariable(Queue<Token> tokens, Token idTok) {
|
---|
| 517 | // variable
|
---|
| 518 | if (tokens.Peek().TokenType == TokenType.Eq) {
|
---|
| 519 | // binary factor
|
---|
| 520 | tokens.Dequeue(); // skip Eq
|
---|
| 521 | var valTok = tokens.Dequeue();
|
---|
| 522 | if (valTok.TokenType != TokenType.Identifier) throw new ArgumentException("expected identifier");
|
---|
| 523 | var binFactorNode = (BinaryFactorVariableTreeNode)binaryFactorVar.CreateTreeNode();
|
---|
| 524 | binFactorNode.Weight = 1.0;
|
---|
| 525 | binFactorNode.VariableName = idTok.strVal;
|
---|
| 526 | binFactorNode.VariableValue = valTok.strVal;
|
---|
| 527 | return binFactorNode;
|
---|
| 528 | } else if (tokens.Peek().TokenType == TokenType.LeftBracket) {
|
---|
| 529 | // factor variable
|
---|
| 530 | var factorVariableNode = (FactorVariableTreeNode)factorVar.CreateTreeNode();
|
---|
| 531 | factorVariableNode.VariableName = idTok.strVal;
|
---|
| 532 |
|
---|
| 533 | tokens.Dequeue(); // skip [
|
---|
| 534 | var weights = new List<double>();
|
---|
| 535 | // at least one weight is necessary
|
---|
| 536 | var sign = 1.0;
|
---|
| 537 | if (tokens.Peek().TokenType == TokenType.Operator) {
|
---|
| 538 | var opToken = tokens.Dequeue();
|
---|
| 539 | if (opToken.strVal == "+") sign = 1.0;
|
---|
| 540 | else if (opToken.strVal == "-") sign = -1.0;
|
---|
| 541 | else throw new ArgumentException();
|
---|
[18100] | 542 | }
|
---|
[18175] | 543 | if (tokens.Peek().TokenType != TokenType.Number) throw new ArgumentException("number expected");
|
---|
| 544 | var weightTok = tokens.Dequeue();
|
---|
| 545 | weights.Add(sign * weightTok.doubleVal);
|
---|
| 546 | while (tokens.Peek().TokenType == TokenType.Comma) {
|
---|
| 547 | // skip comma
|
---|
| 548 | tokens.Dequeue();
|
---|
| 549 | if (tokens.Peek().TokenType == TokenType.Operator) {
|
---|
| 550 | var opToken = tokens.Dequeue();
|
---|
| 551 | if (opToken.strVal == "+") sign = 1.0;
|
---|
| 552 | else if (opToken.strVal == "-") sign = -1.0;
|
---|
| 553 | else throw new ArgumentException();
|
---|
| 554 | }
|
---|
| 555 | weightTok = tokens.Dequeue();
|
---|
| 556 | if (weightTok.TokenType != TokenType.Number) throw new ArgumentException("number expected");
|
---|
| 557 | weights.Add(sign * weightTok.doubleVal);
|
---|
| 558 | }
|
---|
| 559 | var rightBracketToken = tokens.Dequeue();
|
---|
| 560 | if (rightBracketToken.TokenType != TokenType.RightBracket) throw new ArgumentException("closing bracket ] expected");
|
---|
| 561 | factorVariableNode.Weights = weights.ToArray();
|
---|
| 562 | return factorVariableNode;
|
---|
| 563 | } else {
|
---|
| 564 | // variable
|
---|
| 565 | var varNode = (VariableTreeNode)variable.CreateTreeNode();
|
---|
| 566 | varNode.Weight = 1.0;
|
---|
| 567 | varNode.VariableName = idTok.strVal;
|
---|
| 568 | return varNode;
|
---|
| 569 | }
|
---|
| 570 | }
|
---|
[18100] | 571 |
|
---|
[18175] | 572 | private ISymbolicExpressionTreeNode ParseFunctionOrLaggedVariable(Queue<Token> tokens, Token idTok) {
|
---|
| 573 | var funcId = idTok.strVal.ToUpperInvariant();
|
---|
| 574 |
|
---|
| 575 | var funcNode = GetSymbol(funcId).CreateTreeNode();
|
---|
| 576 | var lPar = tokens.Dequeue();
|
---|
| 577 | if (lPar.TokenType != TokenType.LeftPar)
|
---|
| 578 | throw new ArgumentException("expected (");
|
---|
| 579 |
|
---|
| 580 | // handle 'lag' specifically
|
---|
| 581 | if (funcNode.Symbol is LaggedVariable) {
|
---|
| 582 | ParseLaggedVariable(tokens, funcNode);
|
---|
[14024] | 583 | } else {
|
---|
[18175] | 584 | // functions
|
---|
| 585 | var args = ParseArgList(tokens);
|
---|
| 586 | // check number of arguments
|
---|
| 587 | if (funcNode.Symbol.MinimumArity > args.Length || funcNode.Symbol.MaximumArity < args.Length) {
|
---|
| 588 | throw new ArgumentException(string.Format("Symbol {0} requires between {1} and {2} arguments.", funcId,
|
---|
| 589 | funcNode.Symbol.MinimumArity, funcNode.Symbol.MaximumArity));
|
---|
| 590 | }
|
---|
| 591 | foreach (var arg in args) funcNode.AddSubtree(arg);
|
---|
[14024] | 592 | }
|
---|
[18175] | 593 |
|
---|
| 594 | var rPar = tokens.Dequeue();
|
---|
| 595 | if (rPar.TokenType != TokenType.RightPar)
|
---|
| 596 | throw new ArgumentException("expected )");
|
---|
| 597 |
|
---|
| 598 |
|
---|
| 599 | return funcNode;
|
---|
[14024] | 600 | }
|
---|
[14347] | 601 |
|
---|
[18175] | 602 | private static void ParseLaggedVariable(Queue<Token> tokens, ISymbolicExpressionTreeNode funcNode) {
|
---|
| 603 | var varId = tokens.Dequeue();
|
---|
| 604 | if (varId.TokenType != TokenType.Identifier) throw new ArgumentException("Identifier expected. Format for lagged variables: \"lag(x, -1)\"");
|
---|
| 605 | var comma = tokens.Dequeue();
|
---|
| 606 | if (comma.TokenType != TokenType.Comma) throw new ArgumentException("',' expected, Format for lagged variables: \"lag(x, -1)\"");
|
---|
| 607 | double sign = 1.0;
|
---|
| 608 | if (tokens.Peek().strVal == "+" || tokens.Peek().strVal == "-") {
|
---|
| 609 | // read sign
|
---|
| 610 | var signTok = tokens.Dequeue();
|
---|
| 611 | if (signTok.strVal == "-") sign = -1.0;
|
---|
| 612 | }
|
---|
| 613 | var lagToken = tokens.Dequeue();
|
---|
| 614 | if (lagToken.TokenType != TokenType.Number) throw new ArgumentException("Number expected, Format for lagged variables: \"lag(x, -1)\"");
|
---|
| 615 | if (!lagToken.doubleVal.IsAlmost(Math.Round(lagToken.doubleVal)))
|
---|
| 616 | throw new ArgumentException("Time lags must be integer values");
|
---|
| 617 | var laggedVarNode = funcNode as LaggedVariableTreeNode;
|
---|
| 618 | laggedVarNode.VariableName = varId.strVal;
|
---|
| 619 | laggedVarNode.Lag = (int)Math.Round(sign * lagToken.doubleVal);
|
---|
| 620 | laggedVarNode.Weight = 1.0;
|
---|
| 621 | }
|
---|
| 622 |
|
---|
[14347] | 623 | // ArgList = Expr { ',' Expr }
|
---|
| 624 | private ISymbolicExpressionTreeNode[] ParseArgList(Queue<Token> tokens) {
|
---|
| 625 | var exprList = new List<ISymbolicExpressionTreeNode>();
|
---|
| 626 | exprList.Add(ParseExpr(tokens));
|
---|
| 627 | while (tokens.Peek().TokenType != TokenType.RightPar) {
|
---|
| 628 | var comma = tokens.Dequeue();
|
---|
| 629 | if (comma.TokenType != TokenType.Comma) throw new ArgumentException("expected ',' ");
|
---|
| 630 | exprList.Add(ParseExpr(tokens));
|
---|
| 631 | }
|
---|
| 632 | return exprList.ToArray();
|
---|
| 633 | }
|
---|
[18175] | 634 |
|
---|
| 635 | private bool IsAssociative(ISymbol sy) {
|
---|
| 636 | return sy == GetSymbol("+") || sy == GetSymbol("-") ||
|
---|
| 637 | sy == GetSymbol("*") || sy == GetSymbol("/") ||
|
---|
| 638 | sy == GetSymbol("AND") || sy == GetSymbol("OR") || sy == GetSymbol("XOR");
|
---|
| 639 | }
|
---|
[14024] | 640 | }
|
---|
| 641 | }
|
---|