[14024] | 1 | #region License Information
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| 2 | /* HeuristicLab
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| 3 | * Copyright (C) 2002-2016 Heuristic and Evolutionary Algorithms Laboratory (HEAL)
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| 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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[14351] | 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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[14251] | 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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[14251] | 39 | ///
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| 40 | ///
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| 41 | /// S = Expr EOF
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| 42 | /// Expr = ['-' | '+'] Term { '+' Term | '-' Term }
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| 43 | /// Term = Fact { '*' Fact | '/' Fact }
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| 44 | /// Fact = '(' Expr ')' | funcId '(' Expr ')' | VarExpr | number
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| 45 | /// VarExpr = varId [ '=' varVal]
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| 46 | /// varId = ident | ' ident ' | " ident "
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| 47 | /// varVal = ident | ' ident ' | " ident "
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| 48 | /// ident = '_' | letter { '_' | letter | digit }
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[14024] | 49 | /// </summary>
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[14026] | 50 | public sealed class InfixExpressionParser {
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[14351] | 51 | private enum TokenType { Operator, Identifier, Number, LeftPar, RightPar, Comma, Eq, End, NA };
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[14024] | 52 | private class Token {
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| 53 | internal double doubleVal;
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| 54 | internal string strVal;
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| 55 | internal TokenType TokenType;
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| 56 | }
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| 57 |
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| 58 | private class SymbolNameComparer : IEqualityComparer<ISymbol>, IComparer<ISymbol> {
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| 59 | public int Compare(ISymbol x, ISymbol y) {
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| 60 | return x.Name.CompareTo(y.Name);
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| 61 | }
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| 62 |
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| 63 | public bool Equals(ISymbol x, ISymbol y) {
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| 64 | return Compare(x, y) == 0;
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| 65 | }
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| 66 |
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| 67 | public int GetHashCode(ISymbol obj) {
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| 68 | return obj.Name.GetHashCode();
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| 69 | }
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| 70 | }
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| 71 | // format name <-> symbol
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| 72 | // the lookup table is also used in the corresponding formatter
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| 73 | internal static readonly BidirectionalLookup<string, ISymbol>
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| 74 | knownSymbols = new BidirectionalLookup<string, ISymbol>(StringComparer.InvariantCulture, new SymbolNameComparer());
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| 75 |
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| 76 | private Constant constant = new Constant();
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| 77 | private Variable variable = new Variable();
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[14251] | 78 | private BinaryFactorVariable binaryFactorVar = new BinaryFactorVariable();
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[14024] | 79 |
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| 80 | private ProgramRootSymbol programRootSymbol = new ProgramRootSymbol();
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| 81 | private StartSymbol startSymbol = new StartSymbol();
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| 82 |
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| 83 | static InfixExpressionParser() {
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| 84 | // populate bidirectional lookup
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| 85 | var dict = new Dictionary<string, ISymbol>
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| 86 | {
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| 87 | { "+", new Addition()},
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| 88 | { "/", new Division()},
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| 89 | { "*", new Multiplication()},
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| 90 | { "-", new Subtraction()},
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| 91 | { "EXP", new Exponential()},
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| 92 | { "LOG", new Logarithm()},
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| 93 | { "POW", new Power()},
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| 94 | { "ROOT", new Root()},
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| 95 | { "SQR", new Square() },
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| 96 | { "SQRT", new SquareRoot() },
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| 97 | { "SIN",new Sine()},
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| 98 | { "COS", new Cosine()},
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| 99 | { "TAN", new Tangent()},
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| 100 | { "AIRYA", new AiryA()},
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| 101 | { "AIRYB", new AiryB()},
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| 102 | { "BESSEL", new Bessel()},
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| 103 | { "COSINT", new CosineIntegral()},
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| 104 | { "SININT", new SineIntegral()},
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| 105 | { "HYPCOSINT", new HyperbolicCosineIntegral()},
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| 106 | { "HYPSININT", new HyperbolicSineIntegral()},
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| 107 | { "FRESNELSININT", new FresnelSineIntegral()},
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| 108 | { "FRESNELCOSINT", new FresnelCosineIntegral()},
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| 109 | { "NORM", new Norm()},
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| 110 | { "ERF", new Erf()},
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| 111 | { "GAMMA", new Gamma()},
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| 112 | { "PSI", new Psi()},
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| 113 | { "DAWSON", new Dawson()},
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| 114 | { "EXPINT", new ExponentialIntegralEi()},
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| 115 | { "MEAN", new Average()},
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| 116 | { "IF", new IfThenElse()},
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[14351] | 117 | { "GT", new GreaterThan()},
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| 118 | { "LT", new LessThan()},
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[14024] | 119 | { "AND", new And()},
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| 120 | { "OR", new Or()},
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| 121 | { "NOT", new Not()},
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| 122 | { "XOR", new Xor()},
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| 123 | { "DIFF", new Derivative()},
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[14351] | 124 | { "LAG", new LaggedVariable() },
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[14024] | 125 | };
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| 126 |
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| 127 |
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| 128 | foreach (var kvp in dict) {
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| 129 | knownSymbols.Add(kvp.Key, kvp.Value);
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| 130 | }
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| 131 | }
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| 132 |
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| 133 | public ISymbolicExpressionTree Parse(string str) {
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| 134 | ISymbolicExpressionTreeNode root = programRootSymbol.CreateTreeNode();
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| 135 | ISymbolicExpressionTreeNode start = startSymbol.CreateTreeNode();
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| 136 | var allTokens = GetAllTokens(str).ToArray();
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| 137 | ISymbolicExpressionTreeNode mainBranch = ParseS(new Queue<Token>(allTokens));
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| 138 |
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| 139 | // only a main branch was given => insert the main branch into the default tree template
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| 140 | root.AddSubtree(start);
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| 141 | start.AddSubtree(mainBranch);
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| 142 | return new SymbolicExpressionTree(root);
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| 143 | }
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| 144 |
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| 145 | private IEnumerable<Token> GetAllTokens(string str) {
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| 146 | int pos = 0;
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| 147 | while (true) {
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| 148 | while (pos < str.Length && Char.IsWhiteSpace(str[pos])) pos++;
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| 149 | if (pos >= str.Length) {
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| 150 | yield return new Token { TokenType = TokenType.End, strVal = "" };
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| 151 | yield break;
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| 152 | }
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| 153 | if (char.IsDigit(str[pos])) {
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[14351] | 154 | // read number (=> read until white space or operator or comma)
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[14024] | 155 | var sb = new StringBuilder();
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| 156 | sb.Append(str[pos]);
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| 157 | pos++;
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| 158 | while (pos < str.Length && !char.IsWhiteSpace(str[pos])
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[14251] | 159 | && (str[pos] != '+' || str[pos - 1] == 'e' || str[pos - 1] == 'E') // continue reading exponents
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[14024] | 160 | && (str[pos] != '-' || str[pos - 1] == 'e' || str[pos - 1] == 'E')
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[14251] | 161 | && str[pos] != '*'
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[14024] | 162 | && str[pos] != '/'
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[14351] | 163 | && str[pos] != ')'
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| 164 | && str[pos] != ',') {
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[14024] | 165 | sb.Append(str[pos]);
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| 166 | pos++;
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| 167 | }
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| 168 | double dblVal;
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| 169 | if (double.TryParse(sb.ToString(), NumberStyles.Float, CultureInfo.InvariantCulture, out dblVal))
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| 170 | yield return new Token { TokenType = TokenType.Number, strVal = sb.ToString(), doubleVal = dblVal };
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| 171 | else yield return new Token { TokenType = TokenType.NA, strVal = sb.ToString() };
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| 172 | } else if (char.IsLetter(str[pos]) || str[pos] == '_') {
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| 173 | // read ident
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| 174 | var sb = new StringBuilder();
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| 175 | sb.Append(str[pos]);
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| 176 | pos++;
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| 177 | while (pos < str.Length &&
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| 178 | (char.IsLetter(str[pos]) || str[pos] == '_' || char.IsDigit(str[pos]))) {
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| 179 | sb.Append(str[pos]);
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| 180 | pos++;
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| 181 | }
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| 182 | yield return new Token { TokenType = TokenType.Identifier, strVal = sb.ToString() };
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| 183 | } else if (str[pos] == '"') {
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| 184 | // read to next "
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| 185 | pos++;
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| 186 | var sb = new StringBuilder();
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| 187 | while (pos < str.Length && str[pos] != '"') {
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| 188 | sb.Append(str[pos]);
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| 189 | pos++;
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| 190 | }
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| 191 | if (pos < str.Length && str[pos] == '"') {
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| 192 | pos++; // skip "
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| 193 | yield return new Token { TokenType = TokenType.Identifier, strVal = sb.ToString() };
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| 194 | } else
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| 195 | yield return new Token { TokenType = TokenType.NA };
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| 196 |
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| 197 | } else if (str[pos] == '\'') {
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| 198 | // read to next '
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| 199 | pos++;
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| 200 | var sb = new StringBuilder();
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| 201 | while (pos < str.Length && str[pos] != '\'') {
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| 202 | sb.Append(str[pos]);
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| 203 | pos++;
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| 204 | }
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| 205 | if (pos < str.Length && str[pos] == '\'') {
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| 206 | pos++; // skip '
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| 207 | yield return new Token { TokenType = TokenType.Identifier, strVal = sb.ToString() };
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| 208 | } else
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| 209 | yield return new Token { TokenType = TokenType.NA };
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| 210 | } else if (str[pos] == '+') {
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| 211 | pos++;
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| 212 | yield return new Token { TokenType = TokenType.Operator, strVal = "+" };
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| 213 | } else if (str[pos] == '-') {
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| 214 | pos++;
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| 215 | yield return new Token { TokenType = TokenType.Operator, strVal = "-" };
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| 216 | } else if (str[pos] == '/') {
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| 217 | pos++;
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| 218 | yield return new Token { TokenType = TokenType.Operator, strVal = "/" };
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| 219 | } else if (str[pos] == '*') {
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| 220 | pos++;
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| 221 | yield return new Token { TokenType = TokenType.Operator, strVal = "*" };
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| 222 | } else if (str[pos] == '(') {
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| 223 | pos++;
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| 224 | yield return new Token { TokenType = TokenType.LeftPar, strVal = "(" };
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| 225 | } else if (str[pos] == ')') {
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| 226 | pos++;
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| 227 | yield return new Token { TokenType = TokenType.RightPar, strVal = ")" };
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[14251] | 228 | } else if (str[pos] == '=') {
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| 229 | pos++;
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| 230 | yield return new Token { TokenType = TokenType.Eq, strVal = "=" };
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[14351] | 231 | } else if (str[pos] == ',') {
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| 232 | pos++;
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| 233 | yield return new Token { TokenType = TokenType.Comma, strVal = "," };
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[14330] | 234 | } else {
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| 235 | throw new ArgumentException("Invalid character: " + str[pos]);
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[14024] | 236 | }
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| 237 | }
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| 238 | }
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| 239 |
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[14351] | 240 | // S = Expr EOF
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| 241 | // Expr = ['-' | '+'] Term { '+' Term | '-' Term }
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| 242 | // Term = Fact { '*' Fact | '/' Fact }
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| 243 | // Fact = '(' Expr ')' | funcId '(' ArgList ')' | varId | number
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| 244 | // ArgList = Expr { ',' Expr }
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[14024] | 245 | private ISymbolicExpressionTreeNode ParseS(Queue<Token> tokens) {
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| 246 | var expr = ParseExpr(tokens);
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| 247 |
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| 248 | var endTok = tokens.Dequeue();
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| 249 | if (endTok.TokenType != TokenType.End)
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| 250 | throw new ArgumentException(string.Format("Expected end of expression (got {0})", endTok.strVal));
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| 251 |
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| 252 | return expr;
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| 253 | }
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| 254 | private ISymbolicExpressionTreeNode ParseExpr(Queue<Token> tokens) {
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| 255 | var next = tokens.Peek();
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| 256 | var posTerms = new List<ISymbolicExpressionTreeNode>();
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| 257 | var negTerms = new List<ISymbolicExpressionTreeNode>();
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| 258 | bool negateFirstTerm = false;
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| 259 | if (next.TokenType == TokenType.Operator && (next.strVal == "+" || next.strVal == "-")) {
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| 260 | tokens.Dequeue();
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| 261 | if (next.strVal == "-")
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| 262 | negateFirstTerm = true;
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| 263 | }
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| 264 | var t = ParseTerm(tokens);
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| 265 | if (negateFirstTerm) negTerms.Add(t);
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| 266 | else posTerms.Add(t);
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| 267 |
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| 268 | next = tokens.Peek();
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| 269 | while (next.strVal == "+" || next.strVal == "-") {
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| 270 | switch (next.strVal) {
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| 271 | case "+": {
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| 272 | tokens.Dequeue();
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| 273 | var term = ParseTerm(tokens);
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| 274 | posTerms.Add(term);
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| 275 | break;
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| 276 | }
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| 277 | case "-": {
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| 278 | tokens.Dequeue();
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| 279 | var term = ParseTerm(tokens);
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| 280 | negTerms.Add(term);
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| 281 | break;
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| 282 | }
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| 283 | }
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| 284 | next = tokens.Peek();
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| 285 | }
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| 286 |
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| 287 | var sum = GetSymbol("+").CreateTreeNode();
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| 288 | foreach (var posTerm in posTerms) sum.AddSubtree(posTerm);
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| 289 | if (negTerms.Any()) {
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| 290 | if (negTerms.Count == 1) {
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| 291 | var sub = GetSymbol("-").CreateTreeNode();
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| 292 | sub.AddSubtree(negTerms.Single());
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| 293 | sum.AddSubtree(sub);
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| 294 | } else {
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| 295 | var sumNeg = GetSymbol("+").CreateTreeNode();
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| 296 | foreach (var negTerm in negTerms) sumNeg.AddSubtree(negTerm);
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| 297 |
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| 298 | var constNode = (ConstantTreeNode)constant.CreateTreeNode();
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| 299 | constNode.Value = -1.0;
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| 300 | var prod = GetSymbol("*").CreateTreeNode();
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| 301 | prod.AddSubtree(constNode);
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| 302 | prod.AddSubtree(sumNeg);
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| 303 |
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| 304 | sum.AddSubtree(prod);
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| 305 | }
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| 306 | }
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| 307 | if (sum.SubtreeCount == 1) return sum.Subtrees.First();
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| 308 | else return sum;
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| 309 | }
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| 310 |
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| 311 | private ISymbol GetSymbol(string tok) {
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| 312 | var symb = knownSymbols.GetByFirst(tok).FirstOrDefault();
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| 313 | if (symb == null) throw new ArgumentException(string.Format("Unknown token {0} found.", tok));
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| 314 | return symb;
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| 315 | }
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| 316 |
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| 317 | // Term = Fact { '*' Fact | '/' Fact }
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| 318 | private ISymbolicExpressionTreeNode ParseTerm(Queue<Token> tokens) {
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| 319 | var factors = new List<ISymbolicExpressionTreeNode>();
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| 320 | var firstFactor = ParseFact(tokens);
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| 321 | factors.Add(firstFactor);
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| 322 |
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| 323 | var next = tokens.Peek();
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| 324 | while (next.strVal == "*" || next.strVal == "/") {
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| 325 | switch (next.strVal) {
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| 326 | case "*": {
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| 327 | tokens.Dequeue();
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| 328 | var fact = ParseFact(tokens);
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| 329 | factors.Add(fact);
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| 330 | break;
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| 331 | }
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| 332 | case "/": {
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| 333 | tokens.Dequeue();
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| 334 | var invFact = ParseFact(tokens);
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| 335 | var divNode = GetSymbol("/").CreateTreeNode(); // 1/x
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| 336 | divNode.AddSubtree(invFact);
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| 337 | factors.Add(divNode);
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| 338 | break;
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| 339 | }
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| 340 | }
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| 341 |
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| 342 | next = tokens.Peek();
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| 343 | }
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| 344 | if (factors.Count == 1) return factors.First();
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| 345 | else {
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| 346 | var prod = GetSymbol("*").CreateTreeNode();
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| 347 | foreach (var f in factors) prod.AddSubtree(f);
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| 348 | return prod;
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| 349 | }
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| 350 | }
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| 351 |
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[14351] | 352 | // Fact = '(' Expr ')' | 'LAG' '(' varId ',' ['+' | '-' ] number ')' | funcId '(' Expr ')' | varId [ = valId ] | number
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[14024] | 353 | private ISymbolicExpressionTreeNode ParseFact(Queue<Token> tokens) {
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| 354 | var next = tokens.Peek();
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| 355 | if (next.TokenType == TokenType.LeftPar) {
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| 356 | tokens.Dequeue();
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| 357 | var expr = ParseExpr(tokens);
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| 358 | var rPar = tokens.Dequeue();
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| 359 | if (rPar.TokenType != TokenType.RightPar)
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| 360 | throw new ArgumentException("expected )");
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| 361 | return expr;
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| 362 | } else if (next.TokenType == TokenType.Identifier) {
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| 363 | var idTok = tokens.Dequeue();
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| 364 | if (tokens.Peek().TokenType == TokenType.LeftPar) {
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| 365 | // function identifier
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| 366 | var funcId = idTok.strVal.ToUpperInvariant();
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| 367 |
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| 368 | var funcNode = GetSymbol(funcId).CreateTreeNode();
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| 369 | var lPar = tokens.Dequeue();
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| 370 | if (lPar.TokenType != TokenType.LeftPar)
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| 371 | throw new ArgumentException("expected (");
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[14351] | 372 |
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| 373 | // handle 'lag' specifically
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| 374 | if (funcNode.Symbol is LaggedVariable) {
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| 375 | var varId = tokens.Dequeue();
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| 376 | if (varId.TokenType != TokenType.Identifier) throw new ArgumentException("Identifier expected. Format for lagged variables: \"lag(x, -1)\"");
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| 377 | var comma = tokens.Dequeue();
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| 378 | if (comma.TokenType != TokenType.Comma) throw new ArgumentException("',' expected, Format for lagged variables: \"lag(x, -1)\"");
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| 379 | double sign = 1.0;
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| 380 | if (tokens.Peek().strVal == "+" || tokens.Peek().strVal == "-") {
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| 381 | // read sign
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| 382 | var signTok = tokens.Dequeue();
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| 383 | if (signTok.strVal == "-") sign = -1.0;
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| 384 | }
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| 385 | var lagToken = tokens.Dequeue();
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| 386 | if (lagToken.TokenType != TokenType.Number) throw new ArgumentException("Number expected, Format for lagged variables: \"lag(x, -1)\"");
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| 387 | if (!lagToken.doubleVal.IsAlmost(Math.Round(lagToken.doubleVal)))
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| 388 | throw new ArgumentException("Time lags must be integer values");
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| 389 | var laggedVarNode = funcNode as LaggedVariableTreeNode;
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| 390 | laggedVarNode.VariableName = varId.strVal;
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| 391 | laggedVarNode.Lag = (int)Math.Round(sign * lagToken.doubleVal);
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| 392 | laggedVarNode.Weight = 1.0;
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| 393 | } else {
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| 394 | // functions
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| 395 | var args = ParseArgList(tokens);
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| 396 | // check number of arguments
|
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| 397 | if (funcNode.Symbol.MinimumArity > args.Length || funcNode.Symbol.MaximumArity < args.Length) {
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| 398 | throw new ArgumentException(string.Format("Symbol {0} requires between {1} and {2} arguments.", funcId,
|
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| 399 | funcNode.Symbol.MinimumArity, funcNode.Symbol.MaximumArity));
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| 400 | }
|
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| 401 | foreach (var arg in args) funcNode.AddSubtree(arg);
|
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| 402 | }
|
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| 403 |
|
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[14024] | 404 | var rPar = tokens.Dequeue();
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| 405 | if (rPar.TokenType != TokenType.RightPar)
|
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| 406 | throw new ArgumentException("expected )");
|
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| 407 |
|
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| 408 | return funcNode;
|
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| 409 | } else {
|
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| 410 | // variable
|
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[14251] | 411 | if (tokens.Peek().TokenType == TokenType.Eq) {
|
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| 412 | // binary factor
|
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| 413 | tokens.Dequeue(); // skip Eq
|
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| 414 | var valTok = tokens.Dequeue();
|
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| 415 | if (valTok.TokenType != TokenType.Identifier) throw new ArgumentException("expected identifier");
|
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| 416 | var binFactorNode = (BinaryFactorVariableTreeNode)binaryFactorVar.CreateTreeNode();
|
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| 417 | binFactorNode.Weight = 1.0;
|
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| 418 | binFactorNode.VariableName = idTok.strVal;
|
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| 419 | binFactorNode.VariableValue = valTok.strVal;
|
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| 420 | return binFactorNode;
|
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| 421 | } else {
|
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| 422 | // variable
|
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| 423 | var varNode = (VariableTreeNode)variable.CreateTreeNode();
|
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| 424 | varNode.Weight = 1.0;
|
---|
| 425 | varNode.VariableName = idTok.strVal;
|
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| 426 | return varNode;
|
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| 427 | }
|
---|
[14024] | 428 | }
|
---|
| 429 | } else if (next.TokenType == TokenType.Number) {
|
---|
| 430 | var numTok = tokens.Dequeue();
|
---|
| 431 | var constNode = (ConstantTreeNode)constant.CreateTreeNode();
|
---|
| 432 | constNode.Value = numTok.doubleVal;
|
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| 433 | return constNode;
|
---|
| 434 | } else {
|
---|
| 435 | throw new ArgumentException(string.Format("unexpected token in expression {0}", next.strVal));
|
---|
| 436 | }
|
---|
| 437 | }
|
---|
[14251] | 438 |
|
---|
[14351] | 439 | // ArgList = Expr { ',' Expr }
|
---|
| 440 | private ISymbolicExpressionTreeNode[] ParseArgList(Queue<Token> tokens) {
|
---|
| 441 | var exprList = new List<ISymbolicExpressionTreeNode>();
|
---|
| 442 | exprList.Add(ParseExpr(tokens));
|
---|
| 443 | while (tokens.Peek().TokenType != TokenType.RightPar) {
|
---|
| 444 | var comma = tokens.Dequeue();
|
---|
| 445 | if (comma.TokenType != TokenType.Comma) throw new ArgumentException("expected ',' ");
|
---|
| 446 | exprList.Add(ParseExpr(tokens));
|
---|
| 447 | }
|
---|
| 448 | return exprList.ToArray();
|
---|
| 449 | }
|
---|
[14024] | 450 | }
|
---|
| 451 | }
|
---|