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source: branches/HeuristicLab.EvolutionTracking/HeuristicLab.Problems.DataAnalysis.Symbolic/3.4/Formatters/SymbolicDataAnalysisExpressionLatexFormatter.cs @ 16130

Last change on this file since 16130 was 16130, checked in by bburlacu, 6 years ago

#1772: Merge trunk changes

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1#region License Information
2/* HeuristicLab
3 * Copyright (C) 2002-2018 Heuristic and Evolutionary Algorithms Laboratory (HEAL)
4 *
5 * This file is part of HeuristicLab.
6 *
7 * HeuristicLab is free software: you can redistribute it and/or modify
8 * it under the terms of the GNU General Public License as published by
9 * the Free Software Foundation, either version 3 of the License, or
10 * (at your option) any later version.
11 *
12 * HeuristicLab is distributed in the hope that it will be useful,
13 * but WITHOUT ANY WARRANTY; without even the implied warranty of
14 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
15 * GNU General Public License for more details.
16 *
17 * You should have received a copy of the GNU General Public License
18 * along with HeuristicLab. If not, see <http://www.gnu.org/licenses/>.
19 */
20#endregion
21
22using System;
23using System.Collections.Generic;
24using System.Linq;
25using System.Text;
26using HeuristicLab.Common;
27using HeuristicLab.Core;
28using HeuristicLab.Encodings.SymbolicExpressionTreeEncoding;
29using HeuristicLab.Persistence.Default.CompositeSerializers.Storable;
30
31namespace HeuristicLab.Problems.DataAnalysis.Symbolic {
32  [Item("LaTeX String Formatter", "Formatter for symbolic expression trees for import into LaTeX documents.")]
33  [StorableClass]
34  public sealed class SymbolicDataAnalysisExpressionLatexFormatter : NamedItem, ISymbolicExpressionTreeStringFormatter {
35    private readonly List<KeyValuePair<string, double>> constants;
36    private int constIndex;
37    private int targetCount;
38    private int currentLag;
39    private string targetVariable;
40    private bool containsTimeSeriesSymbol;
41
42    [StorableConstructor]
43    private SymbolicDataAnalysisExpressionLatexFormatter(bool deserializing) : base(deserializing) { }
44    private SymbolicDataAnalysisExpressionLatexFormatter(SymbolicDataAnalysisExpressionLatexFormatter original, Cloner cloner)
45      : base(original, cloner) {
46      constants = new List<KeyValuePair<string, double>>(original.constants);
47      constIndex = original.constIndex;
48      currentLag = original.currentLag;
49      targetCount = original.targetCount;
50    }
51    public SymbolicDataAnalysisExpressionLatexFormatter()
52      : base() {
53      Name = ItemName;
54      Description = ItemDescription;
55      constants = new List<KeyValuePair<string, double>>();
56    }
57
58    public override IDeepCloneable Clone(Cloner cloner) {
59      return new SymbolicDataAnalysisExpressionLatexFormatter(this, cloner);
60    }
61
62    public string Format(ISymbolicExpressionTree symbolicExpressionTree) {
63      return Format(symbolicExpressionTree, null);
64    }
65    public string Format(ISymbolicExpressionTree symbolicExpressionTree, string targetVariable) {
66      try {
67        StringBuilder strBuilder = new StringBuilder();
68        constants.Clear();
69        constIndex = 0;
70        this.targetVariable = targetVariable;
71        containsTimeSeriesSymbol = symbolicExpressionTree.IterateNodesBreadth().Any(n => IsTimeSeriesSymbol(n.Symbol));
72        strBuilder.AppendLine(FormatRecursively(symbolicExpressionTree.Root));
73        return strBuilder.ToString();
74      } catch (NotImplementedException ex) {
75        return ex.Message + Environment.NewLine + ex.StackTrace;
76      }
77    }
78    static bool IsTimeSeriesSymbol(ISymbol s) {
79      return s is TimeLag || s is Integral || s is Derivative || s is LaggedVariable;
80    }
81
82    private string FormatRecursively(ISymbolicExpressionTreeNode node) {
83      StringBuilder strBuilder = new StringBuilder();
84      currentLag = 0;
85      FormatBegin(node, strBuilder);
86
87      if (node.SubtreeCount > 0) {
88        strBuilder.Append(FormatRecursively(node.GetSubtree(0)));
89      }
90      int i = 1;
91      foreach (var subTree in node.Subtrees.Skip(1)) {
92        FormatSep(node, strBuilder, i);
93        // format the whole subtree
94        strBuilder.Append(FormatRecursively(subTree));
95        i++;
96      }
97
98      FormatEnd(node, strBuilder);
99
100      return strBuilder.ToString();
101    }
102
103    private void FormatBegin(ISymbolicExpressionTreeNode node, StringBuilder strBuilder) {
104      if (node.Symbol is Addition) {
105        strBuilder.Append(@" \left( ");
106      } else if (node.Symbol is Subtraction) {
107        if (node.SubtreeCount == 1) {
108          strBuilder.Append(@"- \left( ");
109        } else {
110          strBuilder.Append(@" \left( ");
111        }
112      } else if (node.Symbol is Multiplication) {
113      } else if (node.Symbol is Division) {
114        if (node.SubtreeCount == 1) {
115          strBuilder.Append(@" \cfrac{1}{");
116        } else {
117          strBuilder.Append(@" \cfrac{ ");
118        }
119      } else if (node.Symbol is Average) {
120        // skip output of (1/1) if only one subtree
121        if (node.SubtreeCount > 1) {
122          strBuilder.Append(@" \cfrac{1}{" + node.SubtreeCount + @"}");
123        }
124        strBuilder.Append(@" \left( ");
125      } else if (node.Symbol is Logarithm) {
126        strBuilder.Append(@"\log \left( ");
127      } else if (node.Symbol is Exponential) {
128        strBuilder.Append(@"\exp \left( ");
129      } else if (node.Symbol is Square) {
130        strBuilder.Append(@"\left(");
131      } else if (node.Symbol is SquareRoot) {
132        strBuilder.Append(@"\sqrt{");
133      } else if (node.Symbol is Sine) {
134        strBuilder.Append(@"\sin \left( ");
135      } else if (node.Symbol is Cosine) {
136        strBuilder.Append(@"\cos \left( ");
137      } else if (node.Symbol is Tangent) {
138        strBuilder.Append(@"\tan \left( ");
139      } else if (node.Symbol is AiryA) {
140        strBuilder.Append(@"\operatorname{airy}_a \left( ");
141      } else if (node.Symbol is AiryB) {
142        strBuilder.Append(@"\operatorname{airy}_b \left( ");
143      } else if (node.Symbol is Bessel) {
144        strBuilder.Append(@"\operatorname{bessel}_1 \left( ");
145      } else if (node.Symbol is CosineIntegral) {
146        strBuilder.Append(@"\operatorname{cosInt} \left( ");
147      } else if (node.Symbol is Dawson) {
148        strBuilder.Append(@"\operatorname{dawson} \left( ");
149      } else if (node.Symbol is Erf) {
150        strBuilder.Append(@"\operatorname{erf} \left( ");
151      } else if (node.Symbol is ExponentialIntegralEi) {
152        strBuilder.Append(@"\operatorname{expInt}_i \left( ");
153      } else if (node.Symbol is FresnelCosineIntegral) {
154        strBuilder.Append(@"\operatorname{fresnel}_\operatorname{cosInt} \left( ");
155      } else if (node.Symbol is FresnelSineIntegral) {
156        strBuilder.Append(@"\operatorname{fresnel}_\operatorname{sinInt} \left( ");
157      } else if (node.Symbol is Gamma) {
158        strBuilder.Append(@"\Gamma \left( ");
159      } else if (node.Symbol is HyperbolicCosineIntegral) {
160        strBuilder.Append(@"\operatorname{hypCosInt} \left( ");
161      } else if (node.Symbol is HyperbolicSineIntegral) {
162        strBuilder.Append(@"\operatorname{hypSinInt} \left( ");
163      } else if (node.Symbol is Norm) {
164        strBuilder.Append(@"\operatorname{norm} \left( ");
165      } else if (node.Symbol is Psi) {
166        strBuilder.Append(@"\operatorname{digamma} \left( ");
167      } else if (node.Symbol is SineIntegral) {
168        strBuilder.Append(@"\operatorname{sinInt} \left( ");
169      } else if (node.Symbol is GreaterThan) {
170        strBuilder.Append(@"  \left( ");
171      } else if (node.Symbol is LessThan) {
172        strBuilder.Append(@"  \left( ");
173      } else if (node.Symbol is And) {
174        strBuilder.Append(@"  \left( \left( ");
175      } else if (node.Symbol is Or) {
176        strBuilder.Append(@"   \left( \left( ");
177      } else if (node.Symbol is Not) {
178        strBuilder.Append(@" \neg \left( ");
179      } else if (node.Symbol is IfThenElse) {
180        strBuilder.Append(@" \operatorname{if}  \left( ");
181      } else if (node.Symbol is Constant) {
182        var constName = "c_{" + constIndex + "}";
183        constIndex++;
184        var constNode = node as ConstantTreeNode;
185        if (constNode.Value.IsAlmost(1.0)) {
186          strBuilder.Append("1 ");
187        } else {
188          strBuilder.Append(constName);
189          constants.Add(new KeyValuePair<string, double>(constName, constNode.Value));
190        }
191
192      } else if (node.Symbol is FactorVariable) {
193        var factorNode = node as FactorVariableTreeNode;
194        var constName = "c_{" + constIndex + "}";
195        strBuilder.Append(constName + " ");
196        foreach (var e in factorNode.Symbol.GetVariableValues(factorNode.VariableName)
197          .Zip(factorNode.Weights, Tuple.Create)) {
198          constants.Add(new KeyValuePair<string, double>("c_{" + constIndex + ", " + EscapeLatexString(factorNode.VariableName) + "=" + EscapeLatexString(e.Item1) + "}", e.Item2));
199        }
200        constIndex++;
201      } else if (node.Symbol is BinaryFactorVariable) {
202        var binFactorNode = node as BinaryFactorVariableTreeNode;
203        if (!binFactorNode.Weight.IsAlmost((1.0))) {
204          var constName = "c_{" + constIndex + "}";
205          strBuilder.Append(constName + "  \\cdot");
206          constants.Add(new KeyValuePair<string, double>(constName, binFactorNode.Weight));
207          constIndex++;
208        }
209        strBuilder.Append("(" + EscapeLatexString(binFactorNode.VariableName));
210        strBuilder.Append(LagToString(currentLag));
211        strBuilder.Append(" = " + EscapeLatexString(binFactorNode.VariableValue) + " )");
212      } else if (node.Symbol is LaggedVariable) {
213        var laggedVarNode = node as LaggedVariableTreeNode;
214        if (!laggedVarNode.Weight.IsAlmost(1.0)) {
215          var constName = "c_{" + constIndex + "}";
216          strBuilder.Append(constName + "  \\cdot");
217          constants.Add(new KeyValuePair<string, double>(constName, laggedVarNode.Weight));
218          constIndex++;
219        }
220        strBuilder.Append(EscapeLatexString(laggedVarNode.VariableName));
221        strBuilder.Append(LagToString(currentLag + laggedVarNode.Lag));
222
223      } else if (node.Symbol is Variable) {
224        var varNode = node as VariableTreeNode;
225        if (!varNode.Weight.IsAlmost((1.0))) {
226          var constName = "c_{" + constIndex + "}";
227          strBuilder.Append(constName + "  \\cdot");
228          constants.Add(new KeyValuePair<string, double>(constName, varNode.Weight));
229          constIndex++;
230        }
231        strBuilder.Append(EscapeLatexString(varNode.VariableName));
232        strBuilder.Append(LagToString(currentLag));
233      } else if (node.Symbol is ProgramRootSymbol) {
234        strBuilder
235          .AppendLine("\\begin{align*}")
236          .AppendLine("\\nonumber");
237      } else if (node.Symbol is Defun) {
238        var defunNode = node as DefunTreeNode;
239        strBuilder.Append(defunNode.FunctionName + " & = ");
240      } else if (node.Symbol is InvokeFunction) {
241        var invokeNode = node as InvokeFunctionTreeNode;
242        strBuilder.Append(invokeNode.Symbol.FunctionName + @" \left( ");
243      } else if (node.Symbol is StartSymbol) {
244        FormatStartSymbol(strBuilder);
245      } else if (node.Symbol is Argument) {
246        var argSym = node.Symbol as Argument;
247        strBuilder.Append(" ARG+" + argSym.ArgumentIndex + " ");
248      } else if (node.Symbol is Derivative) {
249        strBuilder.Append(@" \cfrac{d \left( ");
250      } else if (node.Symbol is TimeLag) {
251        var laggedNode = node as ILaggedTreeNode;
252        currentLag += laggedNode.Lag;
253      } else if (node.Symbol is Power) {
254        strBuilder.Append(@" \left( ");
255      } else if (node.Symbol is Root) {
256        strBuilder.Append(@" \left( ");
257      } else if (node.Symbol is Integral) {
258        // actually a new variable for t is needed in all subtrees (TODO)
259        var laggedTreeNode = node as ILaggedTreeNode;
260        strBuilder.Append(@"\sum_{t=" + (laggedTreeNode.Lag + currentLag) + @"}^0 \left( ");
261      } else if (node.Symbol is VariableCondition) {
262        var conditionTreeNode = node as VariableConditionTreeNode;
263        var constName = "c_{" + constants.Count + "}";
264        string p = @"1 /  1 + \exp  - " + constName + " ";
265        constants.Add(new KeyValuePair<string, double>(constName, conditionTreeNode.Slope));
266        constIndex++;
267        var const2Name = "c_{" + constants.Count + @"}";
268        p += @" \cdot " + EscapeLatexString(conditionTreeNode.VariableName) + LagToString(currentLag) + " - " + const2Name + "   ";
269        constants.Add(new KeyValuePair<string, double>(const2Name, conditionTreeNode.Threshold));
270        constIndex++;
271        strBuilder.Append(@" \left( " + p + @"\cdot ");
272      } else {
273        throw new NotImplementedException("Export of " + node.Symbol + " is not implemented.");
274      }
275    }
276
277    private void FormatSep(ISymbolicExpressionTreeNode node, StringBuilder strBuilder, int step) {
278      if (node.Symbol is Addition) {
279        strBuilder.Append(" + ");
280      } else if (node.Symbol is Subtraction) {
281        strBuilder.Append(" - ");
282      } else if (node.Symbol is Multiplication) {
283        strBuilder.Append(@" \cdot ");
284      } else if (node.Symbol is Division) {
285        if (step + 1 == node.SubtreeCount)
286          strBuilder.Append(@"}{");
287        else
288          strBuilder.Append(@" }{ \cfrac{ ");
289      } else if (node.Symbol is Average) {
290        strBuilder.Append(@" + ");
291      } else if (node.Symbol is Logarithm) {
292        throw new InvalidOperationException();
293      } else if (node.Symbol is Exponential) {
294        throw new InvalidOperationException();
295      } else if (node.Symbol is Square) {
296        throw new InvalidOperationException();
297      } else if (node.Symbol is SquareRoot) {
298        throw new InvalidOperationException();
299      } else if (node.Symbol is Sine) {
300        throw new InvalidOperationException();
301      } else if (node.Symbol is Cosine) {
302        throw new InvalidOperationException();
303      } else if (node.Symbol is Tangent) {
304        throw new InvalidOperationException();
305      } else if (node.Symbol is AiryA) {
306        throw new InvalidOperationException();
307      } else if (node.Symbol is AiryB) {
308        throw new InvalidOperationException();
309      } else if (node.Symbol is Bessel) {
310        throw new InvalidOperationException();
311      } else if (node.Symbol is CosineIntegral) {
312        throw new InvalidOperationException();
313      } else if (node.Symbol is Dawson) {
314        throw new InvalidOperationException();
315      } else if (node.Symbol is Erf) {
316        throw new InvalidOperationException();
317      } else if (node.Symbol is ExponentialIntegralEi) {
318        throw new InvalidOperationException();
319      } else if (node.Symbol is FresnelCosineIntegral) {
320        throw new InvalidOperationException();
321      } else if (node.Symbol is FresnelSineIntegral) {
322        throw new InvalidOperationException();
323      } else if (node.Symbol is Gamma) {
324        throw new InvalidOperationException();
325      } else if (node.Symbol is HyperbolicCosineIntegral) {
326        throw new InvalidOperationException();
327      } else if (node.Symbol is HyperbolicSineIntegral) {
328        throw new InvalidOperationException();
329      } else if (node.Symbol is Norm) {
330        throw new InvalidOperationException();
331      } else if (node.Symbol is Psi) {
332        throw new InvalidOperationException();
333      } else if (node.Symbol is SineIntegral) {
334        throw new InvalidOperationException();
335      } else if (node.Symbol is GreaterThan) {
336        strBuilder.Append(@" > ");
337      } else if (node.Symbol is LessThan) {
338        strBuilder.Append(@" < ");
339      } else if (node.Symbol is And) {
340        strBuilder.Append(@" > 0  \right) \land \left(");
341      } else if (node.Symbol is Or) {
342        strBuilder.Append(@" > 0  \right) \lor \left(");
343      } else if (node.Symbol is Not) {
344        throw new InvalidOperationException();
345      } else if (node.Symbol is IfThenElse) {
346        strBuilder.Append(@" , ");
347      } else if (node.Symbol is ProgramRootSymbol) {
348        strBuilder.Append(@"\\" + Environment.NewLine);
349      } else if (node.Symbol is Defun) {
350      } else if (node.Symbol is InvokeFunction) {
351        strBuilder.Append(" , ");
352      } else if (node.Symbol is StartSymbol) {
353        strBuilder.Append(@"\\" + Environment.NewLine);
354        FormatStartSymbol(strBuilder);
355      } else if (node.Symbol is Power) {
356        strBuilder.Append(@"\right) ^ { \operatorname{round} \left(");
357      } else if (node.Symbol is Root) {
358        strBuilder.Append(@"\right) ^ {  \cfrac{1}{ \operatorname{round} \left(");
359      } else if (node.Symbol is VariableCondition) {
360        var conditionTreeNode = node as VariableConditionTreeNode;
361        var const1Name = "c_{" + constants.Count + "}";
362        string p = @"1 / \left( 1 + \exp \left( - " + const1Name + " ";
363        constants.Add(new KeyValuePair<string, double>(const1Name, conditionTreeNode.Slope));
364        constIndex++;
365        var const2Name = "c_{" + constants.Count + "}";
366        p += @" \cdot " + EscapeLatexString(conditionTreeNode.VariableName) + LagToString(currentLag) + " - " + const2Name + " \right) \right) \right)   ";
367        constants.Add(new KeyValuePair<string, double>(const2Name, conditionTreeNode.Threshold));
368        constIndex++;
369        strBuilder.Append(@" +  \left( 1 - " + p + @" \right) \cdot ");
370      } else {
371        throw new NotImplementedException("Export of " + node.Symbol + " is not implemented.");
372      }
373    }
374
375    private void FormatEnd(ISymbolicExpressionTreeNode node, StringBuilder strBuilder) {
376      if (node.Symbol is Addition) {
377        strBuilder.Append(@" \right) ");
378      } else if (node.Symbol is Subtraction) {
379        strBuilder.Append(@" \right) ");
380      } else if (node.Symbol is Multiplication) {
381      } else if (node.Symbol is Division) {
382        strBuilder.Append(" } ");
383        for (int i = 2; i < node.SubtreeCount; i++)
384          strBuilder.Append(" } ");
385      } else if (node.Symbol is Average) {
386        strBuilder.Append(@" \right) ");
387      } else if (node.Symbol is Logarithm) {
388        strBuilder.Append(@" \right) ");
389      } else if (node.Symbol is Exponential) {
390        strBuilder.Append(@" \right) ");
391      } else if (node.Symbol is Square) {
392        strBuilder.Append(@"\right)^2");
393      } else if (node.Symbol is SquareRoot) {
394        strBuilder.Append(@"}");
395      } else if (node.Symbol is Sine) {
396        strBuilder.Append(@" \right) ");
397      } else if (node.Symbol is Cosine) {
398        strBuilder.Append(@" \right) ");
399      } else if (node.Symbol is Tangent) {
400        strBuilder.Append(@" \right) ");
401      } else if (node.Symbol is AiryA) {
402        strBuilder.Append(@" \right) ");
403      } else if (node.Symbol is AiryB) {
404        strBuilder.Append(@" \right) ");
405      } else if (node.Symbol is Bessel) {
406        strBuilder.Append(@" \right) ");
407      } else if (node.Symbol is CosineIntegral) {
408        strBuilder.Append(@" \right) ");
409      } else if (node.Symbol is Dawson) {
410        strBuilder.Append(@" \right) ");
411      } else if (node.Symbol is Erf) {
412        strBuilder.Append(@" \right) ");
413      } else if (node.Symbol is ExponentialIntegralEi) {
414        strBuilder.Append(@" \right) ");
415      } else if (node.Symbol is FresnelCosineIntegral) {
416        strBuilder.Append(@" \right) ");
417      } else if (node.Symbol is FresnelSineIntegral) {
418        strBuilder.Append(@" \right) ");
419      } else if (node.Symbol is Gamma) {
420        strBuilder.Append(@" \right) ");
421      } else if (node.Symbol is HyperbolicCosineIntegral) {
422        strBuilder.Append(@" \right) ");
423      } else if (node.Symbol is HyperbolicSineIntegral) {
424        strBuilder.Append(@" \right) ");
425      } else if (node.Symbol is Norm) {
426        strBuilder.Append(@" \right) ");
427      } else if (node.Symbol is Psi) {
428        strBuilder.Append(@" \right) ");
429      } else if (node.Symbol is SineIntegral) {
430        strBuilder.Append(@" \right) ");
431      } else if (node.Symbol is GreaterThan) {
432        strBuilder.Append(@" \right) ");
433      } else if (node.Symbol is LessThan) {
434        strBuilder.Append(@" \right) ");
435      } else if (node.Symbol is And) {
436        strBuilder.Append(@" > 0 \right) \right) ");
437      } else if (node.Symbol is Or) {
438        strBuilder.Append(@" > 0 \right) \right) ");
439      } else if (node.Symbol is Not) {
440        strBuilder.Append(@" \right) ");
441      } else if (node.Symbol is IfThenElse) {
442        strBuilder.Append(@" \right) ");
443      } else if (node.Symbol is Constant) {
444      } else if (node.Symbol is LaggedVariable) {
445      } else if (node.Symbol is Variable) {
446      } else if (node.Symbol is FactorVariable) {
447      } else if (node.Symbol is BinaryFactorVariable) {
448      } else if (node.Symbol is ProgramRootSymbol) {
449        strBuilder
450          .AppendLine("\\end{align*}")
451          .AppendLine("\\begin{align*}")
452          .AppendLine("\\nonumber");
453        // output all constant values
454        if (constants.Count > 0) {
455          foreach (var constant in constants) {
456            // replace "." with ".&" to align decimal points
457            var constStr = string.Format(System.Globalization.NumberFormatInfo.InvariantInfo, "{0:G5}", constant.Value);
458            if (!constStr.Contains(".")) constStr = constStr + ".0";
459            constStr = constStr.Replace(".", "&.");  // fix problem in rendering of aligned expressions
460            strBuilder.Append(constant.Key + "& = & " + constStr);
461            strBuilder.Append(@"\\");
462          }
463        }
464        strBuilder.AppendLine("\\end{align*}");
465      } else if (node.Symbol is Defun) {
466      } else if (node.Symbol is InvokeFunction) {
467        strBuilder.Append(@" \right) ");
468      } else if (node.Symbol is StartSymbol) {
469      } else if (node.Symbol is Argument) {
470      } else if (node.Symbol is Derivative) {
471        strBuilder.Append(@" \right) }{dt} ");
472      } else if (node.Symbol is TimeLag) {
473        var laggedNode = node as ILaggedTreeNode;
474        currentLag -= laggedNode.Lag;
475      } else if (node.Symbol is Power) {
476        strBuilder.Append(@" \right) } ");
477      } else if (node.Symbol is Root) {
478        strBuilder.Append(@" \right) } } ");
479      } else if (node.Symbol is Integral) {
480        strBuilder.Append(@" \right) ");
481      } else if (node.Symbol is VariableCondition) {
482        strBuilder.Append(@"\right) ");
483      } else {
484        throw new NotImplementedException("Export of " + node.Symbol + " is not implemented.");
485      }
486    }
487
488    private void FormatStartSymbol(StringBuilder strBuilder) {
489      strBuilder.Append(targetVariable ?? "target_" + (targetCount++));
490      if (containsTimeSeriesSymbol)
491        strBuilder.Append("(t)");
492      strBuilder.Append(" & = ");
493    }
494
495    private string LagToString(int lag) {
496      if (lag < 0) {
497        return "(t" + lag + ")";
498      } else if (lag > 0) {
499        return "(t+" + lag + ")";
500      } else return "";
501    }
502
503    private string EscapeLatexString(string s) {
504      return "\\text{" +
505        s
506         .Replace("\\", "\\\\")
507         .Replace("{", "\\{")
508         .Replace("}", "\\}")
509        + "}";
510    }
511  }
512}
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