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source: branches/crossvalidation-2434/HeuristicLab.Problems.DataAnalysis.Symbolic.Regression/3.4/SingleObjective/Evaluators/SymbolicRegressionConstantOptimizationEvaluator.cs @ 14029

Last change on this file since 14029 was 14029, checked in by gkronber, 8 years ago

#2434: merged trunk changes r12934:14026 from trunk to branch

File size: 23.5 KB
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1#region License Information
2/* HeuristicLab
3 * Copyright (C) 2002-2015 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 AutoDiff;
26using HeuristicLab.Common;
27using HeuristicLab.Core;
28using HeuristicLab.Data;
29using HeuristicLab.Encodings.SymbolicExpressionTreeEncoding;
30using HeuristicLab.Parameters;
31using HeuristicLab.Persistence.Default.CompositeSerializers.Storable;
32
33namespace HeuristicLab.Problems.DataAnalysis.Symbolic.Regression {
34  [Item("Constant Optimization Evaluator", "Calculates Pearson R² of a symbolic regression solution and optimizes the constant used.")]
35  [StorableClass]
36  public class SymbolicRegressionConstantOptimizationEvaluator : SymbolicRegressionSingleObjectiveEvaluator {
37    private const string ConstantOptimizationIterationsParameterName = "ConstantOptimizationIterations";
38    private const string ConstantOptimizationImprovementParameterName = "ConstantOptimizationImprovement";
39    private const string ConstantOptimizationProbabilityParameterName = "ConstantOptimizationProbability";
40    private const string ConstantOptimizationRowsPercentageParameterName = "ConstantOptimizationRowsPercentage";
41    private const string UpdateConstantsInTreeParameterName = "UpdateConstantsInSymbolicExpressionTree";
42    private const string UpdateVariableWeightsParameterName = "Update Variable Weights";
43
44    public IFixedValueParameter<IntValue> ConstantOptimizationIterationsParameter {
45      get { return (IFixedValueParameter<IntValue>)Parameters[ConstantOptimizationIterationsParameterName]; }
46    }
47    public IFixedValueParameter<DoubleValue> ConstantOptimizationImprovementParameter {
48      get { return (IFixedValueParameter<DoubleValue>)Parameters[ConstantOptimizationImprovementParameterName]; }
49    }
50    public IFixedValueParameter<PercentValue> ConstantOptimizationProbabilityParameter {
51      get { return (IFixedValueParameter<PercentValue>)Parameters[ConstantOptimizationProbabilityParameterName]; }
52    }
53    public IFixedValueParameter<PercentValue> ConstantOptimizationRowsPercentageParameter {
54      get { return (IFixedValueParameter<PercentValue>)Parameters[ConstantOptimizationRowsPercentageParameterName]; }
55    }
56    public IFixedValueParameter<BoolValue> UpdateConstantsInTreeParameter {
57      get { return (IFixedValueParameter<BoolValue>)Parameters[UpdateConstantsInTreeParameterName]; }
58    }
59    public IFixedValueParameter<BoolValue> UpdateVariableWeightsParameter {
60      get { return (IFixedValueParameter<BoolValue>)Parameters[UpdateVariableWeightsParameterName]; }
61    }
62
63
64    public IntValue ConstantOptimizationIterations {
65      get { return ConstantOptimizationIterationsParameter.Value; }
66    }
67    public DoubleValue ConstantOptimizationImprovement {
68      get { return ConstantOptimizationImprovementParameter.Value; }
69    }
70    public PercentValue ConstantOptimizationProbability {
71      get { return ConstantOptimizationProbabilityParameter.Value; }
72    }
73    public PercentValue ConstantOptimizationRowsPercentage {
74      get { return ConstantOptimizationRowsPercentageParameter.Value; }
75    }
76    public bool UpdateConstantsInTree {
77      get { return UpdateConstantsInTreeParameter.Value.Value; }
78      set { UpdateConstantsInTreeParameter.Value.Value = value; }
79    }
80
81    public bool UpdateVariableWeights {
82      get { return UpdateVariableWeightsParameter.Value.Value; }
83      set { UpdateVariableWeightsParameter.Value.Value = value; }
84    }
85
86    public override bool Maximization {
87      get { return true; }
88    }
89
90    [StorableConstructor]
91    protected SymbolicRegressionConstantOptimizationEvaluator(bool deserializing) : base(deserializing) { }
92    protected SymbolicRegressionConstantOptimizationEvaluator(SymbolicRegressionConstantOptimizationEvaluator original, Cloner cloner)
93      : base(original, cloner) {
94    }
95    public SymbolicRegressionConstantOptimizationEvaluator()
96      : base() {
97      Parameters.Add(new FixedValueParameter<IntValue>(ConstantOptimizationIterationsParameterName, "Determines how many iterations should be calculated while optimizing the constant of a symbolic expression tree (0 indicates other or default stopping criterion).", new IntValue(10), true));
98      Parameters.Add(new FixedValueParameter<DoubleValue>(ConstantOptimizationImprovementParameterName, "Determines the relative improvement which must be achieved in the constant optimization to continue with it (0 indicates other or default stopping criterion).", new DoubleValue(0), true) { Hidden = true });
99      Parameters.Add(new FixedValueParameter<PercentValue>(ConstantOptimizationProbabilityParameterName, "Determines the probability that the constants are optimized", new PercentValue(1), true));
100      Parameters.Add(new FixedValueParameter<PercentValue>(ConstantOptimizationRowsPercentageParameterName, "Determines the percentage of the rows which should be used for constant optimization", new PercentValue(1), true));
101      Parameters.Add(new FixedValueParameter<BoolValue>(UpdateConstantsInTreeParameterName, "Determines if the constants in the tree should be overwritten by the optimized constants.", new BoolValue(true)) { Hidden = true });
102      Parameters.Add(new FixedValueParameter<BoolValue>(UpdateVariableWeightsParameterName, "Determines if the variable weights in the tree should be  optimized.", new BoolValue(true)) { Hidden = true });
103    }
104
105    public override IDeepCloneable Clone(Cloner cloner) {
106      return new SymbolicRegressionConstantOptimizationEvaluator(this, cloner);
107    }
108
109    [StorableHook(HookType.AfterDeserialization)]
110    private void AfterDeserialization() {
111      if (!Parameters.ContainsKey(UpdateConstantsInTreeParameterName))
112        Parameters.Add(new FixedValueParameter<BoolValue>(UpdateConstantsInTreeParameterName, "Determines if the constants in the tree should be overwritten by the optimized constants.", new BoolValue(true)));
113      if (!Parameters.ContainsKey(UpdateVariableWeightsParameterName))
114        Parameters.Add(new FixedValueParameter<BoolValue>(UpdateVariableWeightsParameterName, "Determines if the variable weights in the tree should be  optimized.", new BoolValue(true)));
115    }
116
117    public override IOperation InstrumentedApply() {
118      var solution = SymbolicExpressionTreeParameter.ActualValue;
119      double quality;
120      if (RandomParameter.ActualValue.NextDouble() < ConstantOptimizationProbability.Value) {
121        IEnumerable<int> constantOptimizationRows = GenerateRowsToEvaluate(ConstantOptimizationRowsPercentage.Value);
122        quality = OptimizeConstants(SymbolicDataAnalysisTreeInterpreterParameter.ActualValue, solution, ProblemDataParameter.ActualValue,
123           constantOptimizationRows, ApplyLinearScalingParameter.ActualValue.Value, ConstantOptimizationIterations.Value, updateVariableWeights: UpdateVariableWeights, lowerEstimationLimit: EstimationLimitsParameter.ActualValue.Lower, upperEstimationLimit: EstimationLimitsParameter.ActualValue.Upper, updateConstantsInTree: UpdateConstantsInTree);
124
125        if (ConstantOptimizationRowsPercentage.Value != RelativeNumberOfEvaluatedSamplesParameter.ActualValue.Value) {
126          var evaluationRows = GenerateRowsToEvaluate();
127          quality = SymbolicRegressionSingleObjectivePearsonRSquaredEvaluator.Calculate(SymbolicDataAnalysisTreeInterpreterParameter.ActualValue, solution, EstimationLimitsParameter.ActualValue.Lower, EstimationLimitsParameter.ActualValue.Upper, ProblemDataParameter.ActualValue, evaluationRows, ApplyLinearScalingParameter.ActualValue.Value);
128        }
129      } else {
130        var evaluationRows = GenerateRowsToEvaluate();
131        quality = SymbolicRegressionSingleObjectivePearsonRSquaredEvaluator.Calculate(SymbolicDataAnalysisTreeInterpreterParameter.ActualValue, solution, EstimationLimitsParameter.ActualValue.Lower, EstimationLimitsParameter.ActualValue.Upper, ProblemDataParameter.ActualValue, evaluationRows, ApplyLinearScalingParameter.ActualValue.Value);
132      }
133      QualityParameter.ActualValue = new DoubleValue(quality);
134
135      return base.InstrumentedApply();
136    }
137
138    public override double Evaluate(IExecutionContext context, ISymbolicExpressionTree tree, IRegressionProblemData problemData, IEnumerable<int> rows) {
139      SymbolicDataAnalysisTreeInterpreterParameter.ExecutionContext = context;
140      EstimationLimitsParameter.ExecutionContext = context;
141      ApplyLinearScalingParameter.ExecutionContext = context;
142
143      // Pearson R² evaluator is used on purpose instead of the const-opt evaluator,
144      // because Evaluate() is used to get the quality of evolved models on
145      // different partitions of the dataset (e.g., best validation model)
146      double r2 = SymbolicRegressionSingleObjectivePearsonRSquaredEvaluator.Calculate(SymbolicDataAnalysisTreeInterpreterParameter.ActualValue, tree, EstimationLimitsParameter.ActualValue.Lower, EstimationLimitsParameter.ActualValue.Upper, problemData, rows, ApplyLinearScalingParameter.ActualValue.Value);
147
148      SymbolicDataAnalysisTreeInterpreterParameter.ExecutionContext = null;
149      EstimationLimitsParameter.ExecutionContext = null;
150      ApplyLinearScalingParameter.ExecutionContext = null;
151
152      return r2;
153    }
154
155    #region derivations of functions
156    // create function factory for arctangent
157    private readonly Func<Term, UnaryFunc> arctan = UnaryFunc.Factory(
158      eval: Math.Atan,
159      diff: x => 1 / (1 + x * x));
160    private static readonly Func<Term, UnaryFunc> sin = UnaryFunc.Factory(
161      eval: Math.Sin,
162      diff: Math.Cos);
163    private static readonly Func<Term, UnaryFunc> cos = UnaryFunc.Factory(
164       eval: Math.Cos,
165       diff: x => -Math.Sin(x));
166    private static readonly Func<Term, UnaryFunc> tan = UnaryFunc.Factory(
167      eval: Math.Tan,
168      diff: x => 1 + Math.Tan(x) * Math.Tan(x));
169    private static readonly Func<Term, UnaryFunc> erf = UnaryFunc.Factory(
170      eval: alglib.errorfunction,
171      diff: x => 2.0 * Math.Exp(-(x * x)) / Math.Sqrt(Math.PI));
172    private static readonly Func<Term, UnaryFunc> norm = UnaryFunc.Factory(
173      eval: alglib.normaldistribution,
174      diff: x => -(Math.Exp(-(x * x)) * Math.Sqrt(Math.Exp(x * x)) * x) / Math.Sqrt(2 * Math.PI));
175    #endregion
176
177
178    public static double OptimizeConstants(ISymbolicDataAnalysisExpressionTreeInterpreter interpreter, ISymbolicExpressionTree tree, IRegressionProblemData problemData, IEnumerable<int> rows, bool applyLinearScaling, int maxIterations, bool updateVariableWeights = true, double lowerEstimationLimit = double.MinValue, double upperEstimationLimit = double.MaxValue, bool updateConstantsInTree = true) {
179
180      List<AutoDiff.Variable> variables = new List<AutoDiff.Variable>();
181      List<AutoDiff.Variable> parameters = new List<AutoDiff.Variable>();
182      List<string> variableNames = new List<string>();
183
184      AutoDiff.Term func;
185      if (!TryTransformToAutoDiff(tree.Root.GetSubtree(0), variables, parameters, variableNames, updateVariableWeights, out func))
186        throw new NotSupportedException("Could not optimize constants of symbolic expression tree due to not supported symbols used in the tree.");
187      if (variableNames.Count == 0) return 0.0;
188
189      AutoDiff.IParametricCompiledTerm compiledFunc = func.Compile(variables.ToArray(), parameters.ToArray());
190
191      List<SymbolicExpressionTreeTerminalNode> terminalNodes = null;
192      if (updateVariableWeights)
193        terminalNodes = tree.Root.IterateNodesPrefix().OfType<SymbolicExpressionTreeTerminalNode>().ToList();
194      else
195        terminalNodes = new List<SymbolicExpressionTreeTerminalNode>(tree.Root.IterateNodesPrefix().OfType<ConstantTreeNode>());
196
197      //extract inital constants
198      double[] c = new double[variables.Count];
199      {
200        c[0] = 0.0;
201        c[1] = 1.0;
202        int i = 2;
203        foreach (var node in terminalNodes) {
204          ConstantTreeNode constantTreeNode = node as ConstantTreeNode;
205          VariableTreeNode variableTreeNode = node as VariableTreeNode;
206          if (constantTreeNode != null)
207            c[i++] = constantTreeNode.Value;
208          else if (updateVariableWeights && variableTreeNode != null)
209            c[i++] = variableTreeNode.Weight;
210        }
211      }
212      double[] originalConstants = (double[])c.Clone();
213      double originalQuality = SymbolicRegressionSingleObjectivePearsonRSquaredEvaluator.Calculate(interpreter, tree, lowerEstimationLimit, upperEstimationLimit, problemData, rows, applyLinearScaling);
214
215      alglib.lsfitstate state;
216      alglib.lsfitreport rep;
217      int info;
218
219      IDataset ds = problemData.Dataset;
220      double[,] x = new double[rows.Count(), variableNames.Count];
221      int row = 0;
222      foreach (var r in rows) {
223        for (int col = 0; col < variableNames.Count; col++) {
224          x[row, col] = ds.GetDoubleValue(variableNames[col], r);
225        }
226        row++;
227      }
228      double[] y = ds.GetDoubleValues(problemData.TargetVariable, rows).ToArray();
229      int n = x.GetLength(0);
230      int m = x.GetLength(1);
231      int k = c.Length;
232
233      alglib.ndimensional_pfunc function_cx_1_func = CreatePFunc(compiledFunc);
234      alglib.ndimensional_pgrad function_cx_1_grad = CreatePGrad(compiledFunc);
235
236      try {
237        alglib.lsfitcreatefg(x, y, c, n, m, k, false, out state);
238        alglib.lsfitsetcond(state, 0.0, 0.0, maxIterations);
239        //alglib.lsfitsetgradientcheck(state, 0.001);
240        alglib.lsfitfit(state, function_cx_1_func, function_cx_1_grad, null, null);
241        alglib.lsfitresults(state, out info, out c, out rep);
242      }
243      catch (ArithmeticException) {
244        return originalQuality;
245      }
246      catch (alglib.alglibexception) {
247        return originalQuality;
248      }
249
250      //info == -7  => constant optimization failed due to wrong gradient
251      if (info != -7) UpdateConstants(tree, c.Skip(2).ToArray(), updateVariableWeights);
252      var quality = SymbolicRegressionSingleObjectivePearsonRSquaredEvaluator.Calculate(interpreter, tree, lowerEstimationLimit, upperEstimationLimit, problemData, rows, applyLinearScaling);
253
254      if (!updateConstantsInTree) UpdateConstants(tree, originalConstants.Skip(2).ToArray(), updateVariableWeights);
255      if (originalQuality - quality > 0.001 || double.IsNaN(quality)) {
256        UpdateConstants(tree, originalConstants.Skip(2).ToArray(), updateVariableWeights);
257        return originalQuality;
258      }
259      return quality;
260    }
261
262    private static void UpdateConstants(ISymbolicExpressionTree tree, double[] constants, bool updateVariableWeights) {
263      int i = 0;
264      foreach (var node in tree.Root.IterateNodesPrefix().OfType<SymbolicExpressionTreeTerminalNode>()) {
265        ConstantTreeNode constantTreeNode = node as ConstantTreeNode;
266        VariableTreeNode variableTreeNode = node as VariableTreeNode;
267        if (constantTreeNode != null)
268          constantTreeNode.Value = constants[i++];
269        else if (updateVariableWeights && variableTreeNode != null)
270          variableTreeNode.Weight = constants[i++];
271      }
272    }
273
274    private static alglib.ndimensional_pfunc CreatePFunc(AutoDiff.IParametricCompiledTerm compiledFunc) {
275      return (double[] c, double[] x, ref double func, object o) => {
276        func = compiledFunc.Evaluate(c, x);
277      };
278    }
279
280    private static alglib.ndimensional_pgrad CreatePGrad(AutoDiff.IParametricCompiledTerm compiledFunc) {
281      return (double[] c, double[] x, ref double func, double[] grad, object o) => {
282        var tupel = compiledFunc.Differentiate(c, x);
283        func = tupel.Item2;
284        Array.Copy(tupel.Item1, grad, grad.Length);
285      };
286    }
287
288    private static bool TryTransformToAutoDiff(ISymbolicExpressionTreeNode node, List<AutoDiff.Variable> variables, List<AutoDiff.Variable> parameters, List<string> variableNames, bool updateVariableWeights, out AutoDiff.Term term) {
289      if (node.Symbol is Constant) {
290        var var = new AutoDiff.Variable();
291        variables.Add(var);
292        term = var;
293        return true;
294      }
295      if (node.Symbol is Variable) {
296        var varNode = node as VariableTreeNode;
297        var par = new AutoDiff.Variable();
298        parameters.Add(par);
299        variableNames.Add(varNode.VariableName);
300
301        if (updateVariableWeights) {
302          var w = new AutoDiff.Variable();
303          variables.Add(w);
304          term = AutoDiff.TermBuilder.Product(w, par);
305        } else {
306          term = par;
307        }
308        return true;
309      }
310      if (node.Symbol is Addition) {
311        List<AutoDiff.Term> terms = new List<Term>();
312        foreach (var subTree in node.Subtrees) {
313          AutoDiff.Term t;
314          if (!TryTransformToAutoDiff(subTree, variables, parameters, variableNames, updateVariableWeights, out t)) {
315            term = null;
316            return false;
317          }
318          terms.Add(t);
319        }
320        term = AutoDiff.TermBuilder.Sum(terms);
321        return true;
322      }
323      if (node.Symbol is Subtraction) {
324        List<AutoDiff.Term> terms = new List<Term>();
325        for (int i = 0; i < node.SubtreeCount; i++) {
326          AutoDiff.Term t;
327          if (!TryTransformToAutoDiff(node.GetSubtree(i), variables, parameters, variableNames, updateVariableWeights, out t)) {
328            term = null;
329            return false;
330          }
331          if (i > 0) t = -t;
332          terms.Add(t);
333        }
334        term = AutoDiff.TermBuilder.Sum(terms);
335        return true;
336      }
337      if (node.Symbol is Multiplication) {
338        List<AutoDiff.Term> terms = new List<Term>();
339        foreach (var subTree in node.Subtrees) {
340          AutoDiff.Term t;
341          if (!TryTransformToAutoDiff(subTree, variables, parameters, variableNames, updateVariableWeights, out t)) {
342            term = null;
343            return false;
344          }
345          terms.Add(t);
346        }
347        if (terms.Count == 1) term = terms[0];
348        else term = terms.Aggregate((a, b) => new AutoDiff.Product(a, b));
349        return true;
350
351      }
352      if (node.Symbol is Division) {
353        List<AutoDiff.Term> terms = new List<Term>();
354        foreach (var subTree in node.Subtrees) {
355          AutoDiff.Term t;
356          if (!TryTransformToAutoDiff(subTree, variables, parameters, variableNames, updateVariableWeights, out t)) {
357            term = null;
358            return false;
359          }
360          terms.Add(t);
361        }
362        if (terms.Count == 1) term = 1.0 / terms[0];
363        else term = terms.Aggregate((a, b) => new AutoDiff.Product(a, 1.0 / b));
364        return true;
365      }
366      if (node.Symbol is Logarithm) {
367        AutoDiff.Term t;
368        if (!TryTransformToAutoDiff(node.GetSubtree(0), variables, parameters, variableNames, updateVariableWeights, out t)) {
369          term = null;
370          return false;
371        } else {
372          term = AutoDiff.TermBuilder.Log(t);
373          return true;
374        }
375      }
376      if (node.Symbol is Exponential) {
377        AutoDiff.Term t;
378        if (!TryTransformToAutoDiff(node.GetSubtree(0), variables, parameters, variableNames, updateVariableWeights, out t)) {
379          term = null;
380          return false;
381        } else {
382          term = AutoDiff.TermBuilder.Exp(t);
383          return true;
384        }
385      }
386      if (node.Symbol is Square) {
387        AutoDiff.Term t;
388        if (!TryTransformToAutoDiff(node.GetSubtree(0), variables, parameters, variableNames, updateVariableWeights, out t)) {
389          term = null;
390          return false;
391        } else {
392          term = AutoDiff.TermBuilder.Power(t, 2.0);
393          return true;
394        }
395      }
396      if (node.Symbol is SquareRoot) {
397        AutoDiff.Term t;
398        if (!TryTransformToAutoDiff(node.GetSubtree(0), variables, parameters, variableNames, updateVariableWeights, out t)) {
399          term = null;
400          return false;
401        } else {
402          term = AutoDiff.TermBuilder.Power(t, 0.5);
403          return true;
404        }
405      }
406      if (node.Symbol is Sine) {
407        AutoDiff.Term t;
408        if (!TryTransformToAutoDiff(node.GetSubtree(0), variables, parameters, variableNames, updateVariableWeights, out t)) {
409          term = null;
410          return false;
411        } else {
412          term = sin(t);
413          return true;
414        }
415      }
416      if (node.Symbol is Cosine) {
417        AutoDiff.Term t;
418        if (!TryTransformToAutoDiff(node.GetSubtree(0), variables, parameters, variableNames, updateVariableWeights, out t)) {
419          term = null;
420          return false;
421        } else {
422          term = cos(t);
423          return true;
424        }
425      }
426      if (node.Symbol is Tangent) {
427        AutoDiff.Term t;
428        if (!TryTransformToAutoDiff(node.GetSubtree(0), variables, parameters, variableNames, updateVariableWeights, out t)) {
429          term = null;
430          return false;
431        } else {
432          term = tan(t);
433          return true;
434        }
435      }
436      if (node.Symbol is Erf) {
437        AutoDiff.Term t;
438        if (!TryTransformToAutoDiff(node.GetSubtree(0), variables, parameters, variableNames, updateVariableWeights, out t)) {
439          term = null;
440          return false;
441        } else {
442          term = erf(t);
443          return true;
444        }
445      }
446      if (node.Symbol is Norm) {
447        AutoDiff.Term t;
448        if (!TryTransformToAutoDiff(node.GetSubtree(0), variables, parameters, variableNames, updateVariableWeights, out t)) {
449          term = null;
450          return false;
451        } else {
452          term = norm(t);
453          return true;
454        }
455      }
456      if (node.Symbol is StartSymbol) {
457        var alpha = new AutoDiff.Variable();
458        var beta = new AutoDiff.Variable();
459        variables.Add(beta);
460        variables.Add(alpha);
461        AutoDiff.Term branchTerm;
462        if (TryTransformToAutoDiff(node.GetSubtree(0), variables, parameters, variableNames, updateVariableWeights, out branchTerm)) {
463          term = branchTerm * alpha + beta;
464          return true;
465        } else {
466          term = null;
467          return false;
468        }
469      }
470      term = null;
471      return false;
472    }
473
474    public static bool CanOptimizeConstants(ISymbolicExpressionTree tree) {
475      var containsUnknownSymbol = (
476        from n in tree.Root.GetSubtree(0).IterateNodesPrefix()
477        where
478         !(n.Symbol is Variable) &&
479         !(n.Symbol is Constant) &&
480         !(n.Symbol is Addition) &&
481         !(n.Symbol is Subtraction) &&
482         !(n.Symbol is Multiplication) &&
483         !(n.Symbol is Division) &&
484         !(n.Symbol is Logarithm) &&
485         !(n.Symbol is Exponential) &&
486         !(n.Symbol is SquareRoot) &&
487         !(n.Symbol is Square) &&
488         !(n.Symbol is Sine) &&
489         !(n.Symbol is Cosine) &&
490         !(n.Symbol is Tangent) &&
491         !(n.Symbol is Erf) &&
492         !(n.Symbol is Norm) &&
493         !(n.Symbol is StartSymbol)
494        select n).
495      Any();
496      return !containsUnknownSymbol;
497    }
498  }
499}
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