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source: trunk/HeuristicLab.Problems.DataAnalysis.Symbolic/3.4/Converters/TreeToAutoDiffTermConverter.cs @ 16360

Last change on this file since 16360 was 16360, checked in by gkronber, 5 years ago

#2915 renamed class AnalyticalQuotient -> AnalyticQuotient

File size: 13.6 KB
Line 
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.Runtime.Serialization;
26using AutoDiff;
27using HeuristicLab.Encodings.SymbolicExpressionTreeEncoding;
28
29namespace HeuristicLab.Problems.DataAnalysis.Symbolic {
30  public class TreeToAutoDiffTermConverter {
31    public delegate double ParametricFunction(double[] vars, double[] @params);
32
33    public delegate Tuple<double[], double> ParametricFunctionGradient(double[] vars, double[] @params);
34
35    #region helper class
36    public class DataForVariable {
37      public readonly string variableName;
38      public readonly string variableValue; // for factor vars
39      public readonly int lag;
40
41      public DataForVariable(string varName, string varValue, int lag) {
42        this.variableName = varName;
43        this.variableValue = varValue;
44        this.lag = lag;
45      }
46
47      public override bool Equals(object obj) {
48        var other = obj as DataForVariable;
49        if (other == null) return false;
50        return other.variableName.Equals(this.variableName) &&
51               other.variableValue.Equals(this.variableValue) &&
52               other.lag == this.lag;
53      }
54
55      public override int GetHashCode() {
56        return variableName.GetHashCode() ^ variableValue.GetHashCode() ^ lag;
57      }
58    }
59    #endregion
60
61    #region derivations of functions
62    // create function factory for arctangent
63    private static readonly Func<Term, UnaryFunc> arctan = UnaryFunc.Factory(
64      eval: Math.Atan,
65      diff: x => 1 / (1 + x * x));
66
67    private static readonly Func<Term, UnaryFunc> sin = UnaryFunc.Factory(
68      eval: Math.Sin,
69      diff: Math.Cos);
70
71    private static readonly Func<Term, UnaryFunc> cos = UnaryFunc.Factory(
72      eval: Math.Cos,
73      diff: x => -Math.Sin(x));
74
75    private static readonly Func<Term, UnaryFunc> tan = UnaryFunc.Factory(
76      eval: Math.Tan,
77      diff: x => 1 + Math.Tan(x) * Math.Tan(x));
78
79    private static readonly Func<Term, UnaryFunc> erf = UnaryFunc.Factory(
80      eval: alglib.errorfunction,
81      diff: x => 2.0 * Math.Exp(-(x * x)) / Math.Sqrt(Math.PI));
82
83    private static readonly Func<Term, UnaryFunc> norm = UnaryFunc.Factory(
84      eval: alglib.normaldistribution,
85      diff: x => -(Math.Exp(-(x * x)) * Math.Sqrt(Math.Exp(x * x)) * x) / Math.Sqrt(2 * Math.PI));
86
87    private static readonly Func<Term, UnaryFunc> abs = UnaryFunc.Factory(
88      eval: Math.Abs,
89      diff: x => Math.Sign(x)
90      );
91
92    #endregion
93
94    public static bool TryConvertToAutoDiff(ISymbolicExpressionTree tree, bool makeVariableWeightsVariable, bool addLinearScalingTerms,
95      out List<DataForVariable> parameters, out double[] initialConstants,
96      out ParametricFunction func,
97      out ParametricFunctionGradient func_grad) {
98
99      // use a transformator object which holds the state (variable list, parameter list, ...) for recursive transformation of the tree
100      var transformator = new TreeToAutoDiffTermConverter(makeVariableWeightsVariable, addLinearScalingTerms);
101      AutoDiff.Term term;
102      try {
103        term = transformator.ConvertToAutoDiff(tree.Root.GetSubtree(0));
104        var parameterEntries = transformator.parameters.ToArray(); // guarantee same order for keys and values
105        var compiledTerm = term.Compile(transformator.variables.ToArray(),
106          parameterEntries.Select(kvp => kvp.Value).ToArray());
107        parameters = new List<DataForVariable>(parameterEntries.Select(kvp => kvp.Key));
108        initialConstants = transformator.initialConstants.ToArray();
109        func = (vars, @params) => compiledTerm.Evaluate(vars, @params);
110        func_grad = (vars, @params) => compiledTerm.Differentiate(vars, @params);
111        return true;
112      } catch (ConversionException) {
113        func = null;
114        func_grad = null;
115        parameters = null;
116        initialConstants = null;
117      }
118      return false;
119    }
120
121    // state for recursive transformation of trees
122    private readonly
123    List<double> initialConstants;
124    private readonly Dictionary<DataForVariable, AutoDiff.Variable> parameters;
125    private readonly List<AutoDiff.Variable> variables;
126    private readonly bool makeVariableWeightsVariable;
127    private readonly bool addLinearScalingTerms;
128
129    private TreeToAutoDiffTermConverter(bool makeVariableWeightsVariable, bool addLinearScalingTerms) {
130      this.makeVariableWeightsVariable = makeVariableWeightsVariable;
131      this.addLinearScalingTerms = addLinearScalingTerms;
132      this.initialConstants = new List<double>();
133      this.parameters = new Dictionary<DataForVariable, AutoDiff.Variable>();
134      this.variables = new List<AutoDiff.Variable>();
135    }
136
137    private AutoDiff.Term ConvertToAutoDiff(ISymbolicExpressionTreeNode node) {
138      if (node.Symbol is Constant) {
139        initialConstants.Add(((ConstantTreeNode)node).Value);
140        var var = new AutoDiff.Variable();
141        variables.Add(var);
142        return var;
143      }
144      if (node.Symbol is Variable || node.Symbol is BinaryFactorVariable) {
145        var varNode = node as VariableTreeNodeBase;
146        var factorVarNode = node as BinaryFactorVariableTreeNode;
147        // factor variable values are only 0 or 1 and set in x accordingly
148        var varValue = factorVarNode != null ? factorVarNode.VariableValue : string.Empty;
149        var par = FindOrCreateParameter(parameters, varNode.VariableName, varValue);
150
151        if (makeVariableWeightsVariable) {
152          initialConstants.Add(varNode.Weight);
153          var w = new AutoDiff.Variable();
154          variables.Add(w);
155          return AutoDiff.TermBuilder.Product(w, par);
156        } else {
157          return varNode.Weight * par;
158        }
159      }
160      if (node.Symbol is FactorVariable) {
161        var factorVarNode = node as FactorVariableTreeNode;
162        var products = new List<Term>();
163        foreach (var variableValue in factorVarNode.Symbol.GetVariableValues(factorVarNode.VariableName)) {
164          var par = FindOrCreateParameter(parameters, factorVarNode.VariableName, variableValue);
165
166          initialConstants.Add(factorVarNode.GetValue(variableValue));
167          var wVar = new AutoDiff.Variable();
168          variables.Add(wVar);
169
170          products.Add(AutoDiff.TermBuilder.Product(wVar, par));
171        }
172        return AutoDiff.TermBuilder.Sum(products);
173      }
174      if (node.Symbol is LaggedVariable) {
175        var varNode = node as LaggedVariableTreeNode;
176        var par = FindOrCreateParameter(parameters, varNode.VariableName, string.Empty, varNode.Lag);
177
178        if (makeVariableWeightsVariable) {
179          initialConstants.Add(varNode.Weight);
180          var w = new AutoDiff.Variable();
181          variables.Add(w);
182          return AutoDiff.TermBuilder.Product(w, par);
183        } else {
184          return varNode.Weight * par;
185        }
186      }
187      if (node.Symbol is Addition) {
188        List<AutoDiff.Term> terms = new List<Term>();
189        foreach (var subTree in node.Subtrees) {
190          terms.Add(ConvertToAutoDiff(subTree));
191        }
192        return AutoDiff.TermBuilder.Sum(terms);
193      }
194      if (node.Symbol is Subtraction) {
195        List<AutoDiff.Term> terms = new List<Term>();
196        for (int i = 0; i < node.SubtreeCount; i++) {
197          AutoDiff.Term t = ConvertToAutoDiff(node.GetSubtree(i));
198          if (i > 0) t = -t;
199          terms.Add(t);
200        }
201        if (terms.Count == 1) return -terms[0];
202        else return AutoDiff.TermBuilder.Sum(terms);
203      }
204      if (node.Symbol is Multiplication) {
205        List<AutoDiff.Term> terms = new List<Term>();
206        foreach (var subTree in node.Subtrees) {
207          terms.Add(ConvertToAutoDiff(subTree));
208        }
209        if (terms.Count == 1) return terms[0];
210        else return terms.Aggregate((a, b) => new AutoDiff.Product(a, b));
211      }
212      if (node.Symbol is Division) {
213        List<AutoDiff.Term> terms = new List<Term>();
214        foreach (var subTree in node.Subtrees) {
215          terms.Add(ConvertToAutoDiff(subTree));
216        }
217        if (terms.Count == 1) return 1.0 / terms[0];
218        else return terms.Aggregate((a, b) => new AutoDiff.Product(a, 1.0 / b));
219      }
220      if (node.Symbol is Absolute) {
221        var x1 = ConvertToAutoDiff(node.GetSubtree(0));
222        return abs(x1);
223      }
224      if (node.Symbol is AnalyticQuotient) {
225        var x1 = ConvertToAutoDiff(node.GetSubtree(0));
226        var x2 = ConvertToAutoDiff(node.GetSubtree(1));
227        return x1 / (TermBuilder.Power(1 + x2 * x2, 0.5));
228      }
229      if (node.Symbol is Logarithm) {
230        return AutoDiff.TermBuilder.Log(
231          ConvertToAutoDiff(node.GetSubtree(0)));
232      }
233      if (node.Symbol is Exponential) {
234        return AutoDiff.TermBuilder.Exp(
235          ConvertToAutoDiff(node.GetSubtree(0)));
236      }
237      if (node.Symbol is Square) {
238        return AutoDiff.TermBuilder.Power(
239          ConvertToAutoDiff(node.GetSubtree(0)), 2.0);
240      }
241      if (node.Symbol is SquareRoot) {
242        return AutoDiff.TermBuilder.Power(
243          ConvertToAutoDiff(node.GetSubtree(0)), 0.5);
244      }
245      if (node.Symbol is Cube) {
246        return AutoDiff.TermBuilder.Power(
247          ConvertToAutoDiff(node.GetSubtree(0)), 3.0);
248      }
249      if (node.Symbol is CubeRoot) {
250        return AutoDiff.TermBuilder.Power(
251          ConvertToAutoDiff(node.GetSubtree(0)), 1.0/3.0);
252      }
253      if (node.Symbol is Sine) {
254        return sin(
255          ConvertToAutoDiff(node.GetSubtree(0)));
256      }
257      if (node.Symbol is Cosine) {
258        return cos(
259          ConvertToAutoDiff(node.GetSubtree(0)));
260      }
261      if (node.Symbol is Tangent) {
262        return tan(
263          ConvertToAutoDiff(node.GetSubtree(0)));
264      }
265      if (node.Symbol is Erf) {
266        return erf(
267          ConvertToAutoDiff(node.GetSubtree(0)));
268      }
269      if (node.Symbol is Norm) {
270        return norm(
271          ConvertToAutoDiff(node.GetSubtree(0)));
272      }
273      if (node.Symbol is StartSymbol) {
274        if (addLinearScalingTerms) {
275          // scaling variables α, β are given at the beginning of the parameter vector
276          var alpha = new AutoDiff.Variable();
277          var beta = new AutoDiff.Variable();
278          variables.Add(beta);
279          variables.Add(alpha);
280          var t = ConvertToAutoDiff(node.GetSubtree(0));
281          return t * alpha + beta;
282        } else return ConvertToAutoDiff(node.GetSubtree(0));
283      }
284      throw new ConversionException();
285    }
286
287
288    // for each factor variable value we need a parameter which represents a binary indicator for that variable & value combination
289    // each binary indicator is only necessary once. So we only create a parameter if this combination is not yet available
290    private static Term FindOrCreateParameter(Dictionary<DataForVariable, AutoDiff.Variable> parameters,
291      string varName, string varValue = "", int lag = 0) {
292      var data = new DataForVariable(varName, varValue, lag);
293
294      AutoDiff.Variable par = null;
295      if (!parameters.TryGetValue(data, out par)) {
296        // not found -> create new parameter and entries in names and values lists
297        par = new AutoDiff.Variable();
298        parameters.Add(data, par);
299      }
300      return par;
301    }
302
303    public static bool IsCompatible(ISymbolicExpressionTree tree) {
304      var containsUnknownSymbol = (
305        from n in tree.Root.GetSubtree(0).IterateNodesPrefix()
306        where
307          !(n.Symbol is Variable) &&
308          !(n.Symbol is BinaryFactorVariable) &&
309          !(n.Symbol is FactorVariable) &&
310          !(n.Symbol is LaggedVariable) &&
311          !(n.Symbol is Constant) &&
312          !(n.Symbol is Addition) &&
313          !(n.Symbol is Subtraction) &&
314          !(n.Symbol is Multiplication) &&
315          !(n.Symbol is Division) &&
316          !(n.Symbol is Logarithm) &&
317          !(n.Symbol is Exponential) &&
318          !(n.Symbol is SquareRoot) &&
319          !(n.Symbol is Square) &&
320          !(n.Symbol is Sine) &&
321          !(n.Symbol is Cosine) &&
322          !(n.Symbol is Tangent) &&
323          !(n.Symbol is Erf) &&
324          !(n.Symbol is Norm) &&
325          !(n.Symbol is StartSymbol) &&
326          !(n.Symbol is Absolute) &&
327          !(n.Symbol is AnalyticQuotient) &&
328          !(n.Symbol is Cube) &&
329          !(n.Symbol is CubeRoot)
330        select n).Any();
331      return !containsUnknownSymbol;
332    }
333    #region exception class
334    [Serializable]
335    public class ConversionException : Exception {
336
337      public ConversionException() {
338      }
339
340      public ConversionException(string message) : base(message) {
341      }
342
343      public ConversionException(string message, Exception inner) : base(message, inner) {
344      }
345
346      protected ConversionException(
347        SerializationInfo info,
348        StreamingContext context) : base(info, context) {
349      }
350    }
351    #endregion
352  }
353}
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