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source: branches/2974_Constants_Optimization/HeuristicLab.Problems.DataAnalysis.Symbolic/3.4/Converters/TreeToAutoDiffTermConverter.cs @ 17905

Last change on this file since 17905 was 17193, checked in by mkommend, 5 years ago

#2974: Merged trunk changes into branch.

File size: 14.2 KB
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1#region License Information
2/* HeuristicLab
3 * Copyright (C) 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    private static readonly Func<Term, UnaryFunc> tanh = UnaryFunc.Factory(
79      eval: Math.Tanh,
80      diff: x => 1 - Math.Tanh(x) * Math.Tanh(x));
81    private static readonly Func<Term, UnaryFunc> erf = UnaryFunc.Factory(
82      eval: alglib.errorfunction,
83      diff: x => 2.0 * Math.Exp(-(x * x)) / Math.Sqrt(Math.PI));
84
85    private static readonly Func<Term, UnaryFunc> norm = UnaryFunc.Factory(
86      eval: alglib.normaldistribution,
87      diff: x => -(Math.Exp(-(x * x)) * Math.Sqrt(Math.Exp(x * x)) * x) / Math.Sqrt(2 * Math.PI));
88
89    private static readonly Func<Term, UnaryFunc> abs = UnaryFunc.Factory(
90      eval: Math.Abs,
91      diff: x => Math.Sign(x)
92      );
93
94    private static readonly Func<Term, UnaryFunc> cbrt = UnaryFunc.Factory(
95      eval: x => x < 0 ? -Math.Pow(-x, 1.0 / 3) : Math.Pow(x, 1.0 / 3),
96      diff: x => { var cbrt_x = x < 0 ? -Math.Pow(-x, 1.0 / 3) : Math.Pow(x, 1.0 / 3); return 1.0 / (3 * cbrt_x * cbrt_x); }
97      );
98
99
100
101    #endregion
102
103    public static bool TryConvertToAutoDiff(ISymbolicExpressionTree tree, bool makeVariableWeightsVariable, bool addLinearScalingTerms,
104      out List<DataForVariable> parameters, out double[] initialConstants,
105      out ParametricFunction func,
106      out ParametricFunctionGradient func_grad) {
107
108      // use a transformator object which holds the state (variable list, parameter list, ...) for recursive transformation of the tree
109      var transformator = new TreeToAutoDiffTermConverter(makeVariableWeightsVariable, addLinearScalingTerms);
110      AutoDiff.Term term;
111      try {
112        term = transformator.ConvertToAutoDiff(tree.Root.GetSubtree(0));
113        var parameterEntries = transformator.parameters.ToArray(); // guarantee same order for keys and values
114        var compiledTerm = term.Compile(transformator.variables.ToArray(),
115          parameterEntries.Select(kvp => kvp.Value).ToArray());
116        parameters = new List<DataForVariable>(parameterEntries.Select(kvp => kvp.Key));
117        initialConstants = transformator.initialConstants.ToArray();
118        func = (vars, @params) => compiledTerm.Evaluate(vars, @params);
119        func_grad = (vars, @params) => compiledTerm.Differentiate(vars, @params);
120        return true;
121      } catch (ConversionException) {
122        func = null;
123        func_grad = null;
124        parameters = null;
125        initialConstants = null;
126      }
127      return false;
128    }
129
130    // state for recursive transformation of trees
131    private readonly List<double> initialConstants;
132    private readonly Dictionary<DataForVariable, AutoDiff.Variable> parameters;
133    private readonly List<AutoDiff.Variable> variables;
134    private readonly bool makeVariableWeightsVariable;
135    private readonly bool addLinearScalingTerms;
136
137    private TreeToAutoDiffTermConverter(bool makeVariableWeightsVariable, bool addLinearScalingTerms) {
138      this.makeVariableWeightsVariable = makeVariableWeightsVariable;
139      this.addLinearScalingTerms = addLinearScalingTerms;
140      this.initialConstants = new List<double>();
141      this.parameters = new Dictionary<DataForVariable, AutoDiff.Variable>();
142      this.variables = new List<AutoDiff.Variable>();
143    }
144
145    private AutoDiff.Term ConvertToAutoDiff(ISymbolicExpressionTreeNode node) {
146      if (node.Symbol is Constant) {
147        initialConstants.Add(((ConstantTreeNode)node).Value);
148        var var = new AutoDiff.Variable();
149        variables.Add(var);
150        return var;
151      }
152      if (node.Symbol is Variable || node.Symbol is BinaryFactorVariable) {
153        var varNode = node as VariableTreeNodeBase;
154        var factorVarNode = node as BinaryFactorVariableTreeNode;
155        // factor variable values are only 0 or 1 and set in x accordingly
156        var varValue = factorVarNode != null ? factorVarNode.VariableValue : string.Empty;
157        var par = FindOrCreateParameter(parameters, varNode.VariableName, varValue);
158
159        if (makeVariableWeightsVariable) {
160          initialConstants.Add(varNode.Weight);
161          var w = new AutoDiff.Variable();
162          variables.Add(w);
163          return AutoDiff.TermBuilder.Product(w, par);
164        } else {
165          return varNode.Weight * par;
166        }
167      }
168      if (node.Symbol is FactorVariable) {
169        var factorVarNode = node as FactorVariableTreeNode;
170        var products = new List<Term>();
171        foreach (var variableValue in factorVarNode.Symbol.GetVariableValues(factorVarNode.VariableName)) {
172          var par = FindOrCreateParameter(parameters, factorVarNode.VariableName, variableValue);
173
174          initialConstants.Add(factorVarNode.GetValue(variableValue));
175          var wVar = new AutoDiff.Variable();
176          variables.Add(wVar);
177
178          products.Add(AutoDiff.TermBuilder.Product(wVar, par));
179        }
180        return AutoDiff.TermBuilder.Sum(products);
181      }
182      if (node.Symbol is LaggedVariable) {
183        var varNode = node as LaggedVariableTreeNode;
184        var par = FindOrCreateParameter(parameters, varNode.VariableName, string.Empty, varNode.Lag);
185
186        if (makeVariableWeightsVariable) {
187          initialConstants.Add(varNode.Weight);
188          var w = new AutoDiff.Variable();
189          variables.Add(w);
190          return AutoDiff.TermBuilder.Product(w, par);
191        } else {
192          return varNode.Weight * par;
193        }
194      }
195      if (node.Symbol is Addition) {
196        List<AutoDiff.Term> terms = new List<Term>();
197        foreach (var subTree in node.Subtrees) {
198          terms.Add(ConvertToAutoDiff(subTree));
199        }
200        return AutoDiff.TermBuilder.Sum(terms);
201      }
202      if (node.Symbol is Subtraction) {
203        List<AutoDiff.Term> terms = new List<Term>();
204        for (int i = 0; i < node.SubtreeCount; i++) {
205          AutoDiff.Term t = ConvertToAutoDiff(node.GetSubtree(i));
206          if (i > 0) t = -t;
207          terms.Add(t);
208        }
209        if (terms.Count == 1) return -terms[0];
210        else return AutoDiff.TermBuilder.Sum(terms);
211      }
212      if (node.Symbol is Multiplication) {
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 terms[0];
218        else return terms.Aggregate((a, b) => new AutoDiff.Product(a, b));
219      }
220      if (node.Symbol is Division) {
221        List<AutoDiff.Term> terms = new List<Term>();
222        foreach (var subTree in node.Subtrees) {
223          terms.Add(ConvertToAutoDiff(subTree));
224        }
225        if (terms.Count == 1) return 1.0 / terms[0];
226        else return terms.Aggregate((a, b) => new AutoDiff.Product(a, 1.0 / b));
227      }
228      if (node.Symbol is Absolute) {
229        var x1 = ConvertToAutoDiff(node.GetSubtree(0));
230        return abs(x1);
231      }
232      if (node.Symbol is AnalyticQuotient) {
233        var x1 = ConvertToAutoDiff(node.GetSubtree(0));
234        var x2 = ConvertToAutoDiff(node.GetSubtree(1));
235        return x1 / (TermBuilder.Power(1 + x2 * x2, 0.5));
236      }
237      if (node.Symbol is Logarithm) {
238        return AutoDiff.TermBuilder.Log(
239          ConvertToAutoDiff(node.GetSubtree(0)));
240      }
241      if (node.Symbol is Exponential) {
242        return AutoDiff.TermBuilder.Exp(
243          ConvertToAutoDiff(node.GetSubtree(0)));
244      }
245      if (node.Symbol is Square) {
246        return AutoDiff.TermBuilder.Power(
247          ConvertToAutoDiff(node.GetSubtree(0)), 2.0);
248      }
249      if (node.Symbol is SquareRoot) {
250        return AutoDiff.TermBuilder.Power(
251          ConvertToAutoDiff(node.GetSubtree(0)), 0.5);
252      }
253      if (node.Symbol is Cube) {
254        return AutoDiff.TermBuilder.Power(
255          ConvertToAutoDiff(node.GetSubtree(0)), 3.0);
256      }
257      if (node.Symbol is CubeRoot) {
258        return cbrt(ConvertToAutoDiff(node.GetSubtree(0)));
259      }
260      if (node.Symbol is Sine) {
261        return sin(
262          ConvertToAutoDiff(node.GetSubtree(0)));
263      }
264      if (node.Symbol is Cosine) {
265        return cos(
266          ConvertToAutoDiff(node.GetSubtree(0)));
267      }
268      if (node.Symbol is Tangent) {
269        return tan(
270          ConvertToAutoDiff(node.GetSubtree(0)));
271      }
272      if (node.Symbol is HyperbolicTangent) {
273        return tanh(
274          ConvertToAutoDiff(node.GetSubtree(0)));
275      }
276      if (node.Symbol is Erf) {
277        return erf(
278          ConvertToAutoDiff(node.GetSubtree(0)));
279      }
280      if (node.Symbol is Norm) {
281        return norm(
282          ConvertToAutoDiff(node.GetSubtree(0)));
283      }
284      if (node.Symbol is StartSymbol) {
285        if (addLinearScalingTerms) {
286          // scaling variables α, β are given at the beginning of the parameter vector
287          var alpha = new AutoDiff.Variable();
288          var beta = new AutoDiff.Variable();
289          variables.Add(beta);
290          variables.Add(alpha);
291          var t = ConvertToAutoDiff(node.GetSubtree(0));
292          return t * alpha + beta;
293        } else return ConvertToAutoDiff(node.GetSubtree(0));
294      }
295      throw new ConversionException();
296    }
297
298
299    // for each factor variable value we need a parameter which represents a binary indicator for that variable & value combination
300    // each binary indicator is only necessary once. So we only create a parameter if this combination is not yet available
301    private static Term FindOrCreateParameter(Dictionary<DataForVariable, AutoDiff.Variable> parameters,
302      string varName, string varValue = "", int lag = 0) {
303      var data = new DataForVariable(varName, varValue, lag);
304
305      AutoDiff.Variable par = null;
306      if (!parameters.TryGetValue(data, out par)) {
307        // not found -> create new parameter and entries in names and values lists
308        par = new AutoDiff.Variable();
309        parameters.Add(data, par);
310      }
311      return par;
312    }
313
314    public static bool IsCompatible(ISymbolicExpressionTree tree) {
315      var containsUnknownSymbol = (
316        from n in tree.Root.GetSubtree(0).IterateNodesPrefix()
317        where
318          !(n.Symbol is Variable) &&
319          !(n.Symbol is BinaryFactorVariable) &&
320          !(n.Symbol is FactorVariable) &&
321          !(n.Symbol is LaggedVariable) &&
322          !(n.Symbol is Constant) &&
323          !(n.Symbol is Addition) &&
324          !(n.Symbol is Subtraction) &&
325          !(n.Symbol is Multiplication) &&
326          !(n.Symbol is Division) &&
327          !(n.Symbol is Logarithm) &&
328          !(n.Symbol is Exponential) &&
329          !(n.Symbol is SquareRoot) &&
330          !(n.Symbol is Square) &&
331          !(n.Symbol is Sine) &&
332          !(n.Symbol is Cosine) &&
333          !(n.Symbol is Tangent) &&
334          !(n.Symbol is HyperbolicTangent) &&
335          !(n.Symbol is Erf) &&
336          !(n.Symbol is Norm) &&
337          !(n.Symbol is StartSymbol) &&
338          !(n.Symbol is Absolute) &&
339          !(n.Symbol is AnalyticQuotient) &&
340          !(n.Symbol is Cube) &&
341          !(n.Symbol is CubeRoot)
342        select n).Any();
343      return !containsUnknownSymbol;
344    }
345    #region exception class
346    [Serializable]
347    public class ConversionException : Exception {
348
349      public ConversionException() {
350      }
351
352      public ConversionException(string message) : base(message) {
353      }
354
355      public ConversionException(string message, Exception inner) : base(message, inner) {
356      }
357
358      protected ConversionException(
359        SerializationInfo info,
360        StreamingContext context) : base(info, context) {
361      }
362    }
363    #endregion
364  }
365}
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