Ignore:
Timestamp:
07/04/19 15:15:58 (2 years ago)
Author:
mkommend
Message:

#2948: Merged 16206, 16207, 16213, 16216, 16294 to stable.

File:
1 copied

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  • stable/HeuristicLab.Problems.DataAnalysis.Symbolic/3.4/Converters/DerivativeCalculator.cs

    r16207 r17066  
    2121
    2222using System;
     23using System.Collections.Generic;
    2324using System.Linq;
    2425using HeuristicLab.Encodings.SymbolicExpressionTreeEncoding;
     
    2728  public static class DerivativeCalculator {
    2829    public static ISymbolicExpressionTree Derive(ISymbolicExpressionTree tree, string variableName) {
     30      if (tree.Root.SubtreeCount != 1)
     31        throw new NotImplementedException("Derive is not implemented for symbolic expressions with automatically defined functions (ADF)");
     32      if (tree.Root.GetSubtree(0).SubtreeCount != 1)
     33        throw new NotImplementedException("Derive is not implemented for multi-variate symbolic expressions");
    2934      var mainBranch = tree.Root.GetSubtree(0).GetSubtree(0);
    3035      var root = new ProgramRootSymbol().CreateTreeNode();
    3136      root.AddSubtree(new StartSymbol().CreateTreeNode());
    3237      var dTree = TreeSimplifier.GetSimplifiedTree(Derive(mainBranch, variableName));
    33       // var dTree = Derive(mainBranch, variableName);
     38      //var dTree = Derive(mainBranch, variableName);
    3439      root.GetSubtree(0).AddSubtree(dTree);
    3540      return new SymbolicExpressionTree(root);
    3641    }
    3742
    38     private static Constant constantSy = new Constant();
    39     private static Addition addSy = new Addition();
    40     private static Subtraction subSy = new Subtraction();
    41     private static Multiplication mulSy = new Multiplication();
    42     private static Division divSy = new Division();
     43    private static readonly Constant constantSy = new Constant();
     44    private static readonly Addition addSy = new Addition();
     45    private static readonly Subtraction subSy = new Subtraction();
     46    private static readonly Multiplication mulSy = new Multiplication();
     47    private static readonly Division divSy = new Division();
     48    private static readonly Cosine cosSy = new Cosine();
     49    private static readonly Square sqrSy = new Square();
    4350
    4451    public static ISymbolicExpressionTreeNode Derive(ISymbolicExpressionTreeNode branch, string variableName) {
     
    8592          }
    8693          return fgPrime;
    87         } else throw new ArgumentException();
     94        } else
     95          // multiplication with only one argument has no effect -> derive the argument
     96          return Derive(branch.GetSubtree(0), variableName);
    8897      }
    8998      if (branch.Symbol is Division) {
     
    95104          sqrNode.AddSubtree(g);
    96105          return Div(gPrime, sqrNode);
    97         } else if (branch.SubtreeCount == 2) {
     106        } else {
     107          // for two subtrees:
     108          // (f/g)' = (f'g - fg')/g²
     109
     110          // if there are more than 2 subtrees
     111          // div(x,y,z) is interpretered as (x/y)/z
     112          // which is the same as x / (y*z)
     113
     114          // --> make a product of all but the first subtree and differentiate as for the 2-argument case above
    98115          var f = (ISymbolicExpressionTreeNode)branch.GetSubtree(0).Clone();
    99           var g = (ISymbolicExpressionTreeNode)branch.GetSubtree(1).Clone();
     116          var g = Product(branch.Subtrees.Skip(1).Select(n => (ISymbolicExpressionTreeNode)n.Clone()));
    100117          var fprime = Derive(f, variableName);
    101118          var gprime = Derive(g, variableName);
    102           var sqrNode = new Square().CreateTreeNode();
    103           sqrNode.AddSubtree((ISymbolicExpressionTreeNode)branch.GetSubtree(1).Clone());
    104           return Div(Subtract(Product(fprime, g), Product(f, gprime)), sqrNode);
    105         } else throw new NotSupportedException();
     119          var gSqr = Square(g);
     120          return Div(Subtract(Product(fprime, g), Product(f, gprime)), gSqr);
     121        }
    106122      }
    107123      if (branch.Symbol is Logarithm) {
     
    113129        return Product(f, Derive(branch.GetSubtree(0), variableName));
    114130      }
    115       if(branch.Symbol is Square) {
     131      if (branch.Symbol is Square) {
    116132        var f = (ISymbolicExpressionTreeNode)branch.GetSubtree(0).Clone();
    117133        return Product(Product(CreateConstant(2.0), f), Derive(f, variableName));
    118       }     
    119       if(branch.Symbol is SquareRoot) {
     134      }
     135      if (branch.Symbol is SquareRoot) {
    120136        var f = (ISymbolicExpressionTreeNode)branch.Clone();
    121137        var u = (ISymbolicExpressionTreeNode)branch.GetSubtree(0).Clone();
    122         return Div(CreateConstant(1.0), Product(Product(CreateConstant(2.0), f), Derive(u, variableName)));
     138        return Product(Div(CreateConstant(1.0), Product(CreateConstant(2.0), f)), Derive(u, variableName));
    123139      }
    124140      if (branch.Symbol is Sine) {
     
    134150        return Product(CreateConstant(-1.0), Product(sin, Derive(u, variableName)));
    135151      }
    136       throw new NotSupportedException($"Symbol {branch.Symbol} is not supported.");
     152      if (branch.Symbol is Tangent) {
     153        // tan(x)' = 1 / cos²(x)
     154        var fxp = Derive(branch.GetSubtree(0), variableName);
     155        var u = (ISymbolicExpressionTreeNode)branch.GetSubtree(0).Clone();
     156        return Div(fxp, Square(Cosine(u)));
     157      }
     158      throw new NotSupportedException(string.Format("Symbol {0} is not supported.", branch.Symbol));
    137159    }
    138160
     
    144166      return product;
    145167    }
     168    private static ISymbolicExpressionTreeNode Product(IEnumerable<ISymbolicExpressionTreeNode> fs) {
     169      var product = mulSy.CreateTreeNode();
     170      foreach (var f in fs) product.AddSubtree(f);
     171      return product;
     172    }
    146173    private static ISymbolicExpressionTreeNode Div(ISymbolicExpressionTreeNode f, ISymbolicExpressionTreeNode g) {
    147174      var div = divSy.CreateTreeNode();
     
    163190      return sum;
    164191    }
    165                          
     192    private static ISymbolicExpressionTreeNode Cosine(ISymbolicExpressionTreeNode f) {
     193      var cos = cosSy.CreateTreeNode();
     194      cos.AddSubtree(f);
     195      return cos;
     196    }
     197    private static ISymbolicExpressionTreeNode Square(ISymbolicExpressionTreeNode f) {
     198      var sqr = sqrSy.CreateTreeNode();
     199      sqr.AddSubtree(f);
     200      return sqr;
     201    }
     202
    166203    private static ISymbolicExpressionTreeNode CreateConstant(double v) {
    167204      var constNode = (ConstantTreeNode)constantSy.CreateTreeNode();
     
    186223          !(n.Symbol is Sine) &&
    187224          !(n.Symbol is Cosine) &&
     225          !(n.Symbol is Tangent) &&
    188226          !(n.Symbol is StartSymbol)
    189227        select n).Any();
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