source: branches/DataAnalysis/HeuristicLab.Problems.DataAnalysis.MultiVariate.Regression/3.3/Symbolic/Evaluators/PartialSymbolicDifferential.cs @ 5275

#region License Information
/* HeuristicLab
 * Copyright (C) 2002-2008 Heuristic and Evolutionary Algorithms Laboratory (HEAL)
 *
 * This file is part of HeuristicLab.
 *
 * HeuristicLab is free software: you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
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 *
 * HeuristicLab is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
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#endregion

using System;
using System.Diagnostics;
using HeuristicLab.Common;
using System.Linq;

using System.Collections.Generic;
using HeuristicLab.Problems.DataAnalysis.Symbolic.Symbols;
using HeuristicLab.Encodings.SymbolicExpressionTreeEncoding.Symbols;
using HeuristicLab.Encodings.SymbolicExpressionTreeEncoding; // double.IsAlmost extension

namespace HeuristicLab.Problems.DataAnalysis.MultiVariate.Regression.Symbolic.Evaluators {
  public static class PartialSymbolicDifferential {
    private static readonly DifferentialVariable differential = new DifferentialVariable();
    private static readonly Constant @const = new Constant();
    private static readonly ConstantTreeNode const0 = new ConstantTreeNode(@const);
    private static readonly ConstantTreeNode const1 = new ConstantTreeNode(@const);
    private static readonly Symbol addition = new Addition();
    private static readonly Symbol subtraction = new Subtraction();
    private static readonly Symbol multiplication = new Multiplication();
    private static readonly Symbol division = new Division();
    //private static readonly Symbol power = new Power();
    private static readonly Symbol exp = new Exponential();
    private static readonly Symbol ln = new Logarithm();
    private static readonly Symbol cos = new Cosine();
    private static readonly Symbol sin = new Sine();
    private static readonly Symbol tan = new Tangent();

    static PartialSymbolicDifferential() {
      const0.Value = 0.0;
      const1.Value = 1.0;
    }

    public static SymbolicExpressionTreeNode Apply(SymbolicExpressionTreeNode expression, string variableName, params string[] interdependentVariable) {
      Symbol symbol = expression.Symbol;
      if (symbol is Variable) {
        var variable = (VariableTreeNode)expression;
        if (variable.VariableName == variableName) return MakeConstant(variable.Weight);
        else if (interdependentVariable.Contains(variable.VariableName)) {
          return MakeProduct(MakeConstant(variable.Weight), MakeDivision(MakeDifferential(1.0, variable.VariableName), MakeDifferential(1.0, variableName)));
        } else return const0;
      } else if (symbol is Constant) {
        return const0;
      } else if (symbol is Addition) {
        var sum = addition.CreateTreeNode();
        foreach (var subExp in expression.SubTrees) {
          sum.AddSubTree(Apply(subExp, variableName, interdependentVariable));
        }
        return sum;
      } else if (symbol is Subtraction) {
        var diff = subtraction.CreateTreeNode();
        foreach (var subExp in expression.SubTrees) {
          diff.AddSubTree(Apply(subExp, variableName, interdependentVariable));
        }
        return diff;

      } else if (symbol is Multiplication) {
        if (expression.SubTrees.Count() == 1) return Apply(expression.SubTrees[0], variableName, interdependentVariable);
        SymbolicExpressionTreeNode sum = const0;

        for (int i = 0; i < expression.SubTrees.Count; i++) {
          SymbolicExpressionTreeNode prod = const1;

          for (int j = 0; j < expression.SubTrees.Count; j++) {
            if (j != i)
              prod = MakeProduct(prod, expression.SubTrees[j]);
            else
              prod = MakeProduct(prod, Apply(expression.SubTrees[j], variableName, interdependentVariable));
          }
          sum = MakeSum(sum, prod);
        }
        return sum;
      } else if (symbol is Division) {
        // u/v  (v*du/dx-u*dv/dx)/v^2
        if (expression.SubTrees.Count == 1) {
          SymbolicExpressionTreeNode v = expression.SubTrees[0];
          SymbolicExpressionTreeNode dv = Apply(v, variableName, interdependentVariable);
          return MakeDifference(const1, MakeDivision(dv, MakeSqr(v)));
        } else if (expression.SubTrees.Count == 2) {
          SymbolicExpressionTreeNode u = expression.SubTrees[0];
          SymbolicExpressionTreeNode v = expression.SubTrees[1];
          SymbolicExpressionTreeNode du = Apply(u, variableName, interdependentVariable);
          SymbolicExpressionTreeNode dv = Apply(v, variableName, interdependentVariable);
          u = MakeDivision(MakeDifference(MakeProduct(v, du), MakeProduct(u, dv)), MakeSqr(v));
          for (int i = 2; i < expression.SubTrees.Count; i++) {
            v = expression.SubTrees[i];
            dv = Apply(v, variableName, interdependentVariable);
            du = Apply(u, variableName, interdependentVariable);
            u = MakeDivision(MakeDifference(MakeProduct(v, du), MakeProduct(u, dv)), MakeSqr(v));
          }
          return u;
        } else throw new NotSupportedException("Derivative of division with arity " + expression.SubTrees.Count + " is not supported.");
      } else if (symbol is Exponential) {
        // e^u  e^u*du/dx
        return MakeProduct(MakeExp(expression.SubTrees[0]), Apply(expression.SubTrees[0], variableName, interdependentVariable));
      } else if (symbol is Logarithm) {
        return MakeProduct(MakeDivision(const1, expression.SubTrees[0]), Apply(expression.SubTrees[0], variableName, interdependentVariable));
      }
        //case EvaluatorSymbolTable.POWER: {
        //    var a = expression.SubTrees[0];
        //    var b = expression.SubTrees[1];
        //    return Apply(MakeExp(MakeProduct(b, MakeLn(a))), variableName, interdependentVariable);
        //  }
        //case EvaluatorSymbolTable.SIGNUM: {
        //    return const0;
        //  }
        else if (symbol is Sine) {
        return MakeProduct(MakeCos(expression.SubTrees[0]), Apply(expression.SubTrees[0], variableName, interdependentVariable));
      } else if (symbol is Cosine) {
        return MakeProduct(MakeNegSin(expression.SubTrees[0]), Apply(expression.SubTrees[0], variableName, interdependentVariable));
      } else if (symbol is Tangent) {
        return MakeProduct(MakeSum(const1, MakeTanSqr(expression.SubTrees[0])), Apply(expression.SubTrees[0], variableName, interdependentVariable));
      }
        //else if(symbol is Sqrt) {
        //      var powTree = new FunctionTreeBase(power);
        //      powTree.AddSubTree(expression.SubTrees[0]);
        //      powTree.AddSubTree(MakeConstant(0.5));
        //      return Apply(powTree, variableName, interdependentVariable);
        //    }
      else if (symbol is ProgramRootSymbol) {
        var branch = Apply(expression.SubTrees[0], variableName, interdependentVariable);
        expression.RemoveSubTree(0);
        expression.InsertSubTree(0, branch);
        return expression;
      } else if (symbol is StartSymbol) {
        var branch = Apply(expression.SubTrees[0], variableName, interdependentVariable);
        expression.RemoveSubTree(0);
        expression.InsertSubTree(0, branch);
        return expression;
      } else {
        throw new NotImplementedException();
      }
    }

    private static SymbolicExpressionTreeNode MakeDifferential(double c, string v) {
      DifferentialVariableTreeNode diffTree = (DifferentialVariableTreeNode)differential.CreateTreeNode();
      diffTree.VariableName = v;
      diffTree.Weight = c;
      return diffTree;
    }

    private static SymbolicExpressionTreeNode MakeTanSqr(SymbolicExpressionTreeNode expression) {
      var tanTree1 = tan.CreateTreeNode();
      var tanTree2 = tan.CreateTreeNode();
      tanTree2.AddSubTree(expression);
      tanTree1.AddSubTree(tanTree2);
      return tanTree1;
    }

    private static SymbolicExpressionTreeNode MakeNegSin(SymbolicExpressionTreeNode expression) {
      var sinTree = sin.CreateTreeNode();
      sinTree.AddSubTree(expression);
      return MakeDifference(const0, sinTree);
    }

    private static SymbolicExpressionTreeNode MakeCos(SymbolicExpressionTreeNode expression) {
      var cosTree = cos.CreateTreeNode();
      cosTree.AddSubTree(expression);
      return cosTree;
    }

    private static SymbolicExpressionTreeNode MakeLn(SymbolicExpressionTreeNode a) {
      var lnTree = ln.CreateTreeNode();
      lnTree.AddSubTree(a);
      return lnTree;
    }

    private static SymbolicExpressionTreeNode MakeExp(SymbolicExpressionTreeNode expression) {
      if (IsConstantZero(expression)) return const1;
      var expTree = exp.CreateTreeNode();
      expTree.AddSubTree(expression);
      return expTree;
    }

    private static SymbolicExpressionTreeNode MakeDivision(SymbolicExpressionTreeNode x, SymbolicExpressionTreeNode y) {
      if (IsConstantZero(x)) return const0;
      var div = division.CreateTreeNode();
      div.AddSubTree(x);
      div.AddSubTree(y);
      return div;
    }

    private static SymbolicExpressionTreeNode MakeSqr(SymbolicExpressionTreeNode x) {
      var sqr = multiplication.CreateTreeNode();
      sqr.AddSubTree(x);
      sqr.AddSubTree((SymbolicExpressionTreeNode)x.Clone());
      return sqr;
    }

    private static SymbolicExpressionTreeNode MakeProduct(SymbolicExpressionTreeNode x, SymbolicExpressionTreeNode y) {
      if (IsConstantZero(x) || IsConstantZero(y)) {
        return const0;
      } else if (IsConstantOne(x)) return y;
      else if (IsConstantOne(y)) return x;
      var product = multiplication.CreateTreeNode();
      product.AddSubTree(x);
      product.AddSubTree(y);
      return product;
    }

    private static bool IsConstantOne(SymbolicExpressionTreeNode x) {
      return x == const1;
    }

    private static bool IsConstantZero(SymbolicExpressionTreeNode x) {
      return x == const0;
    }

    private static SymbolicExpressionTreeNode MakeSum(SymbolicExpressionTreeNode a, SymbolicExpressionTreeNode b) {
      if (IsConstantZero(a) && IsConstantZero(b)) return const0;
      else if (IsConstantZero(a)) return b;
      else if (IsConstantZero(b)) return a;
      var product = addition.CreateTreeNode();
      product.AddSubTree(a);
      product.AddSubTree(b);
      return product;
    }

    private static SymbolicExpressionTreeNode MakeDifference(SymbolicExpressionTreeNode a, SymbolicExpressionTreeNode b) {
      if (IsConstantZero(a) && IsConstantZero(b)) return const0;
      else if (IsConstantZero(b)) return a;
      var diff = subtraction.CreateTreeNode();
      diff.AddSubTree(a);
      diff.AddSubTree(b);
      return diff;
    }

    private static SymbolicExpressionTreeNode MakeConstant(double c) {
      if (c.IsAlmost(1.0)) return const1;
      else if (c.IsAlmost(0.0)) return const0;
      var cExp = new ConstantTreeNode(@const);
      cExp.Value = c;
      return cExp;
    }
  }
}