[16206] | 1 | #region License Information
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| 2 | /* HeuristicLab
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[16565] | 3 | * Copyright (C) 2002-2019 Heuristic and Evolutionary Algorithms Laboratory (HEAL)
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[16206] | 4 | *
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| 5 | * This file is part of HeuristicLab.
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| 6 | *
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| 7 | * HeuristicLab is free software: you can redistribute it and/or modify
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| 8 | * it under the terms of the GNU General Public License as published by
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| 9 | * the Free Software Foundation, either version 3 of the License, or
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| 10 | * (at your option) any later version.
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| 11 | *
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| 12 | * HeuristicLab is distributed in the hope that it will be useful,
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| 13 | * but WITHOUT ANY WARRANTY; without even the implied warranty of
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| 14 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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| 15 | * GNU General Public License for more details.
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| 16 | *
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| 17 | * You should have received a copy of the GNU General Public License
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| 18 | * along with HeuristicLab. If not, see <http://www.gnu.org/licenses/>.
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| 19 | */
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| 20 | #endregion
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| 21 |
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| 22 | using System;
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[16294] | 23 | using System.Collections.Generic;
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[16206] | 24 | using System.Linq;
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| 25 | using HeuristicLab.Encodings.SymbolicExpressionTreeEncoding;
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| 26 |
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| 27 | namespace HeuristicLab.Problems.DataAnalysis.Symbolic {
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| 28 | public static class DerivativeCalculator {
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| 29 | public static ISymbolicExpressionTree Derive(ISymbolicExpressionTree tree, string variableName) {
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[16294] | 30 | if (tree.Root.SubtreeCount != 1)
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| 31 | throw new NotImplementedException("Derive is not implemented for symbolic expressions with automatically defined functions (ADF)");
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| 32 | if (tree.Root.GetSubtree(0).SubtreeCount != 1)
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| 33 | throw new NotImplementedException("Derive is not implemented for multi-variate symbolic expressions");
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[16206] | 34 | var mainBranch = tree.Root.GetSubtree(0).GetSubtree(0);
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| 35 | var root = new ProgramRootSymbol().CreateTreeNode();
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| 36 | root.AddSubtree(new StartSymbol().CreateTreeNode());
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| 37 | var dTree = TreeSimplifier.GetSimplifiedTree(Derive(mainBranch, variableName));
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[16294] | 38 | //var dTree = Derive(mainBranch, variableName);
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[16206] | 39 | root.GetSubtree(0).AddSubtree(dTree);
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| 40 | return new SymbolicExpressionTree(root);
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| 41 | }
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| 42 |
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[16294] | 43 | private static readonly Constant constantSy = new Constant();
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| 44 | private static readonly Addition addSy = new Addition();
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| 45 | private static readonly Subtraction subSy = new Subtraction();
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| 46 | private static readonly Multiplication mulSy = new Multiplication();
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| 47 | private static readonly Division divSy = new Division();
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| 48 | private static readonly Cosine cosSy = new Cosine();
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| 49 | private static readonly Square sqrSy = new Square();
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[16543] | 50 | private static readonly Absolute absSy = new Absolute();
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| 51 | private static readonly SquareRoot sqrtSy = new SquareRoot();
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[16206] | 52 |
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| 53 | public static ISymbolicExpressionTreeNode Derive(ISymbolicExpressionTreeNode branch, string variableName) {
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| 54 | if (branch.Symbol is Constant) {
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| 55 | return CreateConstant(0.0);
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| 56 | }
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| 57 | if (branch.Symbol is Variable) {
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| 58 | var varNode = branch as VariableTreeNode;
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| 59 | if (varNode.VariableName == variableName) {
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| 60 | return CreateConstant(varNode.Weight);
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| 61 | } else {
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| 62 | return CreateConstant(0.0);
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| 63 | }
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| 64 | }
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| 65 | if (branch.Symbol is Addition) {
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| 66 | var sum = addSy.CreateTreeNode();
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| 67 | foreach (var subTree in branch.Subtrees) {
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| 68 | sum.AddSubtree(Derive(subTree, variableName));
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| 69 | }
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| 70 | return sum;
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| 71 | }
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| 72 | if (branch.Symbol is Subtraction) {
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| 73 | var sum = subSy.CreateTreeNode();
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| 74 | foreach (var subTree in branch.Subtrees) {
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| 75 | sum.AddSubtree(Derive(subTree, variableName));
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| 76 | }
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| 77 | return sum;
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| 78 | }
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| 79 | if (branch.Symbol is Multiplication) {
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| 80 | // (f * g)' = f'*g + f*g'
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| 81 | // for multiple factors: (f * g * h)' = ((f*g) * h)' = (f*g)' * h + (f*g) * h'
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| 82 |
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| 83 | if (branch.SubtreeCount >= 2) {
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| 84 | var f = (ISymbolicExpressionTreeNode)branch.GetSubtree(0).Clone();
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| 85 | var fprime = Derive(f, variableName);
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[16899] | 86 | for (int i = 1; i < branch.SubtreeCount; i++) {
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| 87 | var g = (ISymbolicExpressionTreeNode)branch.GetSubtree(i).Clone();
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[16206] | 88 | var fg = Product((ISymbolicExpressionTreeNode)f.Clone(), (ISymbolicExpressionTreeNode)g.Clone());
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[16899] | 89 | var gPrime = Derive(g, variableName);
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| 90 | var fgPrime = Sum(Product(fprime, g), Product(gPrime, f));
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| 91 | // prepare for next iteration
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| 92 | f = fg;
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| 93 | fprime = fgPrime;
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[16206] | 94 | }
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[16899] | 95 | return fprime;
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[16294] | 96 | } else
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| 97 | // multiplication with only one argument has no effect -> derive the argument
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| 98 | return Derive(branch.GetSubtree(0), variableName);
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[16206] | 99 | }
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| 100 | if (branch.Symbol is Division) {
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| 101 | // (f/g)' = (f'g - g'f) / g²
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| 102 | if (branch.SubtreeCount == 1) {
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| 103 | var g = (ISymbolicExpressionTreeNode)branch.GetSubtree(0).Clone();
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| 104 | var gPrime = Product(CreateConstant(-1.0), Derive(g, variableName));
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| 105 | var sqrNode = new Square().CreateTreeNode();
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| 106 | sqrNode.AddSubtree(g);
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| 107 | return Div(gPrime, sqrNode);
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[16294] | 108 | } else {
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| 109 | // for two subtrees:
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| 110 | // (f/g)' = (f'g - fg')/g²
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| 111 |
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| 112 | // if there are more than 2 subtrees
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| 113 | // div(x,y,z) is interpretered as (x/y)/z
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| 114 | // which is the same as x / (y*z)
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| 115 |
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| 116 | // --> make a product of all but the first subtree and differentiate as for the 2-argument case above
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[16206] | 117 | var f = (ISymbolicExpressionTreeNode)branch.GetSubtree(0).Clone();
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[16294] | 118 | var g = Product(branch.Subtrees.Skip(1).Select(n => (ISymbolicExpressionTreeNode)n.Clone()));
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[16206] | 119 | var fprime = Derive(f, variableName);
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| 120 | var gprime = Derive(g, variableName);
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[16294] | 121 | var gSqr = Square(g);
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| 122 | return Div(Subtract(Product(fprime, g), Product(f, gprime)), gSqr);
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| 123 | }
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[16206] | 124 | }
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| 125 | if (branch.Symbol is Logarithm) {
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| 126 | var f = (ISymbolicExpressionTreeNode)branch.GetSubtree(0).Clone();
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| 127 | return Product(Div(CreateConstant(1.0), f), Derive(f, variableName));
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| 128 | }
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| 129 | if (branch.Symbol is Exponential) {
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| 130 | var f = (ISymbolicExpressionTreeNode)branch.Clone();
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| 131 | return Product(f, Derive(branch.GetSubtree(0), variableName));
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| 132 | }
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[16294] | 133 | if (branch.Symbol is Square) {
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[16206] | 134 | var f = (ISymbolicExpressionTreeNode)branch.GetSubtree(0).Clone();
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| 135 | return Product(Product(CreateConstant(2.0), f), Derive(f, variableName));
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[16294] | 136 | }
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| 137 | if (branch.Symbol is SquareRoot) {
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[16206] | 138 | var f = (ISymbolicExpressionTreeNode)branch.Clone();
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| 139 | var u = (ISymbolicExpressionTreeNode)branch.GetSubtree(0).Clone();
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[16213] | 140 | return Product(Div(CreateConstant(1.0), Product(CreateConstant(2.0), f)), Derive(u, variableName));
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[16206] | 141 | }
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[16543] | 142 | if (branch.Symbol is CubeRoot) {
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| 143 | var f = (ISymbolicExpressionTreeNode)branch.Clone();
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| 144 | var u = (ISymbolicExpressionTreeNode)branch.GetSubtree(0).Clone();
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| 145 | return Product(Div(CreateConstant(1.0), Product(CreateConstant(3.0), Square(f))), Derive(u, variableName));
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| 146 | }
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| 147 | if (branch.Symbol is Cube) {
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| 148 | var f = (ISymbolicExpressionTreeNode)branch.GetSubtree(0).Clone();
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| 149 | return Product(Product(CreateConstant(3.0), Square(f)), Derive(f, variableName));
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| 150 | }
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| 151 | if (branch.Symbol is Absolute) {
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| 152 | var f = (ISymbolicExpressionTreeNode)branch.GetSubtree(0).Clone();
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| 153 | var absf = Abs((ISymbolicExpressionTreeNode)f.Clone());
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| 154 | return Product(Div(f, absf), Derive(f, variableName));
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| 155 | }
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| 156 | if (branch.Symbol is AnalyticQuotient) {
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| 157 | // aq(a(x), b(x)) = a(x) / sqrt(b(x)²+1)
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| 158 | var a = (ISymbolicExpressionTreeNode)branch.GetSubtree(0).Clone();
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| 159 | var b = (ISymbolicExpressionTreeNode)branch.GetSubtree(1).Clone();
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| 160 |
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| 161 | var definition = Div(a, SquareRoot(Sum(Square(b), CreateConstant(1.0))));
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| 162 | return Derive(definition, variableName);
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| 163 | }
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[16206] | 164 | if (branch.Symbol is Sine) {
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| 165 | var u = (ISymbolicExpressionTreeNode)branch.GetSubtree(0).Clone();
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| 166 | var cos = (new Cosine()).CreateTreeNode();
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| 167 | cos.AddSubtree(u);
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| 168 | return Product(cos, Derive(u, variableName));
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| 169 | }
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| 170 | if (branch.Symbol is Cosine) {
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| 171 | var u = (ISymbolicExpressionTreeNode)branch.GetSubtree(0).Clone();
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| 172 | var sin = (new Sine()).CreateTreeNode();
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| 173 | sin.AddSubtree(u);
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| 174 | return Product(CreateConstant(-1.0), Product(sin, Derive(u, variableName)));
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| 175 | }
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[16294] | 176 | if (branch.Symbol is Tangent) {
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| 177 | // tan(x)' = 1 / cos²(x)
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| 178 | var fxp = Derive(branch.GetSubtree(0), variableName);
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| 179 | var u = (ISymbolicExpressionTreeNode)branch.GetSubtree(0).Clone();
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| 180 | return Div(fxp, Square(Cosine(u)));
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| 181 | }
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[16216] | 182 | throw new NotSupportedException(string.Format("Symbol {0} is not supported.", branch.Symbol));
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[16206] | 183 | }
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| 184 |
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| 185 |
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| 186 | private static ISymbolicExpressionTreeNode Product(ISymbolicExpressionTreeNode f, ISymbolicExpressionTreeNode g) {
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| 187 | var product = mulSy.CreateTreeNode();
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| 188 | product.AddSubtree(f);
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| 189 | product.AddSubtree(g);
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| 190 | return product;
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| 191 | }
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[16294] | 192 | private static ISymbolicExpressionTreeNode Product(IEnumerable<ISymbolicExpressionTreeNode> fs) {
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| 193 | var product = mulSy.CreateTreeNode();
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| 194 | foreach (var f in fs) product.AddSubtree(f);
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| 195 | return product;
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| 196 | }
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[16206] | 197 | private static ISymbolicExpressionTreeNode Div(ISymbolicExpressionTreeNode f, ISymbolicExpressionTreeNode g) {
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| 198 | var div = divSy.CreateTreeNode();
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| 199 | div.AddSubtree(f);
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| 200 | div.AddSubtree(g);
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| 201 | return div;
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| 202 | }
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| 203 |
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| 204 | private static ISymbolicExpressionTreeNode Sum(ISymbolicExpressionTreeNode f, ISymbolicExpressionTreeNode g) {
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| 205 | var sum = addSy.CreateTreeNode();
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| 206 | sum.AddSubtree(f);
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| 207 | sum.AddSubtree(g);
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| 208 | return sum;
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| 209 | }
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| 210 | private static ISymbolicExpressionTreeNode Subtract(ISymbolicExpressionTreeNode f, ISymbolicExpressionTreeNode g) {
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| 211 | var sum = subSy.CreateTreeNode();
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| 212 | sum.AddSubtree(f);
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| 213 | sum.AddSubtree(g);
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| 214 | return sum;
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| 215 | }
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[16294] | 216 | private static ISymbolicExpressionTreeNode Cosine(ISymbolicExpressionTreeNode f) {
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| 217 | var cos = cosSy.CreateTreeNode();
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| 218 | cos.AddSubtree(f);
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| 219 | return cos;
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| 220 | }
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[16543] | 221 | private static ISymbolicExpressionTreeNode Abs(ISymbolicExpressionTreeNode f) {
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| 222 | var abs = absSy.CreateTreeNode();
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| 223 | abs.AddSubtree(f);
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| 224 | return abs;
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| 225 | }
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[16294] | 226 | private static ISymbolicExpressionTreeNode Square(ISymbolicExpressionTreeNode f) {
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| 227 | var sqr = sqrSy.CreateTreeNode();
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| 228 | sqr.AddSubtree(f);
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| 229 | return sqr;
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| 230 | }
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[16543] | 231 | private static ISymbolicExpressionTreeNode SquareRoot(ISymbolicExpressionTreeNode f) {
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| 232 | var sqrt = sqrtSy.CreateTreeNode();
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| 233 | sqrt.AddSubtree(f);
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| 234 | return sqrt;
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| 235 | }
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[16294] | 236 |
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[16206] | 237 | private static ISymbolicExpressionTreeNode CreateConstant(double v) {
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| 238 | var constNode = (ConstantTreeNode)constantSy.CreateTreeNode();
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| 239 | constNode.Value = v;
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| 240 | return constNode;
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| 241 | }
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| 242 |
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| 243 | public static bool IsCompatible(ISymbolicExpressionTree tree) {
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| 244 | var containsUnknownSymbol = (
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| 245 | from n in tree.Root.GetSubtree(0).IterateNodesPrefix()
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| 246 | where
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| 247 | !(n.Symbol is Variable) &&
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| 248 | !(n.Symbol is Constant) &&
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| 249 | !(n.Symbol is Addition) &&
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| 250 | !(n.Symbol is Subtraction) &&
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| 251 | !(n.Symbol is Multiplication) &&
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| 252 | !(n.Symbol is Division) &&
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| 253 | !(n.Symbol is Logarithm) &&
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| 254 | !(n.Symbol is Exponential) &&
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| 255 | !(n.Symbol is Square) &&
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| 256 | !(n.Symbol is SquareRoot) &&
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[16543] | 257 | !(n.Symbol is Cube) &&
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| 258 | !(n.Symbol is CubeRoot) &&
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| 259 | !(n.Symbol is Absolute) &&
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| 260 | !(n.Symbol is AnalyticQuotient) &&
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[16206] | 261 | !(n.Symbol is Sine) &&
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| 262 | !(n.Symbol is Cosine) &&
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[16294] | 263 | !(n.Symbol is Tangent) &&
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[16206] | 264 | !(n.Symbol is StartSymbol)
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| 265 | select n).Any();
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| 266 | return !containsUnknownSymbol;
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| 267 | }
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| 268 | }
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| 269 | }
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