[2616] | 1 | #region License Information
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| 2 | /* HeuristicLab
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| 3 | * Copyright (C) 2002-2008 Heuristic and Evolutionary Algorithms Laboratory (HEAL)
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| 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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| 23 | using System.Collections.Generic;
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| 24 | using System.Linq;
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| 25 | using System.Text;
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| 26 | using HeuristicLab.Core;
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| 27 | using HeuristicLab.Data;
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| 28 | using HeuristicLab.GP.Interfaces;
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| 29 | using HeuristicLab.Modeling;
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| 30 | using HeuristicLab.DataAnalysis;
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| 31 | using System.Diagnostics;
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[2674] | 32 | using HeuristicLab.Common;
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[2616] | 33 |
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| 34 | namespace HeuristicLab.GP.StructureIdentification.Networks {
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| 35 | public class NetworkToFunctionTransformer : OperatorBase {
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| 36 | public NetworkToFunctionTransformer()
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| 37 | : base() {
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| 38 | AddVariableInfo(new VariableInfo("Network", "The network (open expression)", typeof(IGeneticProgrammingModel), VariableKind.In));
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| 39 | AddVariableInfo(new VariableInfo("TargetVariables", "Name of the target variables", typeof(ItemList<StringData>), VariableKind.In));
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| 40 | AddVariableInfo(new VariableInfo("FunctionTree", "The function tree with all targetvaribales", typeof(IGeneticProgrammingModel), VariableKind.New));
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| 41 | }
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| 42 |
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| 43 | public override string Description {
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| 44 | get { return "Extracts the network (function tree with unbound parameters) and creates a closed form function tree for each target variable."; }
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| 45 | }
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| 46 |
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| 47 | public override IOperation Apply(IScope scope) {
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| 48 | IGeneticProgrammingModel model = GetVariableValue<IGeneticProgrammingModel>("Network", scope, true);
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| 49 | ItemList<StringData> targetVariables = GetVariableValue<ItemList<StringData>>("TargetVariables", scope, true);
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| 50 | // clear old sub-scopes
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| 51 | while (scope.SubScopes.Count > 0) scope.RemoveSubScope(scope.SubScopes[0]);
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| 52 |
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[2631] | 53 | var targetVariableEnumerator = targetVariables.Select(x => x.Data).GetEnumerator();
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[2635] | 54 | List<IFunctionTree> transformedTrees = new List<IFunctionTree>(Transform(model.FunctionTree, targetVariables.Select(x => x.Data)));
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[2616] | 55 | // create a new sub-scope for each target variable with the transformed expression
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[2635] | 56 | foreach (IFunctionTree transformedTree in transformedTrees) {
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[2631] | 57 | targetVariableEnumerator.MoveNext();
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[2616] | 58 | Scope exprScope = new Scope();
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| 59 | scope.AddSubScope(exprScope);
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| 60 | exprScope.AddVariable(new HeuristicLab.Core.Variable(scope.TranslateName("FunctionTree"), new GeneticProgrammingModel(transformedTree)));
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[2631] | 61 | exprScope.AddVariable(new HeuristicLab.Core.Variable(scope.TranslateName("TargetVariable"), new StringData(targetVariableEnumerator.Current)));
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[2633] | 62 | Debug.Assert(!(transformedTree is VariableFunctionTree) || ((VariableFunctionTree)transformedTree).VariableName != targetVariableEnumerator.Current);
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[2616] | 63 | }
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| 64 |
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| 65 | return null;
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| 66 | }
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| 67 |
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| 68 | private static IEnumerable<IFunctionTree> Transform(IFunctionTree networkDescription, IEnumerable<string> targetVariables) {
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| 69 | // bind open parameters of network to target variables
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| 70 | //IFunctionTree openExpression = RemoveOpenParameters(networkDescription);
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| 71 | IFunctionTree paritallyEvaluatedOpenExpression = ApplyMetaFunctions((IFunctionTree)networkDescription.Clone());
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[2622] | 72 | IFunctionTree boundExpression = BindVariables(paritallyEvaluatedOpenExpression, targetVariables.GetEnumerator());
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[2616] | 73 |
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| 74 | // create a new sub-scope for each target variable with the transformed expression
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| 75 | foreach (var targetVariable in targetVariables) {
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[2635] | 76 | yield return TransformExpression((IFunctionTree)boundExpression.Clone(), targetVariable, targetVariables.Except(new string[] { targetVariable }));
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[2616] | 77 | }
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| 78 | }
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| 79 |
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[2624] | 80 | /// <summary>
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| 81 | /// applies all tree-transforming meta functions (= cycle and flip)
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| 82 | /// precondition: root is a F2 function (possibly cycle) and the tree contains 0 or n flip functions, each branch has an openparameter symbol in the bottom left
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| 83 | /// postconditon: root is any F2 function (but cycle) and the tree doesn't contains any flips, each branch has an openparameter symbol in the bottom left
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| 84 | /// </summary>
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| 85 | /// <param name="tree"></param>
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| 86 | /// <returns></returns>
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[2616] | 87 | private static IFunctionTree ApplyMetaFunctions(IFunctionTree tree) {
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[2627] | 88 | return ApplyFlips(ApplyCycles(tree));
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[2616] | 89 | }
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| 90 |
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| 91 | private static IFunctionTree ApplyFlips(IFunctionTree tree) {
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| 92 | if (tree.SubTrees.Count == 0) {
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| 93 | return tree;
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| 94 | } else if (tree.Function is Flip) {
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[2630] | 95 | var partiallyAppliedBranch = ApplyFlips(tree.SubTrees[0]);
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[2674] | 96 | if (partiallyAppliedBranch.Function is OpenParameter) {
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| 97 | var openParFunTree = (OpenParameterFunctionTree)partiallyAppliedBranch;
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| 98 | openParFunTree.Weight = 1.0 / openParFunTree.Weight;
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| 99 | return partiallyAppliedBranch;
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| 100 | } else return InvertChain(partiallyAppliedBranch);
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[2616] | 101 | } else {
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[2627] | 102 | List<IFunctionTree> subTrees = new List<IFunctionTree>(tree.SubTrees);
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| 103 | while (tree.SubTrees.Count > 0) tree.RemoveSubTree(0);
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| 104 | foreach (var subTree in subTrees) {
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| 105 | tree.AddSubTree(ApplyFlips(subTree));
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| 106 | }
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[2616] | 107 | return tree;
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| 108 | }
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| 109 | }
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| 110 |
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[2624] | 111 | /// <summary>
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| 112 | /// inverts and reverses chain of functions.
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| 113 | /// precondition: tree is any F1 non-terminal that ends with an openParameter
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| 114 | /// postcondition: tree is inverted and reversed chain of F1 non-terminals and ends with an openparameter.
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| 115 | /// </summary>
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| 116 | /// <param name="tree"></param>
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| 117 | /// <returns></returns>
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| 118 | private static IFunctionTree InvertChain(IFunctionTree tree) {
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| 119 | List<IFunctionTree> currentChain = new List<IFunctionTree>(IterateChain(tree));
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| 120 | // get a list of function trees from bottom to top
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| 121 | List<IFunctionTree> reversedChain = new List<IFunctionTree>(currentChain.Reverse<IFunctionTree>().Skip(1));
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[2674] | 122 | OpenParameterFunctionTree openParam = (OpenParameterFunctionTree)currentChain.Last();
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[2624] | 123 |
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| 124 | // build new tree by inverting every function in the reversed chain and keeping f0 branches untouched.
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| 125 | IFunctionTree parent = reversedChain[0];
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| 126 | IFunctionTree invParent = GetInvertedFunction(parent.Function).GetTreeNode();
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| 127 | for (int j = 1; j < parent.SubTrees.Count; j++) {
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| 128 | invParent.AddSubTree(parent.SubTrees[j]);
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| 129 | }
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| 130 | IFunctionTree root = invParent;
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| 131 | for (int i = 1; i < reversedChain.Count(); i++) {
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| 132 | IFunctionTree child = reversedChain[i];
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| 133 | IFunctionTree invChild = GetInvertedFunction(child.Function).GetTreeNode();
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| 134 | invParent.InsertSubTree(0, invChild);
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| 135 |
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| 136 | parent = child;
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| 137 | invParent = invChild;
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| 138 | for (int j = 1; j < parent.SubTrees.Count; j++) {
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| 139 | invParent.AddSubTree(parent.SubTrees[j]);
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| 140 | }
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| 141 | }
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[2674] | 142 | // invert factor of openParam
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| 143 | openParam.Weight = 1.0 / openParam.Weight;
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[2624] | 144 | // append open param at the end
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[2625] | 145 | invParent.InsertSubTree(0, openParam);
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[2624] | 146 | return root;
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| 147 | }
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| 148 |
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| 149 | private static IEnumerable<IFunctionTree> IterateChain(IFunctionTree tree) {
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| 150 | while (tree.SubTrees.Count > 0) {
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| 151 | yield return tree;
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| 152 | tree = tree.SubTrees[0];
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| 153 | }
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| 154 | yield return tree;
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| 155 | }
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| 156 |
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| 157 |
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| 158 | private static Dictionary<Type, IFunction> invertedFunction = new Dictionary<Type, IFunction>() {
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| 159 | { typeof(AdditionF1), new SubtractionF1() },
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| 160 | { typeof(SubtractionF1), new AdditionF1() },
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| 161 | { typeof(MultiplicationF1), new DivisionF1() },
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| 162 | { typeof(DivisionF1), new MultiplicationF1() },
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| 163 | { typeof(OpenLog), new OpenExp() },
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| 164 | { typeof(OpenExp), new OpenLog() },
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| 165 | //{ typeof(OpenSqr), new OpenSqrt() },
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| 166 | //{ typeof(OpenSqrt), new OpenSqr() },
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| 167 | { typeof(Flip), new Flip()},
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| 168 | { typeof(Addition), new Subtraction()},
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| 169 | { typeof(Subtraction), new Addition()},
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| 170 | { typeof(Multiplication), new Division()},
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| 171 | { typeof(Division), new Multiplication()},
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| 172 | { typeof(Exponential), new Logarithm()},
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| 173 | { typeof(Logarithm), new Exponential()}
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| 174 | };
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| 175 | private static IFunction GetInvertedFunction(IFunction function) {
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| 176 | return invertedFunction[function.GetType()];
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| 177 | }
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| 178 |
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[2616] | 179 | private static IFunctionTree ApplyCycles(IFunctionTree tree) {
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| 180 | int nRotations = 0;
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| 181 | while (tree.Function is Cycle) {
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| 182 | nRotations++;
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| 183 | tree = tree.SubTrees[0];
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| 184 | }
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| 185 | if (nRotations > 0 && nRotations % tree.SubTrees.Count > 0) {
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| 186 | IFunctionTree[] subTrees = tree.SubTrees.ToArray();
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| 187 | while (tree.SubTrees.Count > 0) tree.RemoveSubTree(0);
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| 188 |
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| 189 | nRotations = nRotations % subTrees.Length;
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| 190 | Array.Reverse(subTrees, 0, nRotations);
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| 191 | Array.Reverse(subTrees, nRotations, subTrees.Length - nRotations);
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| 192 | Array.Reverse(subTrees, 0, subTrees.Length);
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| 193 |
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| 194 | for (int i = 0; i < subTrees.Length; i++) {
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| 195 | tree.AddSubTree(subTrees[i]);
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| 196 | }
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| 197 | }
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| 198 | return tree;
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| 199 | }
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| 200 |
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| 201 |
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[2627] | 202 |
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[2674] | 203 | //private static IFunctionTree AppendLeft(IFunctionTree tree, IFunctionTree node) {
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| 204 | // IFunctionTree originalTree = tree;
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| 205 | // while (!IsBottomLeft(tree)) tree = tree.SubTrees[0];
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| 206 | // tree.InsertSubTree(0, node);
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| 207 | // return originalTree;
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| 208 | //}
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[2616] | 209 |
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[2625] | 210 | private static bool IsBottomLeft(IFunctionTree tree) {
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[2627] | 211 | if (tree.SubTrees.Count == 0) return true;
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| 212 | else if (tree.SubTrees[0].Function is Variable) return true;
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| 213 | else if (tree.SubTrees[0].Function is Constant) return true;
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[2625] | 214 | else return false;
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| 215 | }
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| 216 |
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[2624] | 217 | /// <summary>
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[2627] | 218 | /// recieves a function tree transforms it into a function-tree for the given target variable
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[2624] | 219 | /// </summary>
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| 220 | /// <param name="tree"></param>
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| 221 | /// <param name="targetVariable"></param>
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| 222 | /// <returns></returns>
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[2627] | 223 | private static IFunctionTree TransformExpression(IFunctionTree tree, string targetVariable, IEnumerable<string> parameters) {
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[2633] | 224 | if (tree.Function is Constant) return tree;
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| 225 | if (tree.Function is Variable || tree.Function is Differential) {
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| 226 | VariableFunctionTree varTree = (VariableFunctionTree)tree;
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| 227 | varTree.Weight = 1.0;
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| 228 | if (varTree.VariableName == targetVariable) varTree.VariableName = parameters.First();
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| 229 | return varTree;
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| 230 | }
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[2627] | 231 | if (tree.Function is Addition || tree.Function is Subtraction ||
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| 232 | tree.Function is Multiplication || tree.Function is Division ||
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| 233 | tree.Function is Exponential || tree.Function is Logarithm) {
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| 234 | var occuringVariables = from x in FunctionTreeIterator.IteratePrefix(tree)
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| 235 | where x is VariableFunctionTree
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| 236 | let name = ((VariableFunctionTree)x).VariableName
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| 237 | select name;
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| 238 | var openParameters = (new string[] { targetVariable }).Concat(parameters);
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| 239 | var missingVariables = openParameters.Except(occuringVariables);
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| 240 | if (missingVariables.Count() > 0) {
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| 241 | VariableFunctionTree varTree = (VariableFunctionTree)(new Variable()).GetTreeNode();
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| 242 | varTree.VariableName = missingVariables.First();
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| 243 | varTree.SampleOffset = 0;
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| 244 | varTree.Weight = 1.0;
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| 245 | tree = (IFunctionTree)tree.Clone();
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| 246 | tree.InsertSubTree(0, varTree);
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| 247 | }
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| 248 | }
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[2624] | 249 | int targetIndex = -1;
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[2627] | 250 | IFunctionTree combinator = null;
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[2624] | 251 | List<IFunctionTree> subTrees = new List<IFunctionTree>(tree.SubTrees);
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| 252 | if (HasTargetVariable(subTrees[0], targetVariable)) {
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| 253 | targetIndex = 0;
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[2627] | 254 | combinator = FunctionFromCombinator(tree).GetTreeNode();
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[2624] | 255 | } else {
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| 256 | for (int i = 1; i < subTrees.Count; i++) {
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| 257 | if (HasTargetVariable(subTrees[i], targetVariable)) {
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| 258 | targetIndex = i;
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[2627] | 259 | combinator = GetInvertedFunction(FunctionFromCombinator(tree)).GetTreeNode();
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[2624] | 260 | break;
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[2616] | 261 | }
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| 262 | }
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| 263 | }
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[2627] | 264 | if (targetIndex == -1) {
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| 265 | // target variable was not found
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| 266 | return tree;
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| 267 | } else {
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| 268 | // target variable was found
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| 269 | for (int i = 0; i < subTrees.Count; i++) {
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| 270 | if (i != targetIndex)
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| 271 | combinator.AddSubTree(subTrees[i]);
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| 272 | }
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[2674] | 273 | if (subTrees[targetIndex].Function is Variable) return MakeMultiplication(combinator, 1.0 / GetTargetVariableWeight(subTrees[targetIndex]));
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[2627] | 274 | else {
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[2630] | 275 | IFunctionTree bottomLeft;
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| 276 | IFunctionTree targetChain = InvertF0Chain(subTrees[targetIndex], out bottomLeft);
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| 277 | bottomLeft.InsertSubTree(0, combinator);
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[2674] | 278 | return MakeMultiplication(targetChain, 1.0 / GetTargetVariableWeight(subTrees[targetIndex]));
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[2627] | 279 | }
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[2624] | 280 | }
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[2616] | 281 | }
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| 282 |
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[2674] | 283 | private static IFunctionTree MakeMultiplication(IFunctionTree tree, double p) {
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| 284 | if (p.IsAlmost(1.0)) return tree;
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| 285 | var mul = (new Multiplication()).GetTreeNode();
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| 286 | var constP = (ConstantFunctionTree)(new Constant()).GetTreeNode();
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| 287 | constP.Value = p;
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| 288 | mul.AddSubTree(tree);
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| 289 | mul.AddSubTree(constP);
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| 290 | return mul;
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| 291 | }
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| 292 |
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| 293 | private static double GetTargetVariableWeight(IFunctionTree tree) {
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| 294 | while (tree.SubTrees.Count > 0) {
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| 295 | tree = tree.SubTrees[0];
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| 296 | }
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| 297 | return ((VariableFunctionTree)tree).Weight;
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| 298 | }
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| 299 |
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[2624] | 300 | // inverts a chain of F0 functions
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| 301 | // precondition: left bottom is a variable (the selected target variable)
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| 302 | // postcondition: the chain is inverted. the target variable is removed
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[2630] | 303 | private static IFunctionTree InvertF0Chain(IFunctionTree tree, out IFunctionTree bottomLeft) {
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[2624] | 304 | List<IFunctionTree> currentChain = IterateChain(tree).ToList();
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| 305 |
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| 306 | List<IFunctionTree> reversedChain = currentChain.Reverse<IFunctionTree>().Skip(1).ToList();
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| 307 |
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| 308 | // build new tree by inverting every function in the reversed chain and keeping f0 branches untouched.
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| 309 | IFunctionTree parent = reversedChain[0];
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| 310 | IFunctionTree invParent = GetInvertedFunction(parent.Function).GetTreeNode();
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| 311 | for (int j = 1; j < parent.SubTrees.Count; j++) {
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| 312 | invParent.AddSubTree(parent.SubTrees[j]);
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| 313 | }
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| 314 | IFunctionTree root = invParent;
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| 315 | for (int i = 1; i < reversedChain.Count(); i++) {
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| 316 | IFunctionTree child = reversedChain[i];
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| 317 | IFunctionTree invChild = GetInvertedFunction(child.Function).GetTreeNode();
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| 318 | invParent.InsertSubTree(0, invChild);
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| 319 | parent = child;
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| 320 | invParent = invChild;
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| 321 | for (int j = 1; j < parent.SubTrees.Count; j++) {
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| 322 | invParent.AddSubTree(parent.SubTrees[j]);
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[2622] | 323 | }
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| 324 | }
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[2630] | 325 | bottomLeft = invParent;
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[2624] | 326 | return root;
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[2622] | 327 | }
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| 328 |
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[2616] | 329 |
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[2627] | 330 |
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| 331 | //private static IFunctionTree InvertCombinator(IFunctionTree tree) {
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| 332 | // if (tree.Function is OpenAddition) {
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| 333 | // return (new OpenSubtraction()).GetTreeNode();
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| 334 | // } else if (tree.Function is OpenSubtraction) {
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| 335 | // return (new OpenAddition()).GetTreeNode();
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| 336 | // } else if (tree.Function is OpenMultiplication) {
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| 337 | // return (new OpenDivision()).GetTreeNode();
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| 338 | // } else if (tree.Function is OpenDivision) {
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| 339 | // return (new OpenMultiplication()).GetTreeNode();
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| 340 | // } else throw new InvalidOperationException();
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| 341 | //}
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| 342 |
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| 343 | private static Dictionary<Type, IFunction> combinatorFunction = new Dictionary<Type, IFunction>() {
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| 344 | { typeof(OpenAddition), new Addition()},
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| 345 | { typeof(OpenSubtraction), new Subtraction()},
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| 346 | { typeof(OpenDivision), new Division()},
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| 347 | { typeof(OpenMultiplication), new Multiplication()},
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| 348 | { typeof(Addition), new Addition()},
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| 349 | { typeof(Subtraction), new Subtraction()},
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| 350 | { typeof(Division), new Division()},
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| 351 | { typeof(Multiplication), new Multiplication()},
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| 352 | { typeof(Logarithm), new Logarithm()},
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| 353 | { typeof(Exponential), new Exponential()},
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| 354 | };
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| 355 | private static IFunction FunctionFromCombinator(IFunctionTree tree) {
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| 356 | return combinatorFunction[tree.Function.GetType()];
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[2616] | 357 | }
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| 358 |
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| 359 | private static bool HasTargetVariable(IFunctionTree tree, string targetVariable) {
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| 360 | if (tree.SubTrees.Count == 0) {
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[2622] | 361 | var varTree = tree as VariableFunctionTree;
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| 362 | if (varTree != null) return varTree.VariableName == targetVariable;
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| 363 | else return false;
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| 364 | } else return (from x in tree.SubTrees
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| 365 | where HasTargetVariable(x, targetVariable)
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| 366 | select true).Any();
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[2616] | 367 | }
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| 368 |
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[2624] | 369 | private static Dictionary<Type, IFunction> closedForm = new Dictionary<Type, IFunction>() {
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| 370 | {typeof(OpenAddition), new OpenAddition()},
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| 371 | {typeof(OpenSubtraction), new OpenSubtraction()},
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| 372 | {typeof(OpenMultiplication), new OpenMultiplication()},
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| 373 | {typeof(OpenDivision), new OpenDivision()},
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| 374 | {typeof(AdditionF1), new Addition()},
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| 375 | {typeof(SubtractionF1), new Subtraction()},
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| 376 | {typeof(MultiplicationF1), new Multiplication()},
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| 377 | {typeof(DivisionF1), new Division()},
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| 378 | {typeof(OpenExp), new Exponential()},
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[2627] | 379 | {typeof(OpenLog), new Logarithm()},
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[2624] | 380 | //{typeof(OpenSqr), new Power()},
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| 381 | //{typeof(OpenSqrt), new Sqrt()},
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| 382 | {typeof(OpenParameter), new Variable()},
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| 383 | };
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| 384 |
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| 385 | /// <summary>
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| 386 | /// transforms a tree that contains F2 and F1 functions into a tree composed of F2 and F0 functions.
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| 387 | /// precondition: the tree doesn't contains cycle or flip symbols. the tree has openparameters in the bottom left
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| 388 | /// postcondition: all F1 and functions are replaced by matching F0 functions
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| 389 | /// </summary>
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| 390 | /// <param name="tree"></param>
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| 391 | /// <param name="targetVariables"></param>
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| 392 | /// <returns></returns>
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[2622] | 393 | private static IFunctionTree BindVariables(IFunctionTree tree, IEnumerator<string> targetVariables) {
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[2624] | 394 | if (!closedForm.ContainsKey(tree.Function.GetType())) return tree;
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| 395 | IFunction matchingFunction = closedForm[tree.Function.GetType()];
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| 396 | IFunctionTree matchingTree = matchingFunction.GetTreeNode();
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| 397 | if (matchingFunction is Variable) {
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| 398 | targetVariables.MoveNext();
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| 399 | var varTreeNode = (VariableFunctionTree)matchingTree;
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[2622] | 400 | varTreeNode.VariableName = targetVariables.Current;
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| 401 | varTreeNode.SampleOffset = ((OpenParameterFunctionTree)tree).SampleOffset;
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[2674] | 402 | varTreeNode.Weight = ((OpenParameterFunctionTree)tree).Weight;
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[2622] | 403 | return varTreeNode;
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[2624] | 404 | //} else if (matchingFunction is Power) {
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| 405 | // matchingTree.AddSubTree(BindVariables(tree.SubTrees[0], targetVariables));
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| 406 | // var const2 = (ConstantFunctionTree)(new Constant()).GetTreeNode();
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| 407 | // const2.Value = 2.0;
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| 408 | // matchingTree.AddSubTree(const2);
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[2622] | 409 | } else {
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[2624] | 410 | foreach (IFunctionTree subTree in tree.SubTrees) {
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| 411 | matchingTree.AddSubTree(BindVariables(subTree, targetVariables));
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[2616] | 412 | }
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| 413 | }
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[2624] | 414 |
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| 415 | return matchingTree;
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[2616] | 416 | }
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| 417 | }
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| 418 | }
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