source: branches/3073_IA_constraint_splitting/HeuristicLab.Problems.DataAnalysis.Symbolic/3.4/Interpreter/IntervalInterpreter.cs @ 17757

#region License Information

/* HeuristicLab
 * Copyright (C) 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
 * the Free Software Foundation, either version 3 of the License, or
 * (at your option) any later version.
 *
 * 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
 * along with HeuristicLab. If not, see <http://www.gnu.org/licenses/>.
 */

#endregion

using System;
using System.Collections.Generic;
using System.Collections.ObjectModel;
using System.Linq;
using HEAL.Attic;
using HeuristicLab.Common;
using HeuristicLab.Core;
using HeuristicLab.Data;
using HeuristicLab.Encodings.SymbolicExpressionTreeEncoding;
using HeuristicLab.Parameters;

namespace HeuristicLab.Problems.DataAnalysis.Symbolic {
  [StorableType("DE6C1E1E-D7C1-4070-847E-63B68562B10C")]
  [Item("IntervalInterpreter", "Interpreter for calculation of intervals of symbolic models.")]
  public sealed class IntervalInterpreter : ParameterizedNamedItem, IStatefulItem {
    private const string EvaluatedSolutionsParameterName = "EvaluatedSolutions";
    private const string MinSplittingWidthParameterName = "MinSplittingWidth";
    private const string MaxSplittingDepthParameterName = "MaxSplittingDepth";
    private const string UseIntervalSplittingParameterName = "UseIntervalSplitting";

    public IFixedValueParameter<IntValue> EvaluatedSolutionsParameter =>
      (IFixedValueParameter<IntValue>)Parameters[EvaluatedSolutionsParameterName];

    public IFixedValueParameter<IntValue> MinSplittingWithParameter =>
      (IFixedValueParameter<IntValue>)Parameters[MinSplittingWidthParameterName];

    public IFixedValueParameter<IntValue> MaxSplittingDepthParameter =>
      (IFixedValueParameter<IntValue>)Parameters[MaxSplittingDepthParameterName];

    public IFixedValueParameter<BoolValue> UseIntervalSplittingParameter =>
      (IFixedValueParameter<BoolValue>)Parameters[UseIntervalSplittingParameterName];

    public int MinSplittingWidth {
      get => MinSplittingWithParameter.Value.Value;
      set => MinSplittingWithParameter.Value.Value = value;
    }

    public int MaxSplittingDepth {
      get => MaxSplittingDepthParameter.Value.Value;
      set => MaxSplittingDepthParameter.Value.Value = value;
    }

    public bool UseIntervalSplitting {
      get => UseIntervalSplittingParameter.Value.Value;
      set => UseIntervalSplittingParameter.Value.Value = value;
    }

    public int EvaluatedSolutions {
      get => EvaluatedSolutionsParameter.Value.Value;
      set => EvaluatedSolutionsParameter.Value.Value = value;
    }

    [StorableConstructor]
    private IntervalInterpreter(StorableConstructorFlag _) : base(_) { }

    private IntervalInterpreter(IntervalInterpreter original, Cloner cloner)
      : base(original, cloner) { }

    public IntervalInterpreter()
      : base("IntervalInterpreter", "Interpreter for calculation of intervals of symbolic models.") {
      Parameters.Add(new FixedValueParameter<IntValue>(EvaluatedSolutionsParameterName,
        "A counter for the total number of solutions the interpreter has evaluated", new IntValue(0)));
      Parameters.Add(new FixedValueParameter<IntValue>(MinSplittingWidthParameterName,
        "Minimum interval width until splitting is stopped", new IntValue(0)));
      Parameters.Add(new FixedValueParameter<IntValue>(MaxSplittingDepthParameterName,
        "Maximum recursion depth of the splitting", new IntValue(5)));
      Parameters.Add(new FixedValueParameter<BoolValue>(UseIntervalSplittingParameterName, "", new BoolValue(false)));
    }

    public override IDeepCloneable Clone(Cloner cloner) {
      return new IntervalInterpreter(this, cloner);
    }

    private readonly object syncRoot = new object();

    #region IStatefulItem Members

    public void InitializeState() {
      EvaluatedSolutions = 0;
    }

    public void ClearState() { }

    #endregion

    public Interval GetSymbolicExpressionTreeInterval(
      ISymbolicExpressionTree tree, IDataset dataset,
      IEnumerable<int> rows = null) {
      var variableRanges = DatasetUtil.GetVariableRanges(dataset, rows);
      return GetSymbolicExpressionTreeInterval(tree, variableRanges);
    }

    public Interval GetSymbolicExpressionTreeIntervals(
      ISymbolicExpressionTree tree, IDataset dataset,
      out IDictionary<ISymbolicExpressionTreeNode, Interval>
        nodeIntervals, IEnumerable<int> rows = null) {
      var variableRanges = DatasetUtil.GetVariableRanges(dataset, rows);
      return GetSymbolicExpressionTreeIntervals(tree, variableRanges, out nodeIntervals);
    }

    public Interval GetSymbolicExpressionTreeInterval(
      ISymbolicExpressionTree tree,
      IReadOnlyDictionary<string, Interval> variableRanges) {
      lock (syncRoot) {
        EvaluatedSolutions++;
      }

      Interval outputInterval;

      if (UseIntervalSplitting) {
        outputInterval = GetSymbolicExpressionTreeIntervals(tree, variableRanges,
          out var _);
      } else {
        var instructionCount = 0;
        var instructions = PrepareInterpreterState(tree, variableRanges);
        outputInterval = Evaluate(instructions, ref instructionCount);
      }

      return outputInterval.LowerBound <= outputInterval.UpperBound
        ? outputInterval
        : new Interval(outputInterval.UpperBound, outputInterval.LowerBound);
    }


    public Interval GetSymbolicExpressionTreeIntervals(
      ISymbolicExpressionTree tree,
      IReadOnlyDictionary<string, Interval> variableRanges,
      out IDictionary<ISymbolicExpressionTreeNode, Interval>
        nodeIntervals) {
      lock (syncRoot) {
        EvaluatedSolutions++;
      }

      var intervals = new Dictionary<ISymbolicExpressionTreeNode, Interval>();
      var instructions = PrepareInterpreterState(tree, variableRanges);

      Interval outputInterval;
      if (UseIntervalSplitting) {
        var variables = tree.IterateNodesPrefix().OfType<VariableTreeNode>().Select(x => x.VariableName).Distinct()
                            .ToList();
        var containsDependencyProblem = ContainsVariableMultipleTimes(tree);

        if (containsDependencyProblem) {
          var currIndex = 0;
          var currDepth = 0;
          IDictionary<string, Interval> writeableVariableRanges =
            variableRanges.ToDictionary(kvp => kvp.Key, kvp => kvp.Value);
          //outputInterval = EvaluateRecursive(instructions, intervals, writeableVariableRanges, variables, MinSplittingWidth, MaxSplittingDepth,
          //  ref currIndex, ref currDepth, tree);
          outputInterval = EvaluateWithSplitting(instructions, intervals, writeableVariableRanges);
        } else {
          var instructionCount = 0;
          outputInterval = Evaluate(instructions, ref instructionCount, intervals);
        }
      } else {
        var instructionCount = 0;
        outputInterval = Evaluate(instructions, ref instructionCount, intervals);
      }

      nodeIntervals = new Dictionary<ISymbolicExpressionTreeNode, Interval>();
      foreach (var kvp in intervals) {
        var interval = kvp.Value;
        if (interval.IsInfiniteOrUndefined || interval.LowerBound <= interval.UpperBound)
          nodeIntervals.Add(kvp.Key, interval);
        else
          nodeIntervals.Add(kvp.Key, new Interval(interval.UpperBound, interval.LowerBound));
      }

      // because of numerical errors the bounds might be incorrect
      if (outputInterval.IsInfiniteOrUndefined || outputInterval.LowerBound <= outputInterval.UpperBound)
        return outputInterval;

      return new Interval(outputInterval.UpperBound, outputInterval.LowerBound);
    }


    private static Instruction[] PrepareInterpreterState(
      ISymbolicExpressionTree tree,
      IReadOnlyDictionary<string, Interval> variableRanges) {
      if (variableRanges == null)
        throw new ArgumentNullException("No variablew ranges are present!", nameof(variableRanges));

      //Check if all variables used in the tree are present in the dataset
      foreach (var variable in tree.IterateNodesPrefix().OfType<VariableTreeNode>().Select(n => n.VariableName)
                                   .Distinct())
        if (!variableRanges.ContainsKey(variable))
          throw new InvalidOperationException($"No ranges for variable {variable} is present");

      var code = SymbolicExpressionTreeCompiler.Compile(tree, OpCodes.MapSymbolToOpCode);
      foreach (var instr in code.Where(i => i.opCode == OpCodes.Variable)) {
        var variableTreeNode = (VariableTreeNode)instr.dynamicNode;
        instr.data = variableRanges[variableTreeNode.VariableName];
      }

      return code;
    }

    public static Interval EvaluateWithSplitting(Instruction[] instructions,
                                                 IDictionary<ISymbolicExpressionTreeNode, Interval> nodeIntervals,
                                                 IDictionary<string, Interval> variableIntervals) {
      var savedIntervals = variableIntervals.ToDictionary(entry => entry.Key, entry => entry.Value);
      var min = FindBound(instructions, nodeIntervals, variableIntervals, minimization: true);
      var max = FindBound(instructions, nodeIntervals, savedIntervals, minimization: false);

      return new Interval(min, max);
    }


    private static double FindBound(Instruction[] instructions,
                                    IDictionary<ISymbolicExpressionTreeNode, Interval> nodeIntervals,
                                    IDictionary<string, Interval> variableIntervals, bool minimization = true) {
      SortedSet<BoxBound> prioQ = new SortedSet<BoxBound>();

      var ic = 0;
      //Calculate full box
      IReadOnlyDictionary<string, Interval> readonlyRanges = variableIntervals.ToDictionary(k => k.Key, k => k.Value);
      var interval = Evaluate(instructions, ref ic, nodeIntervals, readonlyRanges);
      // the order of keys in a dictionary is guaranteed to be the same order as values in a dictionary
      // https://docs.microsoft.com/en-us/dotnet/api/system.collections.idictionary.keys?view=netcore-3.1#remarks
      var box = variableIntervals.Values;
      if (minimization) {
        prioQ.Add(new BoxBound(box, interval.LowerBound));
      } else {
        prioQ.Add(new BoxBound(box, -interval.UpperBound));
      }

      // TODO a fixed limit for depth?!
      for (var depth = 0; depth < 200; ++depth) {
        var currentBound = prioQ.Min;
        prioQ.Remove(currentBound);

        var newBoxes = Split(currentBound.box);

        foreach (var newBox in newBoxes) {
          var intervalEnum = newBox.GetEnumerator();
          var keyEnum = readonlyRanges.Keys.GetEnumerator();
          while (intervalEnum.MoveNext() & keyEnum.MoveNext()) {
            variableIntervals[keyEnum.Current] = intervalEnum.Current;
          }

          ic = 0;
          var res = Evaluate(instructions, ref ic, nodeIntervals,
            new ReadOnlyDictionary<string, Interval>(variableIntervals));
          if (minimization) {
            prioQ.Add(new BoxBound(newBox, interval.LowerBound));
          } else {
            prioQ.Add(new BoxBound(newBox, -interval.UpperBound));
          }
        }
      }

      return minimization ?
        prioQ.First().bound :
        -prioQ.First().bound;
    }

    private static IEnumerable<IEnumerable<Interval>> Split(List<Interval> box) {
      var boxes = box.Select(region => region.Split()).Select(split => new List<Interval> { split.Item1, split.Item2 })
                     .ToList();

      return boxes.CartesianProduct();
    }

    // a multi-dimensional box with an associated bound
    // boxbounds are ordered first by bound (smaller first), then by size of box (larger first) then by distance of bottom left corner to origin
    private class BoxBound : IComparable<BoxBound> {
      public List<Interval> box;
      public double bound;
      public BoxBound(IEnumerable<Interval> box, double bound) {
        this.box = new List<Interval>(box);
        this.bound = bound;
      }
      public int CompareTo(BoxBound other) {
        if (bound != other.bound) return bound.CompareTo(other.bound);

        var thisSize = box.Aggregate(1.0, (current, dimExtent) => current * dimExtent.Width);
        var otherSize = other.box.Aggregate(1.0, (current, dimExtent) => current * dimExtent.Width);
        if (thisSize != otherSize) return -thisSize.CompareTo(otherSize);

        var thisDist = box.Sum(dimExtent => dimExtent.LowerBound * dimExtent.LowerBound);
        var otherDist = other.box.Sum(dimExtent => dimExtent.LowerBound * dimExtent.LowerBound);
        if (thisDist != otherDist) return thisDist.CompareTo(otherDist);

        // which is smaller first along the dimensions?
        for (int i = 0; i < box.Count; i++) {
          if (box[i].LowerBound != other.box[i].LowerBound) return box[i].LowerBound.CompareTo(other.box[i].LowerBound);
        }

        return 0;
      }

      public static Interval EvaluateRecursive(
        Instruction[] instructions,
        IDictionary<ISymbolicExpressionTreeNode, Interval> nodeIntervals,
        IDictionary<string, Interval> variableIntervals, IList<string> variables,
        double minWidth, int maxDepth, ref int currIndex, ref int currDepth,
        ISymbolicExpressionTree tree) {
        Interval evaluate() {
          var ic = 0;
          IReadOnlyDictionary<string, Interval> readonlyRanges =
            new ReadOnlyDictionary<string, Interval>(variableIntervals);
          return Evaluate(instructions, ref ic, nodeIntervals, readonlyRanges);
        }

        Interval recurse(ref int idx, ref int depth) {
          return EvaluateRecursive(instructions, nodeIntervals, variableIntervals, variables, minWidth, maxDepth, ref idx,
            ref depth, tree);
        }


        var v = variables[currIndex];
        var x = variableIntervals[v];
        if (x.Width < minWidth || currDepth == maxDepth || !MultipleTimes(tree, v)) {
          if (currIndex + 1 < variables.Count) {
            currDepth = 0;
            currIndex++;
            var z = recurse(ref currIndex, ref currDepth);
            currIndex--;
            return z;
          }

          return evaluate();
        }

        var t = x.Split();
        var xa = t.Item1;
        var xb = t.Item2;
        var d = currDepth;
        currDepth = d + 1;
        variableIntervals[v] = xa;
        var ya = recurse(ref currIndex, ref currDepth);
        currDepth = d + 1;
        variableIntervals[v] = xb;
        var yb = recurse(ref currIndex, ref currDepth);
        variableIntervals[v] = x; // restore interval
        return ya | yb;
      }

      public static Interval Evaluate(
        Instruction[] instructions, ref int instructionCounter,
        IDictionary<ISymbolicExpressionTreeNode, Interval> nodeIntervals = null,
        IReadOnlyDictionary<string, Interval> variableIntervals = null) {
        var currentInstr = instructions[instructionCounter];
        //Use ref parameter, because the tree will be iterated through recursively from the left-side branch to the right side
        //Update instructionCounter, whenever Evaluate is called
        instructionCounter++;
        Interval result = null;

        switch (currentInstr.opCode) {
          //Variables, Constants, ...
          case OpCodes.Variable: {
              var variableTreeNode = (VariableTreeNode)currentInstr.dynamicNode;
              var weightInterval = new Interval(variableTreeNode.Weight, variableTreeNode.Weight);
              //var variableInterval = (Interval)currentInstr.data;

              Interval variableInterval;
              if (variableIntervals != null && variableIntervals.ContainsKey(variableTreeNode.VariableName))
                variableInterval = variableIntervals[variableTreeNode.VariableName];
              else
                variableInterval = (Interval)currentInstr.data;

              result = Interval.Multiply(variableInterval, weightInterval);
              break;
            }
          case OpCodes.Constant: {
              var constTreeNode = (ConstantTreeNode)currentInstr.dynamicNode;
              result = new Interval(constTreeNode.Value, constTreeNode.Value);
              break;
            }
          //Elementary arithmetic rules
          case OpCodes.Add: {
              //result = Evaluate(instructions, ref instructionCounter, nodeIntervals);
              result = Evaluate(instructions, ref instructionCounter, nodeIntervals, variableIntervals);
              for (var i = 1; i < currentInstr.nArguments; i++) {
                //var argumentInterval = Evaluate(instructions, ref instructionCounter, nodeIntervals);
                var argumentInterval = Evaluate(instructions, ref instructionCounter, nodeIntervals, variableIntervals);
                result = Interval.Add(result, argumentInterval);
              }

              break;
            }
          case OpCodes.Sub: {
              //result = Evaluate(instructions, ref instructionCounter, nodeIntervals);
              result = Evaluate(instructions, ref instructionCounter, nodeIntervals, variableIntervals);
              if (currentInstr.nArguments == 1)
                result = Interval.Multiply(new Interval(-1, -1), result);

              for (var i = 1; i < currentInstr.nArguments; i++) {
                //var argumentInterval = Evaluate(instructions, ref instructionCounter, nodeIntervals);
                var argumentInterval = Evaluate(instructions, ref instructionCounter, nodeIntervals, variableIntervals);
                result = Interval.Subtract(result, argumentInterval);
              }

              break;
            }
          case OpCodes.Mul: {
              //result = Evaluate(instructions, ref instructionCounter, nodeIntervals);
              result = Evaluate(instructions, ref instructionCounter, nodeIntervals, variableIntervals);
              for (var i = 1; i < currentInstr.nArguments; i++) {
                var argumentInterval = Evaluate(instructions, ref instructionCounter, nodeIntervals, variableIntervals);
                //var argumentInterval = Evaluate(instructions, ref instructionCounter, nodeIntervals);
                result = Interval.Multiply(result, argumentInterval);
              }

              break;
            }
          case OpCodes.Div: {
              //result = Evaluate(instructions, ref instructionCounter, nodeIntervals);
              result = Evaluate(instructions, ref instructionCounter, nodeIntervals, variableIntervals);
              if (currentInstr.nArguments == 1)
                result = Interval.Divide(new Interval(1, 1), result);

              for (var i = 1; i < currentInstr.nArguments; i++) {
                //var argumentInterval = Evaluate(instructions, ref instructionCounter, nodeIntervals);
                var argumentInterval = Evaluate(instructions, ref instructionCounter, nodeIntervals, variableIntervals);
                result = Interval.Divide(result, argumentInterval);
              }

              break;
            }
          //Trigonometric functions
          case OpCodes.Sin: {
              //var argumentInterval = Evaluate(instructions, ref instructionCounter, nodeIntervals);
              var argumentInterval = Evaluate(instructions, ref instructionCounter, nodeIntervals, variableIntervals);
              result = Interval.Sine(argumentInterval);
              break;
            }
          case OpCodes.Cos: {
              //var argumentInterval = Evaluate(instructions, ref instructionCounter, nodeIntervals);
              var argumentInterval = Evaluate(instructions, ref instructionCounter, nodeIntervals, variableIntervals);
              result = Interval.Cosine(argumentInterval);
              break;
            }
          case OpCodes.Tan: {
              //var argumentInterval = Evaluate(instructions, ref instructionCounter, nodeIntervals);
              var argumentInterval = Evaluate(instructions, ref instructionCounter, nodeIntervals, variableIntervals);
              result = Interval.Tangens(argumentInterval);
              break;
            }
          case OpCodes.Tanh: {
              //var argumentInterval = Evaluate(instructions, ref instructionCounter, nodeIntervals);
              var argumentInterval = Evaluate(instructions, ref instructionCounter, nodeIntervals, variableIntervals);
              result = Interval.HyperbolicTangent(argumentInterval);
              break;
            }
          //Exponential functions
          case OpCodes.Log: {
              //var argumentInterval = Evaluate(instructions, ref instructionCounter, nodeIntervals);
              var argumentInterval = Evaluate(instructions, ref instructionCounter, nodeIntervals, variableIntervals);
              result = Interval.Logarithm(argumentInterval);
              break;
            }
          case OpCodes.Exp: {
              //var argumentInterval = Evaluate(instructions, ref instructionCounter, nodeIntervals);
              var argumentInterval = Evaluate(instructions, ref instructionCounter, nodeIntervals, variableIntervals);
              result = Interval.Exponential(argumentInterval);
              break;
            }
          case OpCodes.Square: {
              //var argumentInterval = Evaluate(instructions, ref instructionCounter, nodeIntervals);
              var argumentInterval = Evaluate(instructions, ref instructionCounter, nodeIntervals, variableIntervals);
              result = Interval.Square(argumentInterval);
              break;
            }
          case OpCodes.SquareRoot: {
              //var argumentInterval = Evaluate(instructions, ref instructionCounter, nodeIntervals);
              var argumentInterval = Evaluate(instructions, ref instructionCounter, nodeIntervals, variableIntervals);
              result = Interval.SquareRoot(argumentInterval);
              break;
            }
          case OpCodes.Cube: {
              //var argumentInterval = Evaluate(instructions, ref instructionCounter, nodeIntervals);
              var argumentInterval = Evaluate(instructions, ref instructionCounter, nodeIntervals, variableIntervals);
              result = Interval.Cube(argumentInterval);
              break;
            }
          case OpCodes.CubeRoot: {
              //var argumentInterval = Evaluate(instructions, ref instructionCounter, nodeIntervals);
              var argumentInterval = Evaluate(instructions, ref instructionCounter, nodeIntervals, variableIntervals);
              result = Interval.CubicRoot(argumentInterval);
              break;
            }
          case OpCodes.Absolute: {
              //var argumentInterval = Evaluate(instructions, ref instructionCounter, nodeIntervals);
              var argumentInterval = Evaluate(instructions, ref instructionCounter, nodeIntervals, variableIntervals);
              result = Interval.Absolute(argumentInterval);
              break;
            }
          case OpCodes.AnalyticQuotient: {
              //result = Evaluate(instructions, ref instructionCounter, nodeIntervals);
              result = Evaluate(instructions, ref instructionCounter, nodeIntervals, variableIntervals);
              for (var i = 1; i < currentInstr.nArguments; i++) {
                //var argumentInterval = Evaluate(instructions, ref instructionCounter, nodeIntervals);
                var argumentInterval = Evaluate(instructions, ref instructionCounter, nodeIntervals, variableIntervals);
                result = Interval.AnalyticalQuotient(result, argumentInterval);
              }

              break;
            }
          default:
            throw new NotSupportedException($"The tree contains the unknown symbol {currentInstr.dynamicNode.Symbol}");
        }

        if (!(nodeIntervals == null || nodeIntervals.ContainsKey(currentInstr.dynamicNode)))
          nodeIntervals.Add(currentInstr.dynamicNode, result);

        return result;
      }

      private static bool MultipleTimes(ISymbolicExpressionTree tree, string variable) {
        var varlist = tree.IterateNodesPrefix().OfType<VariableTreeNode>().GroupBy(x => x.VariableName);
        var group = varlist.Select(x => x.Key == variable).Count();

        return group > 1;
      }

      private static bool ContainsVariableMultipleTimes(ISymbolicExpressionTree tree) {
        var varlist = tree.IterateNodesPrefix().OfType<VariableTreeNode>().GroupBy(x => x.VariableName);
        return varlist.Any(group => group.Count() > 1);
      }


      public static bool IsCompatible(ISymbolicExpressionTree tree) {
        var containsUnknownSymbols = (
          from n in tree.Root.GetSubtree(0).IterateNodesPrefix()
          where
            !(n.Symbol is Variable) &&
            !(n.Symbol is Constant) &&
            !(n.Symbol is StartSymbol) &&
            !(n.Symbol is Addition) &&
            !(n.Symbol is Subtraction) &&
            !(n.Symbol is Multiplication) &&
            !(n.Symbol is Division) &&
            !(n.Symbol is Sine) &&
            !(n.Symbol is Cosine) &&
            !(n.Symbol is Tangent) &&
            !(n.Symbol is HyperbolicTangent) &&
            !(n.Symbol is Logarithm) &&
            !(n.Symbol is Exponential) &&
            !(n.Symbol is Square) &&
            !(n.Symbol is SquareRoot) &&
            !(n.Symbol is Cube) &&
            !(n.Symbol is CubeRoot) &&
            !(n.Symbol is Absolute) &&
            !(n.Symbol is AnalyticQuotient)
          select n).Any();
        return !containsUnknownSymbols;
      }
    }
  }