1  #region License Information


2  /* HeuristicLab


3  * Copyright (C) Heuristic and Evolutionary Algorithms Laboratory (HEAL)


4  *


5  * This file is part of HeuristicLab.


6  *


7  * HeuristicLab is free software: you can redistribute it and/or modify


8  * it under the terms of the GNU General Public License as published by


9  * the Free Software Foundation, either version 3 of the License, or


10  * (at your option) any later version.


11  *


12  * HeuristicLab is distributed in the hope that it will be useful,


13  * but WITHOUT ANY WARRANTY; without even the implied warranty of


14  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the


15  * GNU General Public License for more details.


16  *


17  * You should have received a copy of the GNU General Public License


18  * along with HeuristicLab. If not, see <http://www.gnu.org/licenses/>.


19  */


20  #endregion


21 


22  using System;


23  using System.Collections.Generic;


24  using System.Linq;


25  using HeuristicLab.Common;


26  using HEAL.Attic;


27 


28  namespace HeuristicLab.Problems.DataAnalysis {


29  [StorableType("849e42d38934419d9aff64ad81c06b67")]


30  public class Interval : IEquatable<Interval> {


31  [Storable]


32  public double LowerBound { get; private set; }


33  [Storable]


34  public double UpperBound { get; private set; }


35 


36  [StorableConstructor]


37  protected Interval(StorableConstructorFlag _) { }


38 


39  public Interval(double lowerBound, double upperBound) {


40  if (lowerBound > upperBound)


41  throw new ArgumentException("LowerBound must be smaller than UpperBound.");


42 


43  this.LowerBound = lowerBound;


44  this.UpperBound = upperBound;


45  }


46 


47  public bool Contains(double value) {


48  return LowerBound <= value && value <= UpperBound;


49  }


50 


51  public override string ToString() {


52  return "Interval: [" + LowerBound + ", " + UpperBound + "]";


53  }


54 


55  public bool IsInfiniteOrUndefined {


56  get {


57  return double.IsInfinity(LowerBound)  double.IsInfinity(UpperBound) 


58  double.IsNaN(LowerBound)  double.IsNaN(UpperBound);


59  }


60  }


61 


62  public static Interval GetInterval(IEnumerable<double> values) {


63  if (values == null) throw new ArgumentNullException("values");


64  if (!values.Any()) throw new ArgumentException($"No values are present.");


65 


66  var min = double.MaxValue;


67  var max = double.MinValue;


68 


69  foreach (var value in values) {


70  //If an value is NaN return an interval [NaN, NaN]


71  if (double.IsNaN(value)) return new Interval(double.NaN, double.NaN);


72 


73  if (value < min) min = value;


74  if (value > max) max = value;


75  }


76 


77  return new Interval(min, max);


78  }


79 


80  #region Equals, GetHashCode, == , !=


81  public bool Equals(Interval other) {


82  if (other == null)


83  return false;


84 


85  return (UpperBound.IsAlmost(other.UpperBound)  (double.IsNaN(UpperBound) && double.IsNaN(other.UpperBound)))


86  && (LowerBound.IsAlmost(other.LowerBound)  (double.IsNaN(LowerBound) && double.IsNaN(other.LowerBound)));


87  }


88 


89  public override bool Equals(object obj) {


90  return Equals(obj as Interval);


91  }


92 


93  public override int GetHashCode() {


94  return LowerBound.GetHashCode() ^ UpperBound.GetHashCode();


95  }


96 


97  public static bool operator ==(Interval interval1, Interval interval2) {


98  if (ReferenceEquals(interval1, null)) return ReferenceEquals(interval2, null);


99  return interval1.Equals(interval2);


100  }


101  public static bool operator !=(Interval interval1, Interval interval2) {


102  return !(interval1 == interval2);


103  }


104  #endregion


105 


106  #region operations


107 


108  // [x1,x2] + [y1,y2] = [x1 + y1,x2 + y2]


109  public static Interval Add(Interval a, Interval b) {


110  return new Interval(a.LowerBound + b.LowerBound, a.UpperBound + b.UpperBound);


111  }


112 


113  // [x1,x2] − [y1,y2] = [x1 − y2,x2 − y1]


114  public static Interval Subtract(Interval a, Interval b) {


115  return new Interval(a.LowerBound  b.UpperBound, a.UpperBound  b.LowerBound);


116  }


117 


118  // [x1,x2] * [y1,y2] = [min(x1*y1,x1*y2,x2*y1,x2*y2),max(x1*y1,x1*y2,x2*y1,x2*y2)]


119  public static Interval Multiply(Interval a, Interval b) {


120  double v1 = a.LowerBound * b.LowerBound;


121  double v2 = a.LowerBound * b.UpperBound;


122  double v3 = a.UpperBound * b.LowerBound;


123  double v4 = a.UpperBound * b.UpperBound;


124 


125  double min = Math.Min(Math.Min(v1, v2), Math.Min(v3, v4));


126  double max = Math.Max(Math.Max(v1, v2), Math.Max(v3, v4));


127  return new Interval(min, max);


128  }


129 


130  //mkommend: Division by intervals containing 0 is implemented as defined in


131  //http://en.wikipedia.org/wiki/Interval_arithmetic


132  public static Interval Divide(Interval a, Interval b) {


133  if (b.Contains(0.0)) {


134  if (b.LowerBound.IsAlmost(0.0)) return Interval.Multiply(a, new Interval(1.0 / b.UpperBound, double.PositiveInfinity));


135  else if (b.UpperBound.IsAlmost(0.0)) return Interval.Multiply(a, new Interval(double.NegativeInfinity, 1.0 / b.LowerBound));


136  else return new Interval(double.NegativeInfinity, double.PositiveInfinity);


137  }


138  return Interval.Multiply(a, new Interval(1.0 / b.UpperBound, 1.0 / b.LowerBound));


139  }


140 


141  public static Interval Sine(Interval a) {


142  if (Math.Abs(a.UpperBound  a.LowerBound) >= Math.PI * 2) return new Interval(1, 1);


143 


144  //divide the interval by PI/2 so that the optima lie at x element of N (0,1,2,3,4,...)


145  double Pihalf = Math.PI / 2;


146  Interval scaled = Interval.Divide(a, new Interval(Pihalf, Pihalf));


147  //move to positive scale


148  if (scaled.LowerBound < 0) {


149  int periodsToMove = Math.Abs((int)scaled.LowerBound / 4) + 1;


150  scaled = Interval.Add(scaled, new Interval(periodsToMove * 4, periodsToMove * 4));


151  }


152 


153  double scaledLowerBound = scaled.LowerBound % 4.0;


154  double scaledUpperBound = scaled.UpperBound % 4.0;


155  if (scaledUpperBound < scaledLowerBound) scaledUpperBound += 4.0;


156  List<double> sinValues = new List<double>();


157  sinValues.Add(Math.Sin(scaledLowerBound * Pihalf));


158  sinValues.Add(Math.Sin(scaledUpperBound * Pihalf));


159 


160  int startValue = (int)Math.Ceiling(scaledLowerBound);


161  while (startValue < scaledUpperBound) {


162  sinValues.Add(Math.Sin(startValue * Pihalf));


163  startValue += 1;


164  }


165 


166  return new Interval(sinValues.Min(), sinValues.Max());


167  }


168  public static Interval Cosine(Interval a) {


169  return Interval.Sine(Interval.Add(a, new Interval(Math.PI / 2, Math.PI / 2)));


170  }


171  public static Interval Tangens(Interval a) {


172  return Interval.Divide(Interval.Sine(a), Interval.Cosine(a));


173  }


174  public static Interval HyperbolicTangent(Interval a) {


175  return new Interval(Math.Tanh(a.LowerBound), Math.Tanh(a.UpperBound));


176  }


177 


178  public static Interval Logarithm(Interval a) {


179  return new Interval(Math.Log(a.LowerBound), Math.Log(a.UpperBound));


180  }


181  public static Interval Exponential(Interval a) {


182  return new Interval(Math.Exp(a.LowerBound), Math.Exp(a.UpperBound));


183  }


184 


185  public static Interval Power(Interval a, Interval b) {


186  if (a.Contains(0.0) && b.LowerBound < 0) return new Interval(double.NaN, double.NaN);


187 


188  int bLower = (int)Math.Round(b.LowerBound);


189  int bUpper = (int)Math.Round(b.UpperBound);


190 


191  List<double> powerValues = new List<double>();


192  powerValues.Add(Math.Pow(a.UpperBound, bUpper));


193  powerValues.Add(Math.Pow(a.UpperBound, bUpper  1));


194  powerValues.Add(Math.Pow(a.UpperBound, bLower));


195  powerValues.Add(Math.Pow(a.UpperBound, bLower + 1));


196 


197  powerValues.Add(Math.Pow(a.LowerBound, bUpper));


198  powerValues.Add(Math.Pow(a.LowerBound, bUpper  1));


199  powerValues.Add(Math.Pow(a.LowerBound, bLower));


200  powerValues.Add(Math.Pow(a.LowerBound, bLower + 1));


201 


202  return new Interval(powerValues.Min(), powerValues.Max());


203  }


204 


205  public static Interval Square(Interval a) {


206  if (a.UpperBound <= 0) return new Interval(a.UpperBound * a.UpperBound, a.LowerBound * a.LowerBound); // interval is negative


207  else if (a.LowerBound >= 0) return new Interval(a.LowerBound * a.LowerBound, a.UpperBound * a.UpperBound); // interval is positive


208  else return new Interval(0, Math.Max(a.LowerBound*a.LowerBound, a.UpperBound*a.UpperBound)); // interval goes over zero


209  }


210 


211  public static Interval Cube(Interval a) {


212  return new Interval(Math.Pow(a.LowerBound, 3), Math.Pow(a.UpperBound, 3));


213  }


214 


215  public static Interval Root(Interval a, Interval b) {


216  int lower = (int)Math.Round(b.LowerBound);


217  int higher = (int)Math.Round(b.UpperBound);


218 


219  return new Interval(Math.Pow(a.LowerBound, 1.0 / higher), Math.Pow(a.UpperBound, 1.0 / lower));


220  }


221 


222  public static Interval SquareRoot(Interval a) {


223  if (a.LowerBound < 0) return new Interval(double.NaN, double.NaN);


224  return new Interval(Math.Sqrt(a.LowerBound), Math.Sqrt(a.UpperBound));


225  }


226 


227  public static Interval CubicRoot(Interval a) {


228  var lower = (a.LowerBound < 0) ? Math.Pow(a.LowerBound, 1d / 3d) : Math.Pow(a.LowerBound, 1d / 3d);


229  var upper = (a.UpperBound < 0) ? Math.Pow(a.UpperBound, 1d / 3d) : Math.Pow(a.UpperBound, 1d / 3d);


230 


231  return new Interval(lower, upper);


232  }


233  #endregion


234  }


235  }

