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source: trunk/HeuristicLab.Problems.DataAnalysis/3.4/Implementation/Interval.cs @ 17189

Last change on this file since 17189 was 17180, checked in by swagner, 5 years ago

#2875: Removed years in copyrights

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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
22using System;
23using System.Collections.Generic;
24using System.Linq;
25using HeuristicLab.Common;
26using HEAL.Attic;
27
28namespace HeuristicLab.Problems.DataAnalysis {
29  [StorableType("849e42d3-8934-419d-9aff-64ad81c06b67")]
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      if (a.LowerBound < 0) return new Interval(double.NaN, double.NaN);
229      return new Interval(Math.Pow(a.LowerBound, 1.0/3), Math.Pow(a.UpperBound, 1.0/3));
230    }
231    #endregion
232  }
233}
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