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source: stable/HeuristicLab.Problems.DataAnalysis/3.4/Implementation/Interval/Interval.cs @ 17932

Last change on this file since 17932 was 17803, checked in by mkommend, 4 years ago

#2971: Merged r17579, r17580, r17583, r17584, r17754 into stable.

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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 HEAL.Attic;
26using HeuristicLab.Common;
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    /// <summary>
40    /// Creates an interval with given bounds, where lower bound must be smaller than
41    /// the upper bound. Floating point precision errors trough calculations are fixed by,
42    /// checking if the intervals are almost the same (E-12). If this is the case, the bounds
43    /// will be set to the bound closer to zero.
44    /// </summary>
45    /// <param name="lowerBound">Lower bound of the interval</param>
46    /// <param name="upperBound">Upper bound of the interval</param>
47    public Interval(double lowerBound, double upperBound) {
48      if (lowerBound.IsAlmost(upperBound)) {
49        //If the bounds go over zero
50        if (lowerBound <= 0 && upperBound >= 0) {
51          lowerBound = 0.0;
52          upperBound = 0.0;
53          //Interval is negative
54        } else if (upperBound < 0) {
55          lowerBound = upperBound;
56          //Interval is positive
57        } else {
58          upperBound = lowerBound;
59        }
60      }
61
62      if (lowerBound > upperBound)
63        throw new ArgumentException("lowerBound must be smaller than or equal to upperBound.");
64
65      this.LowerBound = lowerBound;
66      this.UpperBound = upperBound;
67    }
68
69    public bool Contains(double value) {
70      return LowerBound <= value && value <= UpperBound;
71    }
72
73    public bool Contains(Interval other) {
74      if (double.IsNegativeInfinity(LowerBound) && double.IsPositiveInfinity(UpperBound)) return true;
75      if (other.LowerBound >= LowerBound && other.UpperBound <= UpperBound) return true;
76 
77      return false;
78    }
79
80    public override string ToString() {
81      return "Interval: [" + LowerBound + ", " + UpperBound + "]";
82    }
83
84    public bool IsInfiniteOrUndefined {
85      get {
86        return double.IsInfinity(LowerBound) || double.IsInfinity(UpperBound) ||
87                double.IsNaN(LowerBound) || double.IsNaN(UpperBound);
88      }
89    }
90
91    /// <summary>
92    /// True if the interval is positive without zero
93    /// </summary>
94    public bool IsPositive {
95      get => LowerBound > 0.0;
96    }
97
98    /// <summary>
99    /// True if the interval is negative without zero
100    /// </summary>
101    public bool IsNegative {
102      get => UpperBound < 0.0;
103    }
104
105    public static Interval GetInterval(IEnumerable<double> values) {
106      if (values == null) throw new ArgumentNullException("values");
107      if (!values.Any()) throw new ArgumentException($"No values are present.");
108
109      var min = double.MaxValue;
110      var max = double.MinValue;
111
112      foreach (var value in values) {
113        //If an value is NaN return an interval [NaN, NaN]
114        if (double.IsNaN(value)) return new Interval(double.NaN, double.NaN);
115
116        if (value < min) min = value;
117        if (value > max) max = value;
118      }
119
120      return new Interval(min, max);
121    }
122
123    #region Equals, GetHashCode, == , !=
124    public bool Equals(Interval other) {
125      if (other == null)
126        return false;
127
128      return (UpperBound.IsAlmost(other.UpperBound) || (double.IsNaN(UpperBound) && double.IsNaN(other.UpperBound)))
129        && (LowerBound.IsAlmost(other.LowerBound) || (double.IsNaN(LowerBound) && double.IsNaN(other.LowerBound)));
130    }
131
132    public override bool Equals(object obj) {
133      return Equals(obj as Interval);
134    }
135
136    public override int GetHashCode() {
137      return LowerBound.GetHashCode() ^ UpperBound.GetHashCode();
138    }
139
140    public static bool operator ==(Interval interval1, Interval interval2) {
141      if (ReferenceEquals(interval1, null)) return ReferenceEquals(interval2, null);
142      return interval1.Equals(interval2);
143    }
144    public static bool operator !=(Interval interval1, Interval interval2) {
145      return !(interval1 == interval2);
146    }
147    #endregion
148
149    #region operations
150
151    // [x1,x2] + [y1,y2] = [x1 + y1,x2 + y2]
152    public static Interval Add(Interval a, Interval b) {
153      return new Interval(a.LowerBound + b.LowerBound, a.UpperBound + b.UpperBound);
154    }
155
156    // [x1,x2] − [y1,y2] = [x1 − y2,x2 − y1]
157    public static Interval Subtract(Interval a, Interval b) {
158      return new Interval(a.LowerBound - b.UpperBound, a.UpperBound - b.LowerBound);
159    }
160
161    // [x1,x2] * [y1,y2] = [min(x1*y1,x1*y2,x2*y1,x2*y2),max(x1*y1,x1*y2,x2*y1,x2*y2)]
162    public static Interval Multiply(Interval a, Interval b) {
163      double v1 = a.LowerBound * b.LowerBound;
164      double v2 = a.LowerBound * b.UpperBound;
165      double v3 = a.UpperBound * b.LowerBound;
166      double v4 = a.UpperBound * b.UpperBound;
167
168      double min = Math.Min(Math.Min(v1, v2), Math.Min(v3, v4));
169      double max = Math.Max(Math.Max(v1, v2), Math.Max(v3, v4));
170      return new Interval(min, max);
171    }
172
173    //Division by intervals containing 0 is implemented as defined in
174    //http://en.wikipedia.org/wiki/Interval_arithmetic
175    public static Interval Divide(Interval a, Interval b) {
176      if (b.Contains(0.0)) {
177        if (b.LowerBound.IsAlmost(0.0)) return Interval.Multiply(a, new Interval(1.0 / b.UpperBound, double.PositiveInfinity));
178        else if (b.UpperBound.IsAlmost(0.0)) return Interval.Multiply(a, new Interval(double.NegativeInfinity, 1.0 / b.LowerBound));
179        else return new Interval(double.NegativeInfinity, double.PositiveInfinity);
180      }
181      return Interval.Multiply(a, new Interval(1.0 / b.UpperBound, 1.0 / b.LowerBound));
182    }
183
184    public static Interval Sine(Interval a) {
185      if (Math.Abs(a.UpperBound - a.LowerBound) >= Math.PI * 2) return new Interval(-1, 1);
186
187      //divide the interval by PI/2 so that the optima lie at x element of N (0,1,2,3,4,...)
188      double Pihalf = Math.PI / 2;
189      Interval scaled = Interval.Divide(a, new Interval(Pihalf, Pihalf));
190      //move to positive scale
191      if (scaled.LowerBound < 0) {
192        int periodsToMove = Math.Abs((int)scaled.LowerBound / 4) + 1;
193        scaled = Interval.Add(scaled, new Interval(periodsToMove * 4, periodsToMove * 4));
194      }
195
196      double scaledLowerBound = scaled.LowerBound % 4.0;
197      double scaledUpperBound = scaled.UpperBound % 4.0;
198      if (scaledUpperBound < scaledLowerBound) scaledUpperBound += 4.0;
199      List<double> sinValues = new List<double>();
200      sinValues.Add(Math.Sin(scaledLowerBound * Pihalf));
201      sinValues.Add(Math.Sin(scaledUpperBound * Pihalf));
202
203      int startValue = (int)Math.Ceiling(scaledLowerBound);
204      while (startValue < scaledUpperBound) {
205        sinValues.Add(Math.Sin(startValue * Pihalf));
206        startValue += 1;
207      }
208
209      return new Interval(sinValues.Min(), sinValues.Max());
210    }
211    public static Interval Cosine(Interval a) {
212      return Interval.Sine(Interval.Add(a, new Interval(Math.PI / 2, Math.PI / 2)));
213    }
214    public static Interval Tangens(Interval a) {
215      return Interval.Divide(Interval.Sine(a), Interval.Cosine(a));
216    }
217    public static Interval HyperbolicTangent(Interval a) {
218      return new Interval(Math.Tanh(a.LowerBound), Math.Tanh(a.UpperBound));
219    }
220
221    public static Interval Logarithm(Interval a) {
222      return new Interval(Math.Log(a.LowerBound), Math.Log(a.UpperBound));
223    }
224    public static Interval Exponential(Interval a) {
225      return new Interval(Math.Exp(a.LowerBound), Math.Exp(a.UpperBound));
226    }
227
228    public static Interval Square(Interval a) {
229      if (a.UpperBound <= 0) return new Interval(a.UpperBound * a.UpperBound, a.LowerBound * a.LowerBound);     // interval is negative
230      else if (a.LowerBound >= 0) return new Interval(a.LowerBound * a.LowerBound, a.UpperBound * a.UpperBound); // interval is positive
231      else return new Interval(0, Math.Max(a.LowerBound * a.LowerBound, a.UpperBound * a.UpperBound)); // interval goes over zero
232    }
233
234    public static Interval Cube(Interval a) {
235      return new Interval(Math.Pow(a.LowerBound, 3), Math.Pow(a.UpperBound, 3));
236    }
237
238    /// <summary>
239    /// The interval contains both possible results of the calculated square root +-sqrt(x). That results in a wider
240    /// interval, but it contains all possible solutions.
241    /// </summary>
242    /// <param name="a">Interval to build square root from.</param>
243    /// <returns></returns>
244    public static Interval SquareRoot(Interval a) {
245      if (a.LowerBound < 0) return new Interval(double.NaN, double.NaN);
246      return new Interval(-Math.Sqrt(a.UpperBound), Math.Sqrt(a.UpperBound));
247    }
248
249    public static Interval CubicRoot(Interval a) {
250      var lower = (a.LowerBound < 0) ? -Math.Pow(-a.LowerBound, 1d / 3d) : Math.Pow(a.LowerBound, 1d / 3d);
251      var upper = (a.UpperBound < 0) ? -Math.Pow(-a.UpperBound, 1d / 3d) : Math.Pow(a.UpperBound, 1d / 3d);
252
253      return new Interval(lower, upper);
254    }
255
256    public static Interval Absolute(Interval a) {
257      var absLower = Math.Abs(a.LowerBound);
258      var absUpper = Math.Abs(a.UpperBound);
259      var min = Math.Min(absLower, absUpper);
260      var max = Math.Max(absLower, absUpper);
261
262      if (a.Contains(0.0)) {
263        min = 0.0;
264      }
265
266      return new Interval(min, max);
267    }
268
269    public static Interval AnalyticalQuotient(Interval a, Interval b) {
270      var dividend = a;
271      var divisor = Add(Square(b), new Interval(1.0, 1.0));
272      divisor = SquareRoot(divisor);
273
274      var quotient = Divide(dividend, divisor);
275      return quotient;
276    }
277    #endregion
278  }
279}
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