source: branches/2971_named_intervals/HeuristicLab.Problems.DataAnalysis/3.4/Implementation/Interval/Interval.cs @ 17549

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    /trunk/HeuristicLab.Problems.DataAnalysis/3.4/Implementation/Interval/Interval.cs16357-17303
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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
81
82    public override string ToString() {
83      return "Interval: [" + LowerBound + ", " + UpperBound + "]";
84    }
85
86    public bool IsInfiniteOrUndefined {
87      get {
88        return double.IsInfinity(LowerBound) || double.IsInfinity(UpperBound) ||
89                double.IsNaN(LowerBound) || double.IsNaN(UpperBound);
90      }
91    }
92
93    /// <summary>
94    /// True if the interval is positive without zero
95    /// </summary>
96    public bool IsPositive {
97      get => LowerBound > 0.0;
98    }
99
100    /// <summary>
101    /// True if the interval is negative without zero
102    /// </summary>
103    public bool IsNegative {
104      get => UpperBound < 0.0;
105    }
106
107    public static Interval GetInterval(IEnumerable<double> values) {
108      if (values == null) throw new ArgumentNullException("values");
109      if (!values.Any()) throw new ArgumentException($"No values are present.");
110
111      var min = double.MaxValue;
112      var max = double.MinValue;
113
114      foreach (var value in values) {
115        //If an value is NaN return an interval [NaN, NaN]
116        if (double.IsNaN(value)) return new Interval(double.NaN, double.NaN);
117
118        if (value < min) min = value;
119        if (value > max) max = value;
120      }
121
122      return new Interval(min, max);
123    }
124
125    #region Equals, GetHashCode, == , !=
126    public bool Equals(Interval other) {
127      if (other == null)
128        return false;
129
130      return (UpperBound.IsAlmost(other.UpperBound) || (double.IsNaN(UpperBound) && double.IsNaN(other.UpperBound)))
131        && (LowerBound.IsAlmost(other.LowerBound) || (double.IsNaN(LowerBound) && double.IsNaN(other.LowerBound)));
132    }
133
134    public override bool Equals(object obj) {
135      return Equals(obj as Interval);
136    }
137
138    public override int GetHashCode() {
139      return LowerBound.GetHashCode() ^ UpperBound.GetHashCode();
140    }
141
142    public static bool operator ==(Interval interval1, Interval interval2) {
143      if (ReferenceEquals(interval1, null)) return ReferenceEquals(interval2, null);
144      return interval1.Equals(interval2);
145    }
146    public static bool operator !=(Interval interval1, Interval interval2) {
147      return !(interval1 == interval2);
148    }
149    #endregion
150
151    #region operations
152
153    // [x1,x2] + [y1,y2] = [x1 + y1,x2 + y2]
154    public static Interval Add(Interval a, Interval b) {
155      return new Interval(a.LowerBound + b.LowerBound, a.UpperBound + b.UpperBound);
156    }
157
158    // [x1,x2] − [y1,y2] = [x1 − y2,x2 − y1]
159    public static Interval Subtract(Interval a, Interval b) {
160      return new Interval(a.LowerBound - b.UpperBound, a.UpperBound - b.LowerBound);
161    }
162
163    // [x1,x2] * [y1,y2] = [min(x1*y1,x1*y2,x2*y1,x2*y2),max(x1*y1,x1*y2,x2*y1,x2*y2)]
164    public static Interval Multiply(Interval a, Interval b) {
165      double v1 = a.LowerBound * b.LowerBound;
166      double v2 = a.LowerBound * b.UpperBound;
167      double v3 = a.UpperBound * b.LowerBound;
168      double v4 = a.UpperBound * b.UpperBound;
169
170      double min = Math.Min(Math.Min(v1, v2), Math.Min(v3, v4));
171      double max = Math.Max(Math.Max(v1, v2), Math.Max(v3, v4));
172      return new Interval(min, max);
173    }
174
175    //Division by intervals containing 0 is implemented as defined in
176    //http://en.wikipedia.org/wiki/Interval_arithmetic
177    public static Interval Divide(Interval a, Interval b) {
178      if (b.Contains(0.0)) {
179        if (b.LowerBound.IsAlmost(0.0)) return Interval.Multiply(a, new Interval(1.0 / b.UpperBound, double.PositiveInfinity));
180        else if (b.UpperBound.IsAlmost(0.0)) return Interval.Multiply(a, new Interval(double.NegativeInfinity, 1.0 / b.LowerBound));
181        else return new Interval(double.NegativeInfinity, double.PositiveInfinity);
182      }
183      return Interval.Multiply(a, new Interval(1.0 / b.UpperBound, 1.0 / b.LowerBound));
184    }
185
186    public static Interval Sine(Interval a) {
187      if (Math.Abs(a.UpperBound - a.LowerBound) >= Math.PI * 2) return new Interval(-1, 1);
188
189      //divide the interval by PI/2 so that the optima lie at x element of N (0,1,2,3,4,...)
190      double Pihalf = Math.PI / 2;
191      Interval scaled = Interval.Divide(a, new Interval(Pihalf, Pihalf));
192      //move to positive scale
193      if (scaled.LowerBound < 0) {
194        int periodsToMove = Math.Abs((int)scaled.LowerBound / 4) + 1;
195        scaled = Interval.Add(scaled, new Interval(periodsToMove * 4, periodsToMove * 4));
196      }
197
198      double scaledLowerBound = scaled.LowerBound % 4.0;
199      double scaledUpperBound = scaled.UpperBound % 4.0;
200      if (scaledUpperBound < scaledLowerBound) scaledUpperBound += 4.0;
201      List<double> sinValues = new List<double>();
202      sinValues.Add(Math.Sin(scaledLowerBound * Pihalf));
203      sinValues.Add(Math.Sin(scaledUpperBound * Pihalf));
204
205      int startValue = (int)Math.Ceiling(scaledLowerBound);
206      while (startValue < scaledUpperBound) {
207        sinValues.Add(Math.Sin(startValue * Pihalf));
208        startValue += 1;
209      }
210
211      return new Interval(sinValues.Min(), sinValues.Max());
212    }
213    public static Interval Cosine(Interval a) {
214      return Interval.Sine(Interval.Add(a, new Interval(Math.PI / 2, Math.PI / 2)));
215    }
216    public static Interval Tangens(Interval a) {
217      return Interval.Divide(Interval.Sine(a), Interval.Cosine(a));
218    }
219    public static Interval HyperbolicTangent(Interval a) {
220      return new Interval(Math.Tanh(a.LowerBound), Math.Tanh(a.UpperBound));
221    }
222
223    public static Interval Logarithm(Interval a) {
224      return new Interval(Math.Log(a.LowerBound), Math.Log(a.UpperBound));
225    }
226    public static Interval Exponential(Interval a) {
227      return new Interval(Math.Exp(a.LowerBound), Math.Exp(a.UpperBound));
228    }
229
230    public static Interval Power(Interval a, Interval b) {
231      if (a.Contains(0.0) && b.LowerBound < 0) return new Interval(double.NaN, double.NaN);
232
233      int bLower = (int)Math.Round(b.LowerBound);
234      int bUpper = (int)Math.Round(b.UpperBound);
235
236      List<double> powerValues = new List<double>();
237      powerValues.Add(Math.Pow(a.UpperBound, bUpper));
238      powerValues.Add(Math.Pow(a.UpperBound, bUpper - 1));
239      powerValues.Add(Math.Pow(a.UpperBound, bLower));
240      powerValues.Add(Math.Pow(a.UpperBound, bLower + 1));
241
242      powerValues.Add(Math.Pow(a.LowerBound, bUpper));
243      powerValues.Add(Math.Pow(a.LowerBound, bUpper - 1));
244      powerValues.Add(Math.Pow(a.LowerBound, bLower));
245      powerValues.Add(Math.Pow(a.LowerBound, bLower + 1));
246
247      return new Interval(powerValues.Min(), powerValues.Max());
248    }
249
250    public static Interval Square(Interval a) {
251      if (a.UpperBound <= 0) return new Interval(a.UpperBound * a.UpperBound, a.LowerBound * a.LowerBound);     // interval is negative
252      else if (a.LowerBound >= 0) return new Interval(a.LowerBound * a.LowerBound, a.UpperBound * a.UpperBound); // interval is positive
253      else return new Interval(0, Math.Max(a.LowerBound * a.LowerBound, a.UpperBound * a.UpperBound)); // interval goes over zero
254    }
255
256    public static Interval Cube(Interval a) {
257      return new Interval(Math.Pow(a.LowerBound, 3), Math.Pow(a.UpperBound, 3));
258    }
259
260    public static Interval Root(Interval a, Interval b) {
261      int lower = (int)Math.Round(b.LowerBound);
262      int higher = (int)Math.Round(b.UpperBound);
263
264      //Root root(0,0) = 0
265      if (a.LowerBound == 0 && b.LowerBound == 0 && lower == 0 && higher == 0)
266        return new Interval(0, 0);
267
268      //Root is zero ==> undefined ==> 5^-(1.0/0)
269      if (higher == 0 || lower == 0)
270        return new Interval(double.NaN, double.NaN);
271
272      if (lower < 0 || higher < 0) {
273        List<double> vals = new List<double>();
274
275        vals.Add(Math.Pow(a.LowerBound, 1.0 / lower));
276        vals.Add(Math.Pow(a.LowerBound, 1.0 / higher));
277
278        vals.Add(Math.Pow(a.UpperBound, 1.0 / lower));
279        vals.Add(Math.Pow(a.UpperBound, 1.0 / higher));
280
281        return new Interval(vals.Min(), vals.Max());
282      }
283
284      return new Interval(Math.Pow(a.LowerBound, 1.0 / higher), Math.Pow(a.UpperBound, 1.0 / lower));
285    }
286
287    public static Interval SquareRoot(Interval a) {
288      if (a.LowerBound < 0) return new Interval(double.NaN, double.NaN);
289      return new Interval(Math.Sqrt(a.LowerBound), Math.Sqrt(a.UpperBound));
290    }
291
292    public static Interval CubicRoot(Interval a) {
293      var lower = (a.LowerBound < 0) ? -Math.Pow(-a.LowerBound, 1d / 3d) : Math.Pow(a.LowerBound, 1d / 3d);
294      var upper = (a.UpperBound < 0) ? -Math.Pow(-a.UpperBound, 1d / 3d) : Math.Pow(a.UpperBound, 1d / 3d);
295
296      return new Interval(lower, upper);
297    }
298
299    public static Interval Absolute(Interval a) {
300      var absLower = Math.Abs(a.LowerBound);
301      var absUpper = Math.Abs(a.UpperBound);
302      var min = Math.Min(absLower, absUpper);
303      var max = Math.Max(absLower, absUpper);
304
305      if (a.Contains(0.0)) {
306        min = 0.0;
307      }
308
309      return new Interval(min, max);
310    }
311
312    public static Interval AnalyticalQuotient(Interval a, Interval b) {
313      var dividend = a;
314      var divisor = Add(Square(b), new Interval(1.0, 1.0));
315      divisor = SquareRoot(divisor);
316
317      var quotient = Divide(dividend, divisor);
318      return quotient;
319    }
320    #endregion
321  }
322}
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