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 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
|
|||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
File size: 10.5 KB |
Line | |
---|---|
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 HEAL.Attic; |
26 | using HeuristicLab.Common; |
27 | |
28 | namespace 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 | } |
Note: See TracBrowser
for help on using the repository browser.