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source: branches/2925_AutoDiffForDynamicalModels/HeuristicLab.Tests/HeuristicLab.Problems.DataAnalysis-3.4/IntervalTest.cs @ 18183

Last change on this file since 18183 was 17409, checked in by gkronber, 5 years ago

#2925: merged r17255:17402 from trunk to branch
File size: 12.2 KB
Line 
1using System;
2using Microsoft.VisualStudio.TestTools.UnitTesting;
3
4namespace HeuristicLab.Problems.DataAnalysis.Tests {
5  [TestClass]
6  public class IntervalTest {
7    private readonly Interval a = new Interval(-1, 1);
8    private readonly Interval b = new Interval(-2, 2);
9    private readonly Interval c = new Interval(0, 3);
10    private readonly Interval d = new Interval(1, 3);
11    private readonly Interval e = new Interval(4, 6);
12
13    [TestMethod]
14    [TestCategory("Problems.DataAnalysis")]
15    [TestProperty("Time", "short")]
16    public void AddIntervalTest() {
17      //add        [x1,x2] + [y1,y2] = [x1 + y1,x2 + y2]
18
19      // [-1,1] + [-2,2] = [-3,3]
20      Assert.AreEqual(Interval.Add(a, b), new Interval(-3, 3));
21      //([-1, 1] + [-2, 2]) + [0, 3] = [-3, 6]
22      Assert.AreEqual(Interval.Add(Interval.Add(a, b), c), new Interval(-3, 6));
23      //([-1, 1] + [0, 3]) + [-2, 2] = [-3, 6]
24      Assert.AreEqual(Interval.Add(Interval.Add(a, c), b), new Interval(-3, 6));
25    }
26
27    [TestMethod]
28    [TestCategory("Problems.DataAnalysis")]
29    [TestProperty("Time", "short")]
30    public void SubtractIntervalTest() {
31      //subtract   [x1,x2] − [y1,y2] = [x1 − y2,x2 − y1]
32
33      //[-1, 1] - [-2, 2] = [-3, 3]
34      Assert.AreEqual<Interval>(Interval.Subtract(a, b), new Interval(-3, 3));
35      //([-1, 1] - [-2, 2]) - [0, 3] = [-6, 3]
36      Assert.AreEqual<Interval>(Interval.Subtract(Interval.Subtract(a, b), c), new Interval(-6, 3));
37      //([-1, 1] - [0, 3]) - [-2, 2] = [-6, 3]
38      Assert.AreEqual<Interval>(Interval.Subtract(Interval.Subtract(a, c), b), new Interval(-6, 3));
39    }
40
41    [TestMethod]
42    [TestCategory("Problems.DataAnalysis")]
43    [TestProperty("Time", "short")]
44    public void MultiplyIntervalTest() {
45      //multiply   [x1,x2] * [y1,y2] = [min(x1*y1,x1*y2,x2*y1,x2*y2),max(x1*y1,x1*y2,x2*y1,x2*y2)]
46
47      //[-1, 1] * [-2, 2] = [-2, 2]
48      Assert.AreEqual<Interval>(Interval.Multiply(a, b), new Interval(-2, 2));
49      //([-1, 1] * [-2, 2]) * [0, 3] = [-6, 6]
50      Assert.AreEqual<Interval>(Interval.Multiply(Interval.Multiply(a, b), c), new Interval(-6, 6));
51      //([-1, 1] * [0, 3]) * [-2, 2] = [-6, 6]
52      Assert.AreEqual<Interval>(Interval.Multiply(Interval.Multiply(a, c), b), new Interval(-6, 6));
53
54      // [-2, 0] * [-2, 0]  = [0, 4]
55      Assert.AreEqual<Interval>(new Interval(0, 4), Interval.Multiply(new Interval(-2, 0), new Interval(-2, 0)));
56    }
57
58    [TestMethod]
59    [TestCategory("Problems.DataAnalysis")]
60    [TestProperty("Time", "short")]
61    public void DivideIntervalTest() {
62      //divide  [x1, x2] / [y1, y2] = [x1, x2] * (1/[y1, y2]), where 1 / [y1,y2] = [1 / y2,1 / y1] if 0 not in [y_1, y_2].
63
64      //[4, 6] / [1, 3] = [4/3, 6]
65      Assert.AreEqual<Interval>(Interval.Divide(e, d), new Interval(4.0 / 3.0, 6));
66      //([4, 6] / [1, 3]) / [1, 3] = [4/9, 6]
67      Assert.AreEqual<Interval>(Interval.Divide(Interval.Divide(e, d), d), new Interval(4.0 / 9.0, 6));
68      //[4, 6] / [0, 3] = [4/3, +Inf]
69      Assert.AreEqual<Interval>(Interval.Divide(e, c), new Interval(4.0 / 3.0, double.PositiveInfinity));
70      //[-1, 1] / [0, 3] = [+Inf, -Inf]
71      Assert.AreEqual<Interval>(Interval.Divide(a, c), new Interval(double.NegativeInfinity, double.PositiveInfinity));
72      //Devision by 0 ==> IsInfiniteOrUndefined == true
73      Assert.IsTrue(Interval.Divide(e, c).IsInfiniteOrUndefined);
74      //Devision by 0 ==> IsInfiniteOrUndefined == true
75      Assert.IsTrue(Interval.Divide(a, c).IsInfiniteOrUndefined);
76      Assert.AreEqual<Interval>(Interval.Divide(d, b), new Interval(double.NegativeInfinity, double.PositiveInfinity));
77    }
78
79    [TestMethod]
80    [TestCategory("Problems.DataAnalysis")]
81    [TestProperty("Time", "short")]
82    public void SineIntervalTest() {
83      //sine depends on interval
84      //sin([0, 2*pi]) = [-1, 1]
85      Assert.AreEqual<Interval>(Interval.Sine(new Interval(0, 2 * Math.PI)), new Interval(-1, 1));
86      //sin([-pi/2, pi/2]) = [sin(-pi/2), sin(pi/2)]
87      Assert.AreEqual<Interval>(Interval.Sine(new Interval(-1 * Math.PI / 2, Math.PI / 2)), new Interval(-1, 1));
88      //sin([0, pi/2]) = [sin(0), sin(pi/2)]
89      Assert.AreEqual<Interval>(Interval.Sine(new Interval(0, Math.PI / 2)), new Interval(0, 1));
90      //sin([pi, 3*pi/2]) = [sin(pi), sin(3*pi/2)]
91      Assert.AreEqual<Interval>(Interval.Sine(new Interval(Math.PI, 3 * Math.PI / 2)), new Interval(-1, 0));
92      Assert.AreEqual<Interval>(Interval.Sine(new Interval(1, 2)), new Interval(Math.Min(Math.Sin(1), Math.Sin(2)), 1));
93      Assert.AreEqual<Interval>(Interval.Sine(new Interval(1, 3)), new Interval(Math.Min(Math.Sin(1), Math.Sin(3)), 1));
94      Assert.AreEqual<Interval>(Interval.Sine(new Interval(Math.PI, 5 * Math.PI / 2)), new Interval(-1, 1));
95    }
96
97    [TestMethod]
98    [TestCategory("Problems.DataAnalysis")]
99    [TestProperty("Time", "short")]
100    public void CosineIntervalTest() {
101      //Cosine uses sine Interval.Sine(Interval.Subtract(a, new Interval(Math.PI / 2, Math.PI / 2)));
102      Assert.AreEqual<Interval>(Interval.Cosine(new Interval(0, 2 * Math.PI)), new Interval(-1, 1));
103      Assert.AreEqual<Interval>(new Interval(-1, 1), Interval.Cosine(new Interval(Math.PI, 4 * Math.PI / 2)));
104    }
105
106    [TestMethod]
107    [TestCategory("Problems.DataAnalysis")]
108    [TestProperty("Time", "short")]
109    public void LogIntervalTest() {
110      //Log([3, 5]) = [log(3), log(5)]
111      Assert.AreEqual<Interval>(new Interval(Math.Log(3), Math.Log(5)), Interval.Logarithm(new Interval(3, 5)));
112      //Log([0.5, 1]) = [log(0.5), log(1)]
113      Assert.AreEqual<Interval>(new Interval(Math.Log(0.5), 0), Interval.Logarithm(new Interval(0.5, 1)));
114      //Log([-1, 5]) = [NaN, log(5)]
115      var result = Interval.Logarithm(new Interval(-1, 5));
116      Assert.AreEqual<Interval>(new Interval(double.NaN, Math.Log(5)),result);
117      Assert.IsTrue(result.IsInfiniteOrUndefined);
118    }
119
120
121    [TestMethod]
122    [TestCategory("Problems.DataAnalysis")]
123    [TestProperty("Time", "short")]
124    public void ExponentialIntervalTest() {
125      //Exp([0, 1]) = [exp(0), exp(1)]
126      Assert.AreEqual<Interval>(new Interval(1, Math.Exp(1)), Interval.Exponential(new Interval(0, 1)));
127    }
128
129
130    [TestMethod]
131    [TestCategory("Problems.DataAnalysis")]
132    [TestProperty("Time", "short")]
133    public void SquareIntervalTest() {
134      Assert.AreEqual<Interval>(new Interval(1, 4), Interval.Square(new Interval(1, 2)));
135      Assert.AreEqual<Interval>(new Interval(1, 4), Interval.Square(new Interval(-2, -1)));
136      Assert.AreEqual<Interval>(new Interval(0, 4), Interval.Square(new Interval(-2, 2)));
137    }
138
139    [TestMethod]
140    [TestCategory("Problems.DataAnalysis")]
141    [TestProperty("Time", "short")]
142    public void SquarerootIntervalTest() {
143      Assert.AreEqual<Interval>(new Interval(1, 2), Interval.SquareRoot(new Interval(1, 4)));
144      Assert.AreEqual<Interval>(new Interval(double.NaN, double.NaN), Interval.SquareRoot(new Interval(-4, -1)));
145    }
146
147    [TestMethod]
148    [TestCategory("Problems.DataAnalysis")]
149    [TestProperty("Time", "short")]
150    public void CubeIntervalTest() {
151      Assert.AreEqual<Interval>(new Interval(1, 8), Interval.Cube(new Interval(1, 2)));
152      Assert.AreEqual<Interval>(new Interval(-8, -1), Interval.Cube(new Interval(-2, -1)));
153      Assert.AreEqual<Interval>(new Interval(-8, 8), Interval.Cube(new Interval(-2, 2)));
154    }
155
156    [TestMethod]
157    [TestCategory("Problems.DataAnalysis")]
158    [TestProperty("Time", "short")]
159    public void CubeRootIntervalTest() {
160      Assert.AreEqual<Interval>(new Interval(1, 2), Interval.CubicRoot(new Interval(1, 8)));
161      Assert.AreEqual<Interval>(new Interval(-2, -2), Interval.CubicRoot(new Interval(-8, -8)));
162      Assert.AreEqual<Interval>(new Interval(-2, 2), Interval.CubicRoot(new Interval(-8, 8)));
163      Assert.AreEqual(new Interval(2, 2), Interval.CubicRoot(new Interval(8, 8)));
164      Assert.AreEqual(new Interval(-Math.Pow(6, 1.0 / 3), 2), Interval.CubicRoot(new Interval(-6, 8)));
165      Assert.AreEqual(new Interval(2, 2), Interval.CubicRoot(new Interval(8, 8)));
166      Assert.AreEqual(new Interval(-2, 0), Interval.CubicRoot(new Interval(-8, 0)));
167    }
168
169    [TestMethod]
170    [TestCategory("Problems.DataAnalysis")]
171    [TestProperty("Time", "short")]
172    public void AbsoluteIntervalTest() {
173      Assert.AreEqual(new Interval(2, 5), Interval.Absolute(new Interval(-5, -2)));
174      Assert.AreEqual(new Interval(2, 5), Interval.Absolute(new Interval(2, 5)));
175      Assert.AreEqual(new Interval(0, 3), Interval.Absolute(new Interval(-3, 0)));
176      Assert.AreEqual(new Interval(0, 5), Interval.Absolute(new Interval(0, 5)));
177      Assert.AreEqual(new Interval(0, 5), Interval.Absolute(new Interval(-2, 5)));
178    }
179
180    [TestMethod]
181    [TestCategory("Problems.DataAnalysis")]
182    [TestProperty("Time", "short")]
183    public void AnalyticalQuotientIntervalTest() {
184      //Analytical Quotient ==> a / sqrt(b^2 + 1)
185      var aPos = new Interval(3, 5);
186      var aZero = new Interval(-3, 5);
187      var aNeg = new Interval(-5, -3);
188
189      var bPos = new Interval(2, 4);
190      var bZero = new Interval(-2, 4);
191      var bNeg = new Interval(-4, -2);
192
193      //Second interval goes over zero
194      Assert.AreEqual(new Interval(aPos.LowerBound/Math.Sqrt(17), aPos.UpperBound), Interval.AnalyticalQuotient(aPos, bZero));
195      Assert.AreEqual(new Interval(aZero.LowerBound, aZero.UpperBound), Interval.AnalyticalQuotient(aZero, bZero));
196      Assert.AreEqual(new Interval(aNeg.LowerBound, aNeg.UpperBound/Math.Sqrt(17)), Interval.AnalyticalQuotient(aNeg, bZero));
197      //Second interval is positive
198      Assert.AreEqual(new Interval(aPos.LowerBound/Math.Sqrt(17), aPos.UpperBound/Math.Sqrt(5)), Interval.AnalyticalQuotient(aPos, bPos));
199      Assert.AreEqual(new Interval(aZero.LowerBound/Math.Sqrt(5), aZero.UpperBound/Math.Sqrt(5)), Interval.AnalyticalQuotient(aZero, bPos));
200      Assert.AreEqual(new Interval(aNeg.LowerBound/Math.Sqrt(5), aNeg.UpperBound/Math.Sqrt(17)), Interval.AnalyticalQuotient(aNeg, bPos));
201      //Second interval is negative
202      Assert.AreEqual(new Interval(aPos.LowerBound/Math.Sqrt(17), aPos.UpperBound/Math.Sqrt(5)), Interval.AnalyticalQuotient(aPos, bNeg));
203      Assert.AreEqual(new Interval(aZero.LowerBound/Math.Sqrt(5), aZero.UpperBound/Math.Sqrt(5)), Interval.AnalyticalQuotient(aZero, bNeg));
204      Assert.AreEqual(new Interval(aNeg.LowerBound/Math.Sqrt(5), aNeg.UpperBound/Math.Sqrt(17)), Interval.AnalyticalQuotient(aNeg, bNeg));
205    }
206
207    [TestMethod]
208    [TestCategory("Problems.DataAnalysis")]
209    [TestProperty("Time", "short")]
210    public void IsNegativeIntervalTest() {
211      Assert.IsTrue(new Interval(-2, -1).IsNegative);
212      Assert.IsFalse(new Interval(-2, 0).IsNegative);
213      Assert.IsFalse(new Interval(-2, 2).IsNegative);
214      Assert.IsFalse(new Interval(2, 4).IsNegative);
215    }
216
217    [TestMethod]
218    [TestCategory("Problems.DataAnalysis")]
219    [TestProperty("Time", "short")]
220    public void IsPositiveIntervalTest() {
221      Assert.IsTrue(new Interval(3, 5).IsPositive);
222      Assert.IsFalse(new Interval(0, 5).IsPositive);
223      Assert.IsFalse(new Interval(-1, 5).IsPositive);
224      Assert.IsFalse(new Interval(-5, -2).IsPositive);
225    }
226
227    [TestMethod]
228    [TestCategory("Problems.DataAnalysis")]
229    [TestProperty("Time", "short")]
230    public void IsAlmostIntervalTest() {
231      var negativeLowerBound = -2E-13;
232      var negativeUpperBound = -1E-13;
233      var positiveLowerBound = 3E-13;
234      var positiveUpperBound = 5E-13;
235
236      var negativeInterval = new Interval(negativeLowerBound, negativeUpperBound);
237      var positiveInterval = new Interval(positiveLowerBound, positiveUpperBound);
238      var zeroInterval = new Interval(negativeUpperBound, positiveLowerBound);
239
240      //Check for right-shift of negative interval
241      Assert.AreEqual(negativeUpperBound, negativeInterval.LowerBound);
242      Assert.AreEqual(negativeUpperBound, negativeInterval.UpperBound);
243      //Check for left-shift of positive interval
244      Assert.AreEqual(positiveLowerBound, positiveInterval.LowerBound);
245      Assert.AreEqual(positiveLowerBound, positiveInterval.UpperBound);
246      //Check for setting interval to zero
247      Assert.AreEqual(0, zeroInterval.LowerBound);
248      Assert.AreEqual(0, zeroInterval.UpperBound);
249
250    }
251  }
252}
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