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source: branches/3106_AnalyticContinuedFractionsRegression/HeuristicLab.Tests/HeuristicLab.Problems.DataAnalysis-3.4/IntervalTest.cs @ 17970

Last change on this file since 17970 was 17970, checked in by gkronber, 3 years ago

#3106 merged r17856:17969 from trunk to branch
File size: 25.5 KB
Line 
1using System;
2using System.Collections.Generic;
3using Microsoft.VisualStudio.TestTools.UnitTesting;
4
5namespace HeuristicLab.Problems.DataAnalysis.Tests {
6  [TestClass]
7  public class IntervalTest {
8    private readonly Interval a = new Interval(-1, 1);
9    private readonly Interval b = new Interval(-2, 2);
10    private readonly Interval c = new Interval(0, 3);
11    private readonly Interval d = new Interval(1, 3);
12    private readonly Interval e = new Interval(4, 6);
13
14    private void CheckLowerAndUpperBoundOfInterval(Interval expected, Interval calculated) {
15      var lowerBoundExpected = expected.LowerBound;
16      var upperBoundExpected = expected.UpperBound;
17      var lowerBoundCalculated = calculated.LowerBound;
18      var upperBoundCalculated = calculated.UpperBound;
19
20      if(double.IsNaN(lowerBoundExpected) && double.IsNaN(lowerBoundCalculated)) {
21        Assert.IsTrue(double.IsNaN(lowerBoundExpected) && double.IsNaN(lowerBoundCalculated));
22      } else if (double.IsNaN(upperBoundExpected) && double.IsNaN(upperBoundCalculated)) {
23        Assert.IsTrue(double.IsNaN(upperBoundExpected) && double.IsNaN(upperBoundCalculated));
24      } else {
25        Assert.AreEqual(lowerBoundExpected, lowerBoundCalculated, 1e-9);
26        Assert.AreEqual(upperBoundExpected, upperBoundCalculated, 1e-9);
27      }
28    }
29
30    [TestMethod]
31    [TestCategory("Problems.DataAnalysis")]
32    [TestProperty("Time", "short")]
33    public void AddIntervalTest() {
34      //add        [x1,x2] + [y1,y2] = [x1 + y1,x2 + y2]
35
36      // [-1,1] + [-2,2] = [-3,3]
37      Assert.AreEqual(Interval.Add(a, b), new Interval(-3, 3));
38      //([-1, 1] + [-2, 2]) + [0, 3] = [-3, 6]
39      Assert.AreEqual(Interval.Add(Interval.Add(a, b), c), new Interval(-3, 6));
40      //([-1, 1] + [0, 3]) + [-2, 2] = [-3, 6]
41      Assert.AreEqual(Interval.Add(Interval.Add(a, c), b), new Interval(-3, 6));
42    }
43
44    [TestMethod]
45    [TestCategory("Problems.DataAnalysis")]
46    [TestProperty("Time", "short")]
47    public void SubtractIntervalTest() {
48      //subtract   [x1,x2] − [y1,y2] = [x1 − y2,x2 − y1]
49
50      //[-1, 1] - [-2, 2] = [-3, 3]
51      CheckLowerAndUpperBoundOfInterval(Interval.Subtract(a, b), new Interval(-3, 3));
52      //([-1, 1] - [-2, 2]) - [0, 3] = [-6, 3]
53      CheckLowerAndUpperBoundOfInterval(Interval.Subtract(Interval.Subtract(a, b), c), new Interval(-6, 3));
54      //([-1, 1] - [0, 3]) - [-2, 2] = [-6, 3]
55      CheckLowerAndUpperBoundOfInterval(Interval.Subtract(Interval.Subtract(a, c), b), new Interval(-6, 3));
56    }
57
58    [TestMethod]
59    [TestCategory("Problems.DataAnalysis")]
60    [TestProperty("Time", "short")]
61    public void MultiplyIntervalTest() {
62      //multiply   [x1,x2] * [y1,y2] = [min(x1*y1,x1*y2,x2*y1,x2*y2),max(x1*y1,x1*y2,x2*y1,x2*y2)]
63
64      //[-1, 1] * [-2, 2] = [-2, 2]
65      CheckLowerAndUpperBoundOfInterval(Interval.Multiply(a, b), new Interval(-2, 2));
66      //([-1, 1] * [-2, 2]) * [0, 3] = [-6, 6]
67      CheckLowerAndUpperBoundOfInterval(Interval.Multiply(Interval.Multiply(a, b), c), new Interval(-6, 6));
68      //([-1, 1] * [0, 3]) * [-2, 2] = [-6, 6]
69      CheckLowerAndUpperBoundOfInterval(Interval.Multiply(Interval.Multiply(a, c), b), new Interval(-6, 6));
70
71      // [-2, 0] * [-2, 0]  = [0, 4]
72      CheckLowerAndUpperBoundOfInterval(new Interval(0, 4), Interval.Multiply(new Interval(-2, 0), new Interval(-2, 0)));
73    }
74
75    [TestMethod]
76    [TestCategory("Problems.DataAnalysis")]
77    [TestProperty("Time", "short")]
78    public void DivideIntervalTest() {
79      //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].
80
81      //[4, 6] / [1, 3] = [4/3, 6]
82      CheckLowerAndUpperBoundOfInterval(Interval.Divide(e, d), new Interval(4.0 / 3.0, 6));
83      //([4, 6] / [1, 3]) / [1, 3] = [4/9, 6]
84      CheckLowerAndUpperBoundOfInterval(Interval.Divide(Interval.Divide(e, d), d), new Interval(4.0 / 9.0, 6));
85      //[4, 6] / [0, 3] = [4/3, +Inf]
86      CheckLowerAndUpperBoundOfInterval(Interval.Divide(e, c), new Interval(4.0 / 3.0, double.PositiveInfinity));
87      //[-1, 1] / [0, 3] = [+Inf, -Inf]
88      CheckLowerAndUpperBoundOfInterval(Interval.Divide(a, c), new Interval(double.NegativeInfinity, double.PositiveInfinity));
89      //Devision by 0 ==> IsInfiniteOrUndefined == true
90      Assert.IsTrue(Interval.Divide(e, c).IsInfiniteOrUndefined);
91      //Devision by 0 ==> IsInfiniteOrUndefined == true
92      Assert.IsTrue(Interval.Divide(a, c).IsInfiniteOrUndefined);
93      CheckLowerAndUpperBoundOfInterval(Interval.Divide(d, b), new Interval(double.NegativeInfinity, double.PositiveInfinity));
94    }
95
96    [TestMethod]
97    [TestCategory("Problems.DataAnalysis")]
98    [TestProperty("Time", "short")]
99    public void SineIntervalTest() {
100      //sine depends on interval
101      //sin([0, 2*pi]) = [-1, 1]
102      CheckLowerAndUpperBoundOfInterval(Interval.Sine(new Interval(0, 2 * Math.PI)), new Interval(-1, 1));
103      //sin([-pi/2, pi/2]) = [sin(-pi/2), sin(pi/2)]
104      CheckLowerAndUpperBoundOfInterval(Interval.Sine(new Interval(-1 * Math.PI / 2, Math.PI / 2)), new Interval(-1, 1));
105      //sin([0, pi/2]) = [sin(0), sin(pi/2)]
106      CheckLowerAndUpperBoundOfInterval(Interval.Sine(new Interval(0, Math.PI / 2)), new Interval(0, 1));
107      //sin([pi, 3*pi/2]) = [sin(pi), sin(3*pi/2)]
108      CheckLowerAndUpperBoundOfInterval(Interval.Sine(new Interval(Math.PI, 3 * Math.PI / 2)), new Interval(-1, 0));
109      CheckLowerAndUpperBoundOfInterval(Interval.Sine(new Interval(1, 2)), new Interval(Math.Min(Math.Sin(1), Math.Sin(2)), 1));
110      CheckLowerAndUpperBoundOfInterval(Interval.Sine(new Interval(1, 3)), new Interval(Math.Min(Math.Sin(1), Math.Sin(3)), 1));
111      CheckLowerAndUpperBoundOfInterval(Interval.Sine(new Interval(Math.PI, 5 * Math.PI / 2)), new Interval(-1, 1));
112    }
113
114    [TestMethod]
115    [TestCategory("Problems.DataAnalysis")]
116    [TestProperty("Time", "short")]
117    public void CosineIntervalTest() {
118      //Cosine uses sine Interval.Sine(Interval.Subtract(a, new Interval(Math.PI / 2, Math.PI / 2)));
119      CheckLowerAndUpperBoundOfInterval(Interval.Cosine(new Interval(0, 2 * Math.PI)), new Interval(-1, 1));
120      CheckLowerAndUpperBoundOfInterval(new Interval(-1, 1), Interval.Cosine(new Interval(Math.PI, 4 * Math.PI / 2)));
121    }
122
123    [TestMethod]
124    [TestCategory("Problems.DataAnalysis")]
125    [TestProperty("Time", "short")]
126    public void LogIntervalTest() {
127      //Log([3, 5]) = [log(3), log(5)]
128      CheckLowerAndUpperBoundOfInterval(new Interval(Math.Log(3), Math.Log(5)), Interval.Logarithm(new Interval(3, 5)));
129      //Log([0.5, 1]) = [log(0.5), log(1)]
130      CheckLowerAndUpperBoundOfInterval(new Interval(Math.Log(0.5), 0), Interval.Logarithm(new Interval(0.5, 1)));
131      //Log([-1, 5]) = [NaN, log(5)]
132      var result = Interval.Logarithm(new Interval(-1, 5));
133      CheckLowerAndUpperBoundOfInterval(new Interval(double.NaN, Math.Log(5)),result);
134      Assert.IsTrue(result.IsInfiniteOrUndefined);
135    }
136
137
138    [TestMethod]
139    [TestCategory("Problems.DataAnalysis")]
140    [TestProperty("Time", "short")]
141    public void ExponentialIntervalTest() {
142      //Exp([0, 1]) = [exp(0), exp(1)]
143      CheckLowerAndUpperBoundOfInterval(new Interval(1, Math.Exp(1)), Interval.Exponential(new Interval(0, 1)));
144    }
145
146
147    [TestMethod]
148    [TestCategory("Problems.DataAnalysis")]
149    [TestProperty("Time", "short")]
150    public void SquareIntervalTest() {
151      CheckLowerAndUpperBoundOfInterval(new Interval(1, 4), Interval.Square(new Interval(1, 2)));
152      CheckLowerAndUpperBoundOfInterval(new Interval(1, 4), Interval.Square(new Interval(-2, -1)));
153      CheckLowerAndUpperBoundOfInterval(new Interval(0, 4), Interval.Square(new Interval(-2, 2)));
154    }
155
156    [TestMethod]
157    [TestCategory("Problems.DataAnalysis")]
158    [TestProperty("Time", "short")]
159    public void SquarerootIntervalTest() {
160      CheckLowerAndUpperBoundOfInterval(new Interval(-2, 2), Interval.SquareRoot(new Interval(1, 4)));
161      CheckLowerAndUpperBoundOfInterval(new Interval(double.NaN, double.NaN), Interval.SquareRoot(new Interval(-4, -1)));
162    }
163
164    [TestMethod]
165    [TestCategory("Problems.DataAnalysis")]
166    [TestProperty("Time", "short")]
167    public void CubeIntervalTest() {
168      CheckLowerAndUpperBoundOfInterval(new Interval(1, 8), Interval.Cube(new Interval(1, 2)));
169      CheckLowerAndUpperBoundOfInterval(new Interval(-8, -1), Interval.Cube(new Interval(-2, -1)));
170      CheckLowerAndUpperBoundOfInterval(new Interval(-8, 8), Interval.Cube(new Interval(-2, 2)));
171    }
172
173    [TestMethod]
174    [TestCategory("Problems.DataAnalysis")]
175    [TestProperty("Time", "short")]
176    public void CubeRootIntervalTest() {
177      CheckLowerAndUpperBoundOfInterval(new Interval(1, 2), Interval.CubicRoot(new Interval(1, 8)));
178      CheckLowerAndUpperBoundOfInterval(new Interval(-2, -2), Interval.CubicRoot(new Interval(-8, -8)));
179      CheckLowerAndUpperBoundOfInterval(new Interval(-2, 2), Interval.CubicRoot(new Interval(-8, 8)));
180      Assert.AreEqual(new Interval(2, 2), Interval.CubicRoot(new Interval(8, 8)));
181      Assert.AreEqual(new Interval(-Math.Pow(6, 1.0 / 3), 2), Interval.CubicRoot(new Interval(-6, 8)));
182      Assert.AreEqual(new Interval(2, 2), Interval.CubicRoot(new Interval(8, 8)));
183      Assert.AreEqual(new Interval(-2, 0), Interval.CubicRoot(new Interval(-8, 0)));
184    }
185
186    [TestMethod]
187    [TestCategory("Problems.DataAnalysis")]
188    [TestProperty("Time", "short")]
189    public void AbsoluteIntervalTest() {
190      Assert.AreEqual(new Interval(2, 5), Interval.Absolute(new Interval(-5, -2)));
191      Assert.AreEqual(new Interval(2, 5), Interval.Absolute(new Interval(2, 5)));
192      Assert.AreEqual(new Interval(0, 3), Interval.Absolute(new Interval(-3, 0)));
193      Assert.AreEqual(new Interval(0, 5), Interval.Absolute(new Interval(0, 5)));
194      Assert.AreEqual(new Interval(0, 5), Interval.Absolute(new Interval(-2, 5)));
195    }
196
197    [TestMethod]
198    [TestCategory("Problems.DataAnalysis")]
199    [TestProperty("Time", "short")]
200    public void AnalyticalQuotientIntervalTest() {
201      //Analytical Quotient ==> a / sqrt(b^2 + 1)
202      var aPos = new Interval(3, 5);
203      var aZero = new Interval(-3, 5);
204      var aNeg = new Interval(-5, -3);
205
206      var bPos = new Interval(2, 4);
207      var bZero = new Interval(-2, 4);
208      var bNeg = new Interval(-4, -2);
209
210      //Second interval goes over zero
211      //Assert.AreEqual(new Interval(aPos.LowerBound/Math.Sqrt(17), aPos.UpperBound), Interval.AnalyticalQuotient(aPos, bZero));
212      //Assert.AreEqual(new Interval(aZero.LowerBound, aZero.UpperBound), Interval.AnalyticalQuotient(aZero, bZero));
213      //Assert.AreEqual(new Interval(aNeg.LowerBound, aNeg.UpperBound/Math.Sqrt(17)), Interval.AnalyticalQuotient(aNeg, bZero));
214      ////Second interval is positive
215      //Assert.AreEqual(new Interval(aPos.LowerBound/Math.Sqrt(17), aPos.UpperBound/Math.Sqrt(5)), Interval.AnalyticalQuotient(aPos, bPos));
216      //Assert.AreEqual(new Interval(aZero.LowerBound/Math.Sqrt(5), aZero.UpperBound/Math.Sqrt(5)), Interval.AnalyticalQuotient(aZero, bPos));
217      //Assert.AreEqual(new Interval(aNeg.LowerBound/Math.Sqrt(5), aNeg.UpperBound/Math.Sqrt(17)), Interval.AnalyticalQuotient(aNeg, bPos));
218      ////Second interval is negative
219      //Assert.AreEqual(new Interval(aPos.LowerBound/Math.Sqrt(17), aPos.UpperBound/Math.Sqrt(5)), Interval.AnalyticalQuotient(aPos, bNeg));
220      //Assert.AreEqual(new Interval(aZero.LowerBound/Math.Sqrt(5), aZero.UpperBound/Math.Sqrt(5)), Interval.AnalyticalQuotient(aZero, bNeg));
221      //Assert.AreEqual(new Interval(aNeg.LowerBound/Math.Sqrt(5), aNeg.UpperBound/Math.Sqrt(17)), Interval.AnalyticalQuotient(aNeg, bNeg));
222      Assert.AreEqual(new Interval(double.NegativeInfinity, double.PositiveInfinity), Interval.AnalyticQuotient(aPos, bZero));
223      Assert.AreEqual(new Interval(double.NegativeInfinity, double.PositiveInfinity), Interval.AnalyticQuotient(aPos, bPos));
224      Assert.AreEqual(new Interval(double.NegativeInfinity, double.PositiveInfinity), Interval.AnalyticQuotient(aZero, bNeg));
225    }
226
227    [TestMethod]
228    [TestCategory("Problems.DataAnalysis")]
229    [TestProperty("Time", "short")]
230    public void IsNegativeIntervalTest() {
231      Assert.IsTrue(new Interval(-2, -1).IsNegative);
232      Assert.IsFalse(new Interval(-2, 0).IsNegative);
233      Assert.IsFalse(new Interval(-2, 2).IsNegative);
234      Assert.IsFalse(new Interval(2, 4).IsNegative);
235    }
236
237    [TestMethod]
238    [TestCategory("Problems.DataAnalysis")]
239    [TestProperty("Time", "short")]
240    public void IsPositiveIntervalTest() {
241      Assert.IsTrue(new Interval(3, 5).IsPositive);
242      Assert.IsFalse(new Interval(0, 5).IsPositive);
243      Assert.IsFalse(new Interval(-1, 5).IsPositive);
244      Assert.IsFalse(new Interval(-5, -2).IsPositive);
245    }
246
247    [TestMethod]
248    [TestCategory("Problems.DataAnalysis")]
249    [TestProperty("Time", "short")]
250    public void IsAlmostIntervalTest() {
251      var negativeLowerBound = -2E-13;
252      var negativeUpperBound = -1E-13;
253      var positiveLowerBound = 3E-13;
254      var positiveUpperBound = 5E-13;
255
256      var negativeInterval = new Interval(negativeLowerBound, negativeUpperBound);
257      var positiveInterval = new Interval(positiveLowerBound, positiveUpperBound);
258      var zeroInterval = new Interval(negativeUpperBound, positiveLowerBound);
259
260      //Check for right-shift of negative interval
261      Assert.AreEqual(negativeUpperBound, negativeInterval.LowerBound);
262      Assert.AreEqual(negativeUpperBound, negativeInterval.UpperBound);
263      //Check for left-shift of positive interval
264      Assert.AreEqual(positiveLowerBound, positiveInterval.LowerBound);
265      Assert.AreEqual(positiveLowerBound, positiveInterval.UpperBound);
266      //Check for setting interval to zero
267      Assert.AreEqual(0, zeroInterval.LowerBound);
268      Assert.AreEqual(0, zeroInterval.UpperBound);
269    }
270
271    [TestMethod]
272    [TestCategory("Problems.DataAnalysis")]
273    [TestProperty("Time", "short")]
274    public void ContaintsTest() {
275      var negativeInterval = new Interval(-10, -5);
276      var positiveInterval = new Interval(5, 10);
277      var overZeroInterval = new Interval(-5, 5);
278
279      //Tests for negative intervals
280      Assert.AreEqual(true, negativeInterval.Contains(new Interval(-9, -7)));
281      Assert.AreEqual(false, negativeInterval.Contains(new Interval(-11, -3)));
282      Assert.AreEqual(false, negativeInterval.Contains(positiveInterval));
283      Assert.AreEqual(false, negativeInterval.Contains(overZeroInterval));
284      Assert.AreEqual(true, negativeInterval.Contains(-8));
285      Assert.AreEqual(false, negativeInterval.Contains(-12));
286      Assert.AreEqual(false, negativeInterval.Contains(0));
287      //Testes for positive intervals
288      Assert.AreEqual(true, positiveInterval.Contains(new Interval(6, 10)));
289      Assert.AreEqual(false, positiveInterval.Contains(new Interval(6, 12)));
290      Assert.AreEqual(false, positiveInterval.Contains(negativeInterval));
291      Assert.AreEqual(false, positiveInterval.Contains(overZeroInterval));
292      Assert.AreEqual(true, positiveInterval.Contains(7));
293      Assert.AreEqual(false, positiveInterval.Contains(11));
294      Assert.AreEqual(false, positiveInterval.Contains(0));
295      //Tests for over zero intervals
296      Assert.AreEqual(true, overZeroInterval.Contains(new Interval(-3, 3)));
297      Assert.AreEqual(true, overZeroInterval.Contains(new Interval(-4, -1)));
298      Assert.AreEqual(true, overZeroInterval.Contains(new Interval(1, 5)));
299      Assert.AreEqual(false, overZeroInterval.Contains(new Interval(-6, 0)));
300      Assert.AreEqual(false, overZeroInterval.Contains(new Interval(0, 6)));
301      Assert.AreEqual(false, overZeroInterval.Contains(new Interval(-7, 7)));
302      Assert.AreEqual(true, overZeroInterval.Contains(-3));
303      Assert.AreEqual(true, overZeroInterval.Contains(0));
304      Assert.AreEqual(true, overZeroInterval.Contains(3));
305      Assert.AreEqual(false, overZeroInterval.Contains(12));
306      Assert.AreEqual(false, overZeroInterval.Contains(-7));
307    }
308
309    [TestMethod]
310    [TestCategory("Problems.DataAnalysis")]
311    [TestProperty("Time", "short")]
312    public void GetIntervalTest() {
313      var values = new List<double>() { -2.5, -9, 2, 7, 0 ,12, 12.4, 12.4, 9.29, 1002, -29.9};
314      var valuesNan = new List<double>() { double.NaN, 2, 4, 19, -2, -12.2};
315      var valuesInf = new List<double>() {double.NegativeInfinity, double.PositiveInfinity, 12, 2, -2, -12.2};
316
317      var valuesInterval = new Interval(-29.9, 1002);
318      var valuesNanInterval = new Interval(double.NaN, double.NaN);
319      var valuesInfInterval = new Interval(double.NegativeInfinity, double.PositiveInfinity);
320
321
322      Assert.AreEqual(valuesInterval, Interval.GetInterval(values));
323      Assert.AreEqual(valuesNanInterval, Interval.GetInterval(valuesNan));
324      Assert.AreEqual(valuesInfInterval, Interval.GetInterval(valuesInf));
325    }
326
327    [TestMethod]
328    [TestCategory("Problems.DataAnalysis")]
329    [TestProperty("Time", "short")]
330    public void GeometricTest() {
331      CheckLowerAndUpperBoundOfInterval(new Interval(-1, -0.936456687290796), Interval.Cosine(new Interval(3, 3.5)));
332      CheckLowerAndUpperBoundOfInterval(new Interval(-1, -0.936456687290796), Interval.Cosine(new Interval(-3.5, -3)));
333      CheckLowerAndUpperBoundOfInterval(new Interval(-1, 1), Interval.Cosine(new Interval(-3.5, 3)));
334      CheckLowerAndUpperBoundOfInterval(new Interval(-0.839071529076452, 0.843853958732493), Interval.Cosine(new Interval(10, 12)));
335      CheckLowerAndUpperBoundOfInterval(new Interval(0.136737218207833, 0.907446781450197), Interval.Cosine(new Interval(13, 14)));
336      CheckLowerAndUpperBoundOfInterval(new Interval(-0.839071529076452, 1), Interval.Cosine(new Interval(10, 14)));
337      CheckLowerAndUpperBoundOfInterval(new Interval(-1, 0.136737218207833), Interval.Cosine(new Interval(14, 16)));
338      CheckLowerAndUpperBoundOfInterval(new Interval(-0.839071529076452, 0.004425697988051), Interval.Cosine(new Interval(-11, -10)));
339      CheckLowerAndUpperBoundOfInterval(new Interval(0.136737218207833, 0.907446781450197), Interval.Cosine(new Interval(-14, -13)));
340      CheckLowerAndUpperBoundOfInterval(new Interval(-1, 0.136737218207833), Interval.Cosine(new Interval(-16, -14)));
341      CheckLowerAndUpperBoundOfInterval(new Interval(0.101585703696621, 1), Interval.Cosine(new Interval(-102, -100)));
342      CheckLowerAndUpperBoundOfInterval(new Interval(-1, 1), Interval.Cosine(new Interval(4.6e15, 4.7e15)));
343      CheckLowerAndUpperBoundOfInterval(new Interval(0.87758256189037265, 0.87758256189037276), Interval.Cosine(new Interval(0.5, 0.5)));
344      CheckLowerAndUpperBoundOfInterval(new Interval(-0.09904103659872825, 0.8775825618903728), Interval.Cosine(new Interval(0.5, 1.67)));
345      CheckLowerAndUpperBoundOfInterval(new Interval(-1.0, 0.77556587851025016), Interval.Cosine(new Interval(2.1, 5.6)));
346      CheckLowerAndUpperBoundOfInterval(new Interval(-1.0, 1.0), Interval.Cosine(new Interval(0.5, 8.5)));
347      CheckLowerAndUpperBoundOfInterval(new Interval(-1.0, -0.09904103659872801), Interval.Cosine(new Interval(1.67, 3.2)));
348
349      CheckLowerAndUpperBoundOfInterval(new Interval(double.NegativeInfinity, double.PositiveInfinity), Interval.Tangens(new Interval(double.NegativeInfinity, double.PositiveInfinity)));
350      CheckLowerAndUpperBoundOfInterval(new Interval(0, 1.55740772465490223051), Interval.Tangens(new Interval(0, 1)));
351      CheckLowerAndUpperBoundOfInterval(new Interval(-1.55740772465490223051, 0), Interval.Tangens(new Interval(-1, 0)));
352      CheckLowerAndUpperBoundOfInterval(new Interval(double.NegativeInfinity, double.PositiveInfinity), Interval.Tangens(new Interval(-2, -1)));
353      CheckLowerAndUpperBoundOfInterval(new Interval(double.NegativeInfinity, double.PositiveInfinity), Interval.Tangens(new Interval(202, 203)));
354      CheckLowerAndUpperBoundOfInterval(new Interval(0.54630248984379048, 0.5463024898437906), Interval.Tangens(new Interval(0.5, 0.5)));
355      CheckLowerAndUpperBoundOfInterval(new Interval(double.NegativeInfinity, double.PositiveInfinity), Interval.Tangens(new Interval(0.5,
356        1.67)));
357
358      CheckLowerAndUpperBoundOfInterval(new Interval(double.NegativeInfinity, double.PositiveInfinity), Interval.Tangens(new Interval(
359        6.638314112824137, 8.38263151220128)));
360
361      CheckLowerAndUpperBoundOfInterval(new Interval(0.47942553860420295, 0.47942553860420301), Interval.Sine(new Interval(0.5, 0.5)));
362      CheckLowerAndUpperBoundOfInterval(new Interval(4.7942553860420295e-01, 1.0), Interval.Sine(new Interval(0.5, 1.67)));
363      CheckLowerAndUpperBoundOfInterval(new Interval(-5.8374143427580093e-02, 9.9508334981018021e-01), Interval.Sine(new Interval(1.67,
364        3.2)));
365      CheckLowerAndUpperBoundOfInterval(new Interval(-1.0, 0.863209366648874), Interval.Sine(new Interval(2.1, 5.6)));
366      CheckLowerAndUpperBoundOfInterval(new Interval(-1.0, 1.0), Interval.Sine(new Interval(0.5, 8.5)));
367      CheckLowerAndUpperBoundOfInterval(new Interval(-1.0, 0.9775301176650971), Interval.Sine(new Interval(-4.5, 0.1)));
368      CheckLowerAndUpperBoundOfInterval(new Interval(-1.0, 1.0), Interval.Sine(new Interval(1.3, 6.3)));
369    }
370
371    [TestMethod]
372    [TestCategory("Problems.DataAnalysis")]
373    [TestProperty("Time", "short")]
374    public void EqualsTest() {
375      var interval1 = new Interval(0, 12);
376      var interval2 = new Interval(-12, 8);
377      var interval3 = new Interval(double.NegativeInfinity, 0);
378
379      Assert.AreEqual(true, interval1.Equals(new Interval(0, 12)));
380      Assert.AreEqual(false, interval1.Equals(interval2));
381      Assert.AreEqual(true, interval3 == new Interval(double.NegativeInfinity, 0));
382      Assert.AreEqual(true, interval1 != interval2);
383      Assert.AreEqual(false, interval2 == interval3);
384      Assert.AreEqual(false, interval1 != new Interval(0, 12));
385    }
386    //[TestMethod]
387    //[TestCategory("Problems.DataAnalysis")]
388    //[TestProperty("Time", "short")]
389    //public void RootTest() {
390    //  var posInterval = new Interval(3, 5);
391    //  var negInterval = new Interval(-6, -2);
392    //  var posIntervalConst = new Interval(5, 5);
393    //  var negIntervalConst = new Interval(-3, -3);
394    //  var zeroIntervalConst = new Interval(0, 0);
395    //  var zeroPosInterval = new Interval(0, 2);
396    //  var zeroNegInterval = new Interval(-2, 0);
397
398    //  var posRoot = new Interval(4, 4);
399    //  var negRoot = new Interval(-4, -4);
400    //  var zeroRoot = new Interval(0, 0);
401    //  var oneRoot = new Interval(1, 1);
402
403    //  Assert.AreEqual(Interval.Root(posInterval, posRoot), new Interval(Math.Pow(3, (1.0/4)), Math.Pow(5, (1.0/4))));
404    //  Assert.AreEqual(Interval.Root(posInterval, negRoot), new Interval(Math.Pow(5, -(1.0/4)), Math.Pow(3, -(1.0/4))));
405    //  Assert.AreEqual(Interval.Root(posInterval, zeroRoot), new Interval(double.NaN, double.NaN));
406    //  Assert.AreEqual(Interval.Root(posInterval, oneRoot), new Interval(3, 5));
407
408    //  Assert.AreEqual(Interval.Root(negInterval, posRoot), new Interval(Math.Pow(-6, (1.0 / 4)), Math.Pow(-2, (1.0 / 4))));
409    //  Assert.AreEqual(Interval.Root(negInterval, negRoot), new Interval(Math.Pow(-2, -(1.0 / 4)), Math.Pow(-6, -(1.0 / 4))));
410    //  Assert.AreEqual(Interval.Root(negInterval, zeroRoot), new Interval(double.NaN, double.NaN));
411    //  Assert.AreEqual(Interval.Root(negInterval, oneRoot), new Interval(-6, -2));
412
413    //  Assert.AreEqual(Interval.Root(posIntervalConst, posRoot), new Interval(Math.Pow(5, (1.0 / 4)), Math.Pow(5, (1.0 / 4))));
414    //  Assert.AreEqual(Interval.Root(posIntervalConst, negRoot), new Interval(Math.Pow(5, -(1.0 / 4)), Math.Pow(5, -(1.0 / 4))));
415    //  Assert.AreEqual(Interval.Root(posIntervalConst, zeroRoot), new Interval(double.NaN, double.NaN));
416    //  Assert.AreEqual(Interval.Root(posIntervalConst, oneRoot), new Interval(5, 5));
417
418    //  Assert.AreEqual(Interval.Root(negIntervalConst, posRoot), new Interval(Math.Pow(-3, (1.0 / 4)), Math.Pow(-3, (1.0 / 4))));
419    //  Assert.AreEqual(Interval.Root(negIntervalConst, negRoot), new Interval(Math.Pow(-3, -(1.0 / 4)), Math.Pow(-3, -(1.0 / 4))));
420    //  Assert.AreEqual(Interval.Root(negIntervalConst, zeroRoot), new Interval(double.NaN, double.NaN));
421    //  Assert.AreEqual(Interval.Root(negIntervalConst, oneRoot), new Interval(-3, -3));
422
423    //  Assert.AreEqual(Interval.Root(zeroIntervalConst, posRoot), new Interval(0, 0));
424    //  //Compley Infinity https://www.wolframalpha.com/input/?i=root%28-4%2C+0%29
425    //  Assert.AreEqual(Interval.Root(zeroIntervalConst, negRoot), new Interval(double.PositiveInfinity, double.PositiveInfinity));
426    //  Assert.AreEqual(Interval.Root(zeroIntervalConst, zeroRoot), new Interval(0, 0));
427    //  Assert.AreEqual(Interval.Root(zeroIntervalConst, oneRoot), new Interval(0, 0));
428
429    //  Assert.AreEqual(Interval.Root(zeroPosInterval, posRoot), new Interval(0, Math.Pow(2, (1.0 / 4))));
430    //  //Check for complex infinity
431    //  Assert.AreEqual(Interval.Root(zeroPosInterval, negRoot), new Interval(Math.Pow(2, -(1.0 / 4)), double.PositiveInfinity));
432    //  Assert.AreEqual(Interval.Root(zeroPosInterval, zeroRoot), new Interval(0, 0));
433    //  Assert.AreEqual(Interval.Root(zeroPosInterval, oneRoot), new Interval(0, 2));
434
435    //  Assert.AreEqual(Interval.Root(zeroNegInterval, posRoot), new Interval(Math.Pow(-2, (1.0 / 4)),0));
436    //  //Check for complex infinity
437    //  Assert.AreEqual(Interval.Root(zeroNegInterval, negRoot), new Interval(Math.Pow(-2, -(1.0 / 4)), double.PositiveInfinity));
438    //  Assert.AreEqual(Interval.Root(zeroNegInterval, zeroRoot), new Interval(double.NaN, double.NaN));
439    //  Assert.AreEqual(Interval.Root(zeroNegInterval, oneRoot), new Interval(-2, 0));
440    //}
441  }
442}
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