Free cookie consent management tool by TermsFeed Policy Generator

source:trunk/HeuristicLab.Tests/HeuristicLab.Problems.DataAnalysis-3.4/IntervalTest.cs@17348

Last change on this file since 17348 was 17348, checked in by chaider, 4 years ago

#3032 Added analytical quotient for intervals

File size: 11.6 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")]
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]
23      //([-1, 1] + [0, 3]) + [-2, 2] = [-3, 6]
25    }
26
27    [TestMethod]
28    [TestCategory("Problems.DataAnalysis")]
29    [TestProperty("Time", "short")]
30    public void TestIntervalSubOperation() {
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 TestIntervalMutlipyOperation() {
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 TestIntervalDivideOperation() {
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 TestIntervalSineOperator() {
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 TestIntervalCosineOperator() {
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 TestIntervalLogOperator() {
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 TestIntervalExpOperator() {
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 TestIntervalSqrOperator() {
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 TestIntervalSqrtOperator() {
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 TestIntervalCubeOperator() {
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 TestIntervalCbrtOperator() {
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 TestIntervalAbsoluteOperator() {
173      Assert.AreEqual(new Interval(2, 2), Interval.Absolute(new Interval(-2, -2)));
174      Assert.AreEqual(new Interval(5, 5), Interval.Absolute(new Interval(5, 5)));
175      Assert.AreEqual(new Interval(2, 8), Interval.Absolute(new Interval(2, 8)));
176      Assert.AreEqual(new Interval(5, 14), Interval.Absolute(new Interval(-14, -5)));
177      Assert.AreEqual(new Interval(2, 7), Interval.Absolute(new Interval(-2, 7)));
178      Assert.AreEqual(new Interval(2, 22), Interval.Absolute(new Interval(-22, -2)));
179      Assert.AreEqual(new Interval(6, 22), Interval.Absolute(new Interval(-22, 6)));
180      Assert.AreEqual(new Interval(0, 0), Interval.Absolute(new Interval(0, 0)));
181      Assert.AreEqual(new Interval(0, 2), Interval.Absolute(new Interval(-2, 0)));
182      Assert.AreEqual(new Interval(0, 2), Interval.Absolute(new Interval(0, 2)));
183    }
184
185    [TestMethod]
186    [TestCategory("Problems.DataAnalysis")]
187    [TestProperty("Time", "short")]
188    public void TestIntervalAnalyticalQuotient() {
189      //Second interval goes over zero
190      Assert.AreEqual(new Interval(-4, 2), Interval.AnalyticalQuotient(new Interval(-4, 2), new Interval(0, 5)));
191      Assert.AreEqual(new Interval(-4, 2), Interval.AnalyticalQuotient(new Interval(-4, 2), new Interval(-4, 0)));
192      Assert.AreEqual(new Interval(-4, 2), Interval.AnalyticalQuotient(new Interval(-4, 2), new Interval(-2, 4)));
193      Assert.AreEqual(new Interval(-4, -2), Interval.AnalyticalQuotient(new Interval(-4, -2), new Interval(0, 5)));
194      Assert.AreEqual(new Interval(-4, -2), Interval.AnalyticalQuotient(new Interval(-4, -2), new Interval(-4, 0)));
195      Assert.AreEqual(new Interval(-4, -2), Interval.AnalyticalQuotient(new Interval(-4, -2), new Interval(-2, 4)));
196      Assert.AreEqual(new Interval(3, 7), Interval.AnalyticalQuotient(new Interval(3, 7), new Interval(0, 5)));
197      Assert.AreEqual(new Interval(3, 7), Interval.AnalyticalQuotient(new Interval(3, 7), new Interval(-4, 0)));
198      Assert.AreEqual(new Interval(3, 7), Interval.AnalyticalQuotient(new Interval(3, 7), new Interval(-2, 4)));
199      Assert.AreEqual(new Interval(0, 0), Interval.AnalyticalQuotient(new Interval(0, 0), new Interval(0, 5)));
200      Assert.AreEqual(new Interval(-4, -4), Interval.AnalyticalQuotient(new Interval(-4, -4), new Interval(-4, 0)));
201      Assert.AreEqual(new Interval(4, 4), Interval.AnalyticalQuotient(new Interval(4, 4), new Interval(-2, 4)));
202
203      //First interval goes over zero
204      Assert.AreEqual(new Interval(-2.0/Math.Sqrt(5), 5.0 / Math.Sqrt(5)), Interval.AnalyticalQuotient(new Interval(-2, 5), new Interval(-5, -2)));
205      Assert.AreEqual(new Interval(-2.0 / Math.Sqrt(5), 5.0 / Math.Sqrt(5)), Interval.AnalyticalQuotient(new Interval(-2, 5), new Interval(2, 5)));
206      Assert.AreEqual(new Interval(2.0/Math.Sqrt(26), 5.0/Math.Sqrt(5)), Interval.AnalyticalQuotient(new Interval(2, 5), new Interval(-5, -2)));
207      Assert.AreEqual(new Interval(2.0 / Math.Sqrt(26), 5.0 / Math.Sqrt(5)), Interval.AnalyticalQuotient(new Interval(2, 5), new Interval(2, 5)));
208      Assert.AreEqual(new Interval(-5.0/Math.Sqrt(5), -2.0/Math.Sqrt(26)), Interval.AnalyticalQuotient(new Interval(-5, -2), new Interval(-5, -2)));
209      Assert.AreEqual(new Interval(-5.0 / Math.Sqrt(5), -2.0 / Math.Sqrt(26)), Interval.AnalyticalQuotient(new Interval(-5, -2), new Interval(2, 5)));
210    }
211  }
212}
Note: See TracBrowser for help on using the repository browser.