source: branches/2994-AutoDiffForIntervals/HeuristicLab.Tests/HeuristicLab.Problems.DataAnalysis-3.4/IntervalTest.cs @ 17303

Last change on this file since 17303 was 17303, checked in by gkronber, 3 years ago

#2994 continued refactoring and extended unit tests. Interval calculation still fails for some edge cases (mainly for undefined behaviour). VectorEvaluator and VectorAutoDiffEvaluator produce the same results as the LinearInterpreter. TODO: check gradient calculation

File size: 8.0 KB
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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 TestIntervalAddOperation() {
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 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      // [0, 1] / [0, 1]
79      Assert.AreEqual(Interval.Divide(new Interval(0, 1), new Interval(0, 1)), new Interval(1, double.PositiveInfinity)); // returns [NaN, NaN] because of (0 / 0)
80    }
81
82    [TestMethod]
83    [TestCategory("Problems.DataAnalysis")]
84    [TestProperty("Time", "short")]
85    public void TestIntervalSineOperator() {
86      //sine depends on interval
87      //sin([0, 2*pi]) = [-1, 1]
88      Assert.AreEqual<Interval>(Interval.Sine(new Interval(0, 2 * Math.PI)), new Interval(-1, 1));
89      //sin([-pi/2, pi/2]) = [sin(-pi/2), sin(pi/2)]
90      Assert.AreEqual<Interval>(Interval.Sine(new Interval(-1 * Math.PI / 2, Math.PI / 2)), new Interval(-1, 1));
91      //sin([0, pi/2]) = [sin(0), sin(pi/2)]
92      Assert.AreEqual<Interval>(Interval.Sine(new Interval(0, Math.PI / 2)), new Interval(0, 1));
93      //sin([pi, 3*pi/2]) = [sin(pi), sin(3*pi/2)]
94      Assert.AreEqual<Interval>(Interval.Sine(new Interval(Math.PI, 3 * Math.PI / 2)), new Interval(-1, 0));
95      Assert.AreEqual<Interval>(Interval.Sine(new Interval(1, 2)), new Interval(Math.Min(Math.Sin(1), Math.Sin(2)), 1));
96      Assert.AreEqual<Interval>(Interval.Sine(new Interval(1, 3)), new Interval(Math.Min(Math.Sin(1), Math.Sin(3)), 1));
97      Assert.AreEqual<Interval>(Interval.Sine(new Interval(Math.PI, 5 * Math.PI / 2)), new Interval(-1, 1));
98    }
99
100    [TestMethod]
101    [TestCategory("Problems.DataAnalysis")]
102    [TestProperty("Time", "short")]
103    public void TestIntervalCosineOperator() {
104      //Cosine uses sine Interval.Sine(Interval.Subtract(a, new Interval(Math.PI / 2, Math.PI / 2)));
105      Assert.AreEqual<Interval>(Interval.Cosine(new Interval(0, 2 * Math.PI)), new Interval(-1, 1));
106      Assert.AreEqual<Interval>(new Interval(-1, 1), Interval.Cosine(new Interval(Math.PI, 4 * Math.PI / 2)));
107    }
108
109    [TestMethod]
110    [TestCategory("Problems.DataAnalysis")]
111    [TestProperty("Time", "short")]
112    public void TestIntervalLogOperator() {
113      //Log([3, 5]) = [log(3), log(5)]
114      Assert.AreEqual<Interval>(new Interval(Math.Log(3), Math.Log(5)), Interval.Logarithm(new Interval(3, 5)));
115      //Log([0.5, 1]) = [log(0.5), log(1)]
116      Assert.AreEqual<Interval>(new Interval(Math.Log(0.5), 0), Interval.Logarithm(new Interval(0.5, 1)));
117      //Log([-1, 5]) = [NaN, log(5)]
118      var result = Interval.Logarithm(new Interval(-1, 5));
119      Assert.AreEqual<Interval>(new Interval(double.NaN, Math.Log(5)),result);
120      Assert.IsTrue(result.IsInfiniteOrUndefined);
121    }
122
123
124    [TestMethod]
125    [TestCategory("Problems.DataAnalysis")]
126    [TestProperty("Time", "short")]
127    public void TestIntervalExpOperator() {
128      //Exp([0, 1]) = [exp(0), exp(1)]
129      Assert.AreEqual<Interval>(new Interval(1, Math.Exp(1)), Interval.Exponential(new Interval(0, 1)));
130    }
131
132
133    [TestMethod]
134    [TestCategory("Problems.DataAnalysis")]
135    [TestProperty("Time", "short")]
136    public void TestIntervalSqrOperator() {
137      Assert.AreEqual<Interval>(new Interval(1, 4), Interval.Square(new Interval(1, 2)));
138      Assert.AreEqual<Interval>(new Interval(1, 4), Interval.Square(new Interval(-2, -1)));
139      Assert.AreEqual<Interval>(new Interval(0, 4), Interval.Square(new Interval(-2, 2)));
140    }
141
142    [TestMethod]
143    [TestCategory("Problems.DataAnalysis")]
144    [TestProperty("Time", "short")]
145    public void TestIntervalSqrtOperator() {
146      Assert.AreEqual<Interval>(new Interval(1, 2), Interval.SquareRoot(new Interval(1, 4)));
147      Assert.AreEqual<Interval>(new Interval(double.NaN, double.NaN), Interval.SquareRoot(new Interval(-4, -1)));
148    }
149
150    [TestMethod]
151    [TestCategory("Problems.DataAnalysis")]
152    [TestProperty("Time", "short")]
153    public void TestIntervalCubeOperator() {
154      Assert.AreEqual<Interval>(new Interval(1, 8), Interval.Cube(new Interval(1, 2)));
155      Assert.AreEqual<Interval>(new Interval(-8, -1), Interval.Cube(new Interval(-2, -1)));
156      Assert.AreEqual<Interval>(new Interval(-8, 8), Interval.Cube(new Interval(-2, 2)));
157    }
158
159    [TestMethod]
160    [TestCategory("Problems.DataAnalysis")]
161    [TestProperty("Time", "short")]
162    public void TestIntervalCbrtOperator() {
163      Assert.AreEqual<Interval>(new Interval(1, 2), Interval.CubicRoot(new Interval(1, 8)));
164      Assert.AreEqual<Interval>(new Interval(-2, -1), Interval.CubicRoot(new Interval(-8, -1))); // XXX should be fixed for old interval calculation
165    }
166  }
167}
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