| 1 | using System;
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| 2 | using Microsoft.VisualStudio.TestTools.UnitTesting;
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| 3 |
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| 4 | namespace HeuristicLab.Problems.DataAnalysis.Tests {
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| 5 | [TestClass]
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| 6 | public class IntervalTest {
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| 7 | private readonly Interval a = new Interval(-1, 1);
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| 8 | private readonly Interval b = new Interval(-2, 2);
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| 9 | private readonly Interval c = new Interval(0, 3);
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| 10 | private readonly Interval d = new Interval(1, 3);
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| 11 | private readonly Interval e = new Interval(4, 6);
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| 12 |
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| 13 | [TestMethod]
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| 14 | [TestCategory("Problems.DataAnalysis")]
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| 15 | [TestProperty("Time", "short")]
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| 16 | public void TestIntervalAddOperation() {
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| 17 | //add [x1,x2] + [y1,y2] = [x1 + y1,x2 + y2]
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| 18 |
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| 19 | // [-1,1] + [-2,2] = [-3,3]
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| 20 | Assert.AreEqual(Interval.Add(a, b), new Interval(-3, 3));
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| 21 | //([-1, 1] + [-2, 2]) + [0, 3] = [-3, 6]
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| 22 | Assert.AreEqual(Interval.Add(Interval.Add(a, b), c), new Interval(-3, 6));
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| 23 | //([-1, 1] + [0, 3]) + [-2, 2] = [-3, 6]
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| 24 | Assert.AreEqual(Interval.Add(Interval.Add(a, c), b), new Interval(-3, 6));
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| 25 | }
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| 26 |
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| 27 | [TestMethod]
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| 28 | [TestCategory("Problems.DataAnalysis")]
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| 29 | [TestProperty("Time", "short")]
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| 30 | public void TestIntervalSubOperation() {
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| 31 | //subtract [x1,x2] − [y1,y2] = [x1 − y2,x2 − y1]
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| 32 |
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| 33 | //[-1, 1] - [-2, 2] = [-3, 3]
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| 34 | Assert.AreEqual<Interval>(Interval.Subtract(a, b), new Interval(-3, 3));
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| 35 | //([-1, 1] - [-2, 2]) - [0, 3] = [-6, 3]
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| 36 | Assert.AreEqual<Interval>(Interval.Subtract(Interval.Subtract(a, b), c), new Interval(-6, 3));
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| 37 | //([-1, 1] - [0, 3]) - [-2, 2] = [-6, 3]
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| 38 | Assert.AreEqual<Interval>(Interval.Subtract(Interval.Subtract(a, c), b), new Interval(-6, 3));
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| 39 | }
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| 40 |
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| 41 | [TestMethod]
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| 42 | [TestCategory("Problems.DataAnalysis")]
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| 43 | [TestProperty("Time", "short")]
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| 44 | public void TestIntervalMutlipyOperation() {
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| 45 | //multiply [x1,x2] * [y1,y2] = [min(x1*y1,x1*y2,x2*y1,x2*y2),max(x1*y1,x1*y2,x2*y1,x2*y2)]
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| 46 |
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| 47 | //[-1, 1] * [-2, 2] = [-2, 2]
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| 48 | Assert.AreEqual<Interval>(Interval.Multiply(a, b), new Interval(-2, 2));
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| 49 | //([-1, 1] * [-2, 2]) * [0, 3] = [-6, 6]
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| 50 | Assert.AreEqual<Interval>(Interval.Multiply(Interval.Multiply(a, b), c), new Interval(-6, 6));
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| 51 | //([-1, 1] * [0, 3]) * [-2, 2] = [-6, 6]
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| 52 | Assert.AreEqual<Interval>(Interval.Multiply(Interval.Multiply(a, c), b), new Interval(-6, 6));
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| 53 |
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| 54 | // [-2, 0] * [-2, 0] = [0, 4]
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| 55 | Assert.AreEqual<Interval>(new Interval(0, 4), Interval.Multiply(new Interval(-2, 0), new Interval(-2, 0)));
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| 56 | }
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| 57 |
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| 58 | [TestMethod]
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| 59 | [TestCategory("Problems.DataAnalysis")]
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| 60 | [TestProperty("Time", "short")]
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| 61 | public void TestIntervalDivideOperation() {
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| 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].
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| 63 |
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| 64 | //[4, 6] / [1, 3] = [4/3, 6]
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| 65 | Assert.AreEqual<Interval>(Interval.Divide(e, d), new Interval(4.0 / 3.0, 6));
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| 66 | //([4, 6] / [1, 3]) / [1, 3] = [4/9, 6]
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| 67 | Assert.AreEqual<Interval>(Interval.Divide(Interval.Divide(e, d), d), new Interval(4.0 / 9.0, 6));
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| 68 | //[4, 6] / [0, 3] = [4/3, +Inf]
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| 69 | Assert.AreEqual<Interval>(Interval.Divide(e, c), new Interval(4.0 / 3.0, double.PositiveInfinity));
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| 70 | //[-1, 1] / [0, 3] = [+Inf, -Inf]
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| 71 | Assert.AreEqual<Interval>(Interval.Divide(a, c), new Interval(double.NegativeInfinity, double.PositiveInfinity));
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| 72 | //Devision by 0 ==> IsInfiniteOrUndefined == true
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| 73 | Assert.IsTrue(Interval.Divide(e, c).IsInfiniteOrUndefined);
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| 74 | //Devision by 0 ==> IsInfiniteOrUndefined == true
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| 75 | Assert.IsTrue(Interval.Divide(a, c).IsInfiniteOrUndefined);
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| 76 | Assert.AreEqual<Interval>(Interval.Divide(d, b), new Interval(double.NegativeInfinity, double.PositiveInfinity));
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| 77 | }
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| 78 |
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| 79 | [TestMethod]
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| 80 | [TestCategory("Problems.DataAnalysis")]
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| 81 | [TestProperty("Time", "short")]
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| 82 | public void TestIntervalSineOperator() {
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| 83 | //sine depends on interval
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| 84 | //sin([0, 2*pi]) = [-1, 1]
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| 85 | Assert.AreEqual<Interval>(Interval.Sine(new Interval(0, 2 * Math.PI)), new Interval(-1, 1));
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| 86 | //sin([-pi/2, pi/2]) = [sin(-pi/2), sin(pi/2)]
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| 87 | Assert.AreEqual<Interval>(Interval.Sine(new Interval(-1 * Math.PI / 2, Math.PI / 2)), new Interval(-1, 1));
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| 88 | //sin([0, pi/2]) = [sin(0), sin(pi/2)]
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| 89 | Assert.AreEqual<Interval>(Interval.Sine(new Interval(0, Math.PI / 2)), new Interval(0, 1));
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| 90 | //sin([pi, 3*pi/2]) = [sin(pi), sin(3*pi/2)]
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| 91 | Assert.AreEqual<Interval>(Interval.Sine(new Interval(Math.PI, 3 * Math.PI / 2)), new Interval(-1, 0));
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| 92 | Assert.AreEqual<Interval>(Interval.Sine(new Interval(1, 2)), new Interval(Math.Min(Math.Sin(1), Math.Sin(2)), 1));
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| 93 | Assert.AreEqual<Interval>(Interval.Sine(new Interval(1, 3)), new Interval(Math.Min(Math.Sin(1), Math.Sin(3)), 1));
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| 94 | Assert.AreEqual<Interval>(Interval.Sine(new Interval(Math.PI, 5 * Math.PI / 2)), new Interval(-1, 1));
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| 95 | }
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| 96 |
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| 97 | [TestMethod]
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| 98 | [TestCategory("Problems.DataAnalysis")]
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| 99 | [TestProperty("Time", "short")]
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| 100 | public void TestIntervalCosineOperator() {
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| 101 | //Cosine uses sine Interval.Sine(Interval.Subtract(a, new Interval(Math.PI / 2, Math.PI / 2)));
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| 102 | Assert.AreEqual<Interval>(Interval.Cosine(new Interval(0, 2 * Math.PI)), new Interval(-1, 1));
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| 103 | Assert.AreEqual<Interval>(new Interval(-1, 1), Interval.Cosine(new Interval(Math.PI, 4 * Math.PI / 2)));
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| 104 | }
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| 105 |
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| 106 | [TestMethod]
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| 107 | [TestCategory("Problems.DataAnalysis")]
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| 108 | [TestProperty("Time", "short")]
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| 109 | public void TestIntervalLogOperator() {
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| 110 | //Log([3, 5]) = [log(3), log(5)]
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| 111 | Assert.AreEqual<Interval>(new Interval(Math.Log(3), Math.Log(5)), Interval.Logarithm(new Interval(3, 5)));
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| 112 | //Log([0.5, 1]) = [log(0.5), log(1)]
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| 113 | Assert.AreEqual<Interval>(new Interval(Math.Log(0.5), 0), Interval.Logarithm(new Interval(0.5, 1)));
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| 114 | //Log([-1, 5]) = [NaN, log(5)]
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| 115 | var result = Interval.Logarithm(new Interval(-1, 5));
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| 116 | Assert.AreEqual<Interval>(new Interval(double.NaN, Math.Log(5)),result);
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| 117 | Assert.IsTrue(result.IsInfiniteOrUndefined);
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| 118 | }
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| 119 |
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| 120 |
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| 121 | [TestMethod]
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| 122 | [TestCategory("Problems.DataAnalysis")]
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| 123 | [TestProperty("Time", "short")]
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| 124 | public void TestIntervalExpOperator() {
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| 125 | //Exp([0, 1]) = [exp(0), exp(1)]
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| 126 | Assert.AreEqual<Interval>(new Interval(1, Math.Exp(1)), Interval.Exponential(new Interval(0, 1)));
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| 127 | }
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| 128 |
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| 129 |
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| 130 | [TestMethod]
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| 131 | [TestCategory("Problems.DataAnalysis")]
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| 132 | [TestProperty("Time", "short")]
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| 133 | public void TestIntervalSqrOperator() {
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| 134 | Assert.AreEqual<Interval>(new Interval(1, 4), Interval.Square(new Interval(1, 2)));
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| 135 | Assert.AreEqual<Interval>(new Interval(1, 4), Interval.Square(new Interval(-2, -1)));
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| 136 | Assert.AreEqual<Interval>(new Interval(0, 4), Interval.Square(new Interval(-2, 2)));
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| 137 | }
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| 138 |
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| 139 | [TestMethod]
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| 140 | [TestCategory("Problems.DataAnalysis")]
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| 141 | [TestProperty("Time", "short")]
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| 142 | public void TestIntervalSqrtOperator() {
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| 143 | Assert.AreEqual<Interval>(new Interval(1, 2), Interval.SquareRoot(new Interval(1, 4)));
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| 144 | Assert.AreEqual<Interval>(new Interval(double.NaN, double.NaN), Interval.SquareRoot(new Interval(-4, -1)));
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| 145 | }
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| 146 |
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| 147 | [TestMethod]
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| 148 | [TestCategory("Problems.DataAnalysis")]
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| 149 | [TestProperty("Time", "short")]
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| 150 | public void TestIntervalCubeOperator() {
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| 151 | Assert.AreEqual<Interval>(new Interval(1, 8), Interval.Cube(new Interval(1, 2)));
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| 152 | Assert.AreEqual<Interval>(new Interval(-8, -1), Interval.Cube(new Interval(-2, -1)));
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| 153 | Assert.AreEqual<Interval>(new Interval(-8, 8), Interval.Cube(new Interval(-2, 2)));
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| 154 | }
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| 155 |
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| 156 | [TestMethod]
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| 157 | [TestCategory("Problems.DataAnalysis")]
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| 158 | [TestProperty("Time", "short")]
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| 159 | public void TestIntervalCbrtOperator() {
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| 160 | Assert.AreEqual<Interval>(new Interval(1, 2), Interval.CubicRoot(new Interval(1, 8)));
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| 161 | Assert.AreEqual<Interval>(new Interval(double.NaN, double.NaN), Interval.CubicRoot(new Interval(-8, -1)));
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| 162 | }
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| 163 | }
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| 164 | }
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