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source: branches/2994-AutoDiffForIntervals/HeuristicLab.Tests/HeuristicLab.Problems.DataAnalysis-3.4/AutoDiffIntervalTest.cs @ 17205

Last change on this file since 17205 was 17205, checked in by gkronber, 4 years ago

#2994: added a unit test

File size: 9.1 KB
Line 
1using System;
2using HeuristicLab.Problems.DataAnalysis.Symbolic;
3using Microsoft.VisualStudio.TestTools.UnitTesting;
4
5namespace HeuristicLab.Problems.DataAnalysis.Tests {
6  [TestClass]
7  public class AutoDiffIntervalTest {
8    private readonly AlgebraicInterval a = new AlgebraicInterval(-1, 1);
9    private readonly AlgebraicInterval b = new AlgebraicInterval(-2, 2);
10    private readonly AlgebraicInterval c = new AlgebraicInterval(0, 3);
11    private readonly AlgebraicInterval d = new AlgebraicInterval(1, 3);
12    private readonly AlgebraicInterval e = new AlgebraicInterval(4, 6);
13    private readonly IntervalEvaluator eval = new  IntervalEvaluator();
14
15    [TestMethod]
16    [TestCategory("Problems.DataAnalysis")]
17    [TestProperty("Time", "short")]
18    public void TestIntervalAddOperation() {
19      //add        [x1,x2] + [y1,y2] = [x1 + y1,x2 + y2]
20
21      // [-1,1] + [-2,2] = [-3,3]
22      Assert.AreEqual(Add(a, b), new AlgebraicInterval(-3, 3));
23      //([-1, 1] + [-2, 2]) + [0, 3] = [-3, 6]
24      Assert.AreEqual(Add(Add(a, b), c), new AlgebraicInterval(-3, 6));
25      //([-1, 1] + [0, 3]) + [-2, 2] = [-3, 6]
26      Assert.AreEqual(Add(Add(a, c), b), new AlgebraicInterval(-3, 6));
27    }
28
29    private static AlgebraicInterval Add(AlgebraicInterval a, AlgebraicInterval b) {
30      return a.Clone().Add(b);
31    }
32
33    [TestMethod]
34    [TestCategory("Problems.DataAnalysis")]
35    [TestProperty("Time", "short")]
36    public void TestIntervalSubOperation() {
37      //subtract   [x1,x2] − [y1,y2] = [x1 − y2,x2 − y1]
38
39      //[-1, 1] - [-2, 2] = [-3, 3]
40      Assert.AreEqual(Subtract(a, b), new AlgebraicInterval(-3, 3));
41      //([-1, 1] - [-2, 2]) - [0, 3] = [-6, 3]
42      Assert.AreEqual(Subtract(Subtract(a, b), c), new AlgebraicInterval(-6, 3));
43      //([-1, 1] - [0, 3]) - [-2, 2] = [-6, 3]
44      Assert.AreEqual(Subtract(Subtract(a, c), b), new AlgebraicInterval(-6, 3));
45    }
46
47    private AlgebraicInterval Subtract(AlgebraicInterval a, AlgebraicInterval b) {
48      return a.Clone().Sub(b);
49    }
50
51    [TestMethod]
52    [TestCategory("Problems.DataAnalysis")]
53    [TestProperty("Time", "short")]
54    public void TestIntervalMutlipyOperation() {
55      //multiply   [x1,x2] * [y1,y2] = [min(x1*y1,x1*y2,x2*y1,x2*y2),max(x1*y1,x1*y2,x2*y1,x2*y2)]
56
57      //[-1, 1] * [-2, 2] = [-2, 2]
58      Assert.AreEqual(Multiply(a, b), new AlgebraicInterval(-2, 2));
59      //([-1, 1] * [-2, 2]) * [0, 3] = [-6, 6]
60      Assert.AreEqual(Multiply(Multiply(a, b), c), new AlgebraicInterval(-6, 6));
61      //([-1, 1] * [0, 3]) * [-2, 2] = [-6, 6]
62      Assert.AreEqual(Multiply(Multiply(a, c), b), new AlgebraicInterval(-6, 6));
63
64      // [-2, 0] * [-2, 0]  = [0, 4]
65      Assert.AreEqual(new AlgebraicInterval(0, 4), Multiply(new AlgebraicInterval(-2, 0), new AlgebraicInterval(-2, 0)));
66    }
67
68    private AlgebraicInterval Multiply(AlgebraicInterval a, AlgebraicInterval b) {
69      return a.Clone().Mul(b);
70    }
71
72    [TestMethod]
73    [TestCategory("Problems.DataAnalysis")]
74    [TestProperty("Time", "short")]
75    public void TestIntervalDivideOperation() {
76      //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].
77
78      //[4, 6] / [1, 3] = [4/3, 6]
79      Assert.AreEqual(Divide(e, d), new AlgebraicInterval(4.0 / 3.0, 6));
80      //([4, 6] / [1, 3]) / [1, 3] = [4/9, 6]
81      Assert.AreEqual(Divide(Divide(e, d), d), new AlgebraicInterval(4.0 / 9.0, 6));
82      //[4, 6] / [0, 3] = [4/3, +Inf]
83      Assert.AreEqual(Divide(e, c), new AlgebraicInterval(4.0 / 3.0, double.PositiveInfinity));
84      //[-1, 1] / [0, 3] = [+Inf, -Inf]
85      Assert.AreEqual(Divide(a, c), new AlgebraicInterval(double.NegativeInfinity, double.PositiveInfinity));
86      //Devision by 0 ==> IsInfiniteOrUndefined == true
87     
88      //Devision by 0 ==> IsInfiniteOrUndefined == true
89     
90      Assert.AreEqual(Divide(d, b), new AlgebraicInterval(double.NegativeInfinity, double.PositiveInfinity));
91    }
92
93    private AlgebraicInterval Divide(AlgebraicInterval e, AlgebraicInterval d) {
94      return e.Clone().Div(d);
95    }
96
97    [TestMethod]
98    [TestCategory("Problems.DataAnalysis")]
99    [TestProperty("Time", "short")]
100    public void TestIntervalSineOperator() {
101      //sine depends on interval
102      //sin([0, 2*pi]) = [-1, 1]
103      Assert.AreEqual(Sine(new AlgebraicInterval(0, 2 * Math.PI)), new AlgebraicInterval(-1, 1));
104      //sin([-pi/2, pi/2]) = [sin(-pi/2), sin(pi/2)]
105      Assert.AreEqual(Sine(new AlgebraicInterval(-1 * Math.PI / 2, Math.PI / 2)), new AlgebraicInterval(-1, 1));
106      //sin([0, pi/2]) = [sin(0), sin(pi/2)]
107      Assert.AreEqual(Sine(new AlgebraicInterval(0, Math.PI / 2)), new AlgebraicInterval(0, 1));
108      //sin([pi, 3*pi/2]) = [sin(pi), sin(3*pi/2)]
109      Assert.AreEqual(Sine(new AlgebraicInterval(Math.PI, 3 * Math.PI / 2)), new AlgebraicInterval(-1, 0));
110      Assert.AreEqual(Sine(new AlgebraicInterval(1, 2)), new AlgebraicInterval(Math.Min(Math.Sin(1), Math.Sin(2)), 1));
111      Assert.AreEqual(Sine(new AlgebraicInterval(1, 3)), new AlgebraicInterval(Math.Min(Math.Sin(1), Math.Sin(3)), 1));
112      Assert.AreEqual(Sine(new AlgebraicInterval(Math.PI, 5 * Math.PI / 2)), new AlgebraicInterval(-1, 1));
113    }
114
115    private AlgebraicInterval Sine(AlgebraicInterval algebraicInterval) {
116      return algebraicInterval.Sin();
117    }
118
119    [TestMethod]
120    [TestCategory("Problems.DataAnalysis")]
121    [TestProperty("Time", "short")]
122    public void TestIntervalCosineOperator() {
123      //Cosine uses sine Sine(Subtract(a, new AlgebraicInterval(Math.PI / 2, Math.PI / 2)));
124      Assert.AreEqual(Cosine(new AlgebraicInterval(0, 2 * Math.PI)), new AlgebraicInterval(-1, 1));
125      Assert.AreEqual(new AlgebraicInterval(-1, 1), Cosine(new AlgebraicInterval(Math.PI, 4 * Math.PI / 2)));
126    }
127
128    private AlgebraicInterval Cosine(AlgebraicInterval algebraicInterval) {
129      return algebraicInterval.Cos();
130    }
131
132    [TestMethod]
133    [TestCategory("Problems.DataAnalysis")]
134    [TestProperty("Time", "short")]
135    public void TestIntervalLogOperator() {
136      //Log([3, 5]) = [log(3), log(5)]
137      Assert.AreEqual(new AlgebraicInterval(Math.Log(3), Math.Log(5)), Logarithm(new AlgebraicInterval(3, 5)));
138      //Log([0.5, 1]) = [log(0.5), log(1)]
139      Assert.AreEqual(new AlgebraicInterval(Math.Log(0.5), 0), Logarithm(new AlgebraicInterval(0.5, 1)));
140      //Log([-1, 5]) = [NaN, log(5)]
141      var result = Logarithm(new AlgebraicInterval(-1, 5));
142      Assert.AreEqual(new AlgebraicInterval(double.NaN, Math.Log(5)),result);
143     
144    }
145
146    private AlgebraicInterval Logarithm(AlgebraicInterval algebraicInterval) {
147      return algebraicInterval.Log();
148    }
149
150    [TestMethod]
151    [TestCategory("Problems.DataAnalysis")]
152    [TestProperty("Time", "short")]
153    public void TestIntervalExpOperator() {
154      //Exp([0, 1]) = [exp(0), exp(1)]
155      Assert.AreEqual(new AlgebraicInterval(1, Math.Exp(1)), Exponential(new AlgebraicInterval(0, 1)));
156    }
157
158    private AlgebraicInterval Exponential(AlgebraicInterval algebraicInterval) {
159      return algebraicInterval.Exp();
160    }
161
162    [TestMethod]
163    [TestCategory("Problems.DataAnalysis")]
164    [TestProperty("Time", "short")]
165    public void TestIntervalSqrOperator() {
166      Assert.AreEqual(new AlgebraicInterval(1, 4), Square(new AlgebraicInterval(1, 2)));
167      Assert.AreEqual(new AlgebraicInterval(1, 4), Square(new AlgebraicInterval(-2, -1)));
168      Assert.AreEqual(new AlgebraicInterval(0, 4), Square(new AlgebraicInterval(-2, 2)));
169    }
170
171    private AlgebraicInterval Square(AlgebraicInterval algebraicInterval) {
172      return algebraicInterval.IntPower(2);
173    }
174
175    [TestMethod]
176    [TestCategory("Problems.DataAnalysis")]
177    [TestProperty("Time", "short")]
178    public void TestIntervalSqrtOperator() {
179      Assert.AreEqual(new AlgebraicInterval(1, 2), SquareRoot(new AlgebraicInterval(1, 4)));
180      Assert.AreEqual(new AlgebraicInterval(double.NaN, double.NaN), SquareRoot(new AlgebraicInterval(-4, -1)));
181    }
182
183    private AlgebraicInterval SquareRoot(AlgebraicInterval algebraicInterval) {
184      return algebraicInterval.IntRoot(2);
185    }
186
187    [TestMethod]
188    [TestCategory("Problems.DataAnalysis")]
189    [TestProperty("Time", "short")]
190    public void TestIntervalCubeOperator() {
191      Assert.AreEqual(new AlgebraicInterval(1, 8), Cube(new AlgebraicInterval(1, 2)));
192      Assert.AreEqual(new AlgebraicInterval(-8, -1), Cube(new AlgebraicInterval(-2, -1)));
193      Assert.AreEqual(new AlgebraicInterval(-8, 8), Cube(new AlgebraicInterval(-2, 2)));
194    }
195
196    private AlgebraicInterval Cube(AlgebraicInterval algebraicInterval) {
197      return algebraicInterval.IntPower(3);
198    }
199
200    [TestMethod]
201    [TestCategory("Problems.DataAnalysis")]
202    [TestProperty("Time", "short")]
203    public void TestIntervalCbrtOperator() {
204      Assert.AreEqual(new AlgebraicInterval(1, 2), CubicRoot(new AlgebraicInterval(1, 8)));
205      Assert.AreEqual(new AlgebraicInterval(double.NaN, double.NaN), CubicRoot(new AlgebraicInterval(-8, -1)));
206    }
207
208    private AlgebraicInterval CubicRoot(AlgebraicInterval algebraicInterval) {
209      return algebraicInterval.IntRoot(3);
210    }
211  }
212}
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