source: branches/2994-AutoDiffForIntervals/HeuristicLab.Tests/HeuristicLab.Problems.DataAnalysis-3.4/AutoDiffIntervalTest.cs @ 17212

Last change on this file since 17212 was 17212, checked in by gkronber, 3 years ago

#2994: fixed division, multiplication and cos for intervals based on failing tests

File size: 9.8 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      AssertAreEqualInterval(Add(a, b), new AlgebraicInterval(-3, 3));
23      //([-1, 1] + [-2, 2]) + [0, 3] = [-3, 6]
24      AssertAreEqualInterval(Add(Add(a, b), c), new AlgebraicInterval(-3, 6));
25      //([-1, 1] + [0, 3]) + [-2, 2] = [-3, 6]
26      AssertAreEqualInterval(Add(Add(a, c), b), new AlgebraicInterval(-3, 6));
27    }
28
29    private void AssertAreEqualInterval(AlgebraicInterval a, AlgebraicInterval b) {
30      if (double.IsNaN(a.LowerBound.Value)) {
31        Assert.IsTrue(double.IsNaN(b.LowerBound.Value));
32      } else {
33        Assert.AreEqual(a.LowerBound.Value.Value, b.LowerBound.Value.Value, 1e-10);
34      }
35
36      if (double.IsNaN(a.UpperBound.Value)) {
37        Assert.IsTrue(double.IsNaN(b.UpperBound.Value));
38      } else {
39        Assert.AreEqual(a.UpperBound.Value.Value, b.UpperBound.Value.Value, 1e-10);
40      }
41    }
42
43    private static AlgebraicInterval Add(AlgebraicInterval a, AlgebraicInterval b) {
44      return a.Clone().Add(b);
45    }
46
47    [TestMethod]
48    [TestCategory("Problems.DataAnalysis")]
49    [TestProperty("Time", "short")]
50    public void TestIntervalSubOperation() {
51      //subtract   [x1,x2] − [y1,y2] = [x1 − y2,x2 − y1]
52
53      //[-1, 1] - [-2, 2] = [-3, 3]
54      AssertAreEqualInterval(Subtract(a, b), new AlgebraicInterval(-3, 3));
55      //([-1, 1] - [-2, 2]) - [0, 3] = [-6, 3]
56      AssertAreEqualInterval(Subtract(Subtract(a, b), c), new AlgebraicInterval(-6, 3));
57      //([-1, 1] - [0, 3]) - [-2, 2] = [-6, 3]
58      AssertAreEqualInterval(Subtract(Subtract(a, c), b), new AlgebraicInterval(-6, 3));
59    }
60
61    private AlgebraicInterval Subtract(AlgebraicInterval a, AlgebraicInterval b) {
62      return a.Clone().Sub(b);
63    }
64
65    [TestMethod]
66    [TestCategory("Problems.DataAnalysis")]
67    [TestProperty("Time", "short")]
68    public void TestIntervalMutlipyOperation() {
69      //multiply   [x1,x2] * [y1,y2] = [min(x1*y1,x1*y2,x2*y1,x2*y2),max(x1*y1,x1*y2,x2*y1,x2*y2)]
70
71      //[-1, 1] * [-2, 2] = [-2, 2]
72      AssertAreEqualInterval(Multiply(a, b), new AlgebraicInterval(-2, 2));
73      //([-1, 1] * [-2, 2]) * [0, 3] = [-6, 6]
74      AssertAreEqualInterval(Multiply(Multiply(a, b), c), new AlgebraicInterval(-6, 6));
75      //([-1, 1] * [0, 3]) * [-2, 2] = [-6, 6]
76      AssertAreEqualInterval(Multiply(Multiply(a, c), b), new AlgebraicInterval(-6, 6));
77
78      // [-2, 0] * [-2, 0]  = [0, 4]
79      AssertAreEqualInterval(new AlgebraicInterval(0, 4), Multiply(new AlgebraicInterval(-2, 0), new AlgebraicInterval(-2, 0)));
80    }
81
82    private AlgebraicInterval Multiply(AlgebraicInterval a, AlgebraicInterval b) {
83      return a.Clone().Mul(b);
84    }
85
86    [TestMethod]
87    [TestCategory("Problems.DataAnalysis")]
88    [TestProperty("Time", "short")]
89    public void TestIntervalDivideOperation() {
90      //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].
91
92      //[4, 6] / [1, 3] = [4/3, 6]
93      AssertAreEqualInterval(Divide(e, d), new AlgebraicInterval(4.0 / 3.0, 6));
94      //([4, 6] / [1, 3]) / [1, 3] = [4/9, 6]
95      AssertAreEqualInterval(Divide(Divide(e, d), d), new AlgebraicInterval(4.0 / 9.0, 6));
96      //[4, 6] / [0, 3] = [4/3, +Inf]
97      AssertAreEqualInterval(Divide(e, c), new AlgebraicInterval(4.0 / 3.0, double.PositiveInfinity));
98      //[-1, 1] / [0, 3] = [+Inf, -Inf]
99      AssertAreEqualInterval(Divide(a, c), new AlgebraicInterval(double.NegativeInfinity, double.PositiveInfinity));
100
101      //Division by 0 ==> IsInfiniteOrUndefined == true
102      AssertAreEqualInterval(Divide(d, b), new AlgebraicInterval(double.NegativeInfinity, double.PositiveInfinity));
103    }
104
105    private AlgebraicInterval Divide(AlgebraicInterval e, AlgebraicInterval d) {
106      return e.Clone().Div(d);
107    }
108
109    [TestMethod]
110    [TestCategory("Problems.DataAnalysis")]
111    [TestProperty("Time", "short")]
112    public void TestIntervalSineOperator() {
113      //sine depends on interval
114      //sin([0, 2*pi]) = [-1, 1]
115      AssertAreEqualInterval(Sine(new AlgebraicInterval(0, 2 * Math.PI)), new AlgebraicInterval(-1, 1));
116      //sin([-pi/2, pi/2]) = [sin(-pi/2), sin(pi/2)]
117      AssertAreEqualInterval(Sine(new AlgebraicInterval(-1 * Math.PI / 2, Math.PI / 2)), new AlgebraicInterval(-1, 1));
118      //sin([0, pi/2]) = [sin(0), sin(pi/2)]
119      AssertAreEqualInterval(Sine(new AlgebraicInterval(0, Math.PI / 2)), new AlgebraicInterval(0, 1));
120      //sin([pi, 3*pi/2]) = [sin(pi), sin(3*pi/2)]
121      AssertAreEqualInterval(Sine(new AlgebraicInterval(Math.PI, 3 * Math.PI / 2)), new AlgebraicInterval(-1, 0));
122      AssertAreEqualInterval(Sine(new AlgebraicInterval(1, 2)), new AlgebraicInterval(Math.Min(Math.Sin(1), Math.Sin(2)), 1));
123      AssertAreEqualInterval(Sine(new AlgebraicInterval(1, 3)), new AlgebraicInterval(Math.Min(Math.Sin(1), Math.Sin(3)), 1));
124      AssertAreEqualInterval(Sine(new AlgebraicInterval(Math.PI, 5 * Math.PI / 2)), new AlgebraicInterval(-1, 1));
125    }
126
127    private AlgebraicInterval Sine(AlgebraicInterval algebraicInterval) {
128      return algebraicInterval.Sin();
129    }
130
131    [TestMethod]
132    [TestCategory("Problems.DataAnalysis")]
133    [TestProperty("Time", "short")]
134    public void TestIntervalCosineOperator() {
135      //Cosine uses sine Sine(Subtract(a, new AlgebraicInterval(Math.PI / 2, Math.PI / 2)));
136      AssertAreEqualInterval(Cosine(new AlgebraicInterval(0, 2 * Math.PI)), new AlgebraicInterval(-1, 1));
137      AssertAreEqualInterval(new AlgebraicInterval(-1, 1), Cosine(new AlgebraicInterval(Math.PI, 4 * Math.PI / 2)));
138    }
139
140    private AlgebraicInterval Cosine(AlgebraicInterval algebraicInterval) {
141      return algebraicInterval.Cos();
142    }
143
144    [TestMethod]
145    [TestCategory("Problems.DataAnalysis")]
146    [TestProperty("Time", "short")]
147    public void TestIntervalLogOperator() {
148      //Log([3, 5]) = [log(3), log(5)]
149      AssertAreEqualInterval(new AlgebraicInterval(Math.Log(3), Math.Log(5)), Logarithm(new AlgebraicInterval(3, 5)));
150      //Log([0.5, 1]) = [log(0.5), log(1)]
151      AssertAreEqualInterval(new AlgebraicInterval(Math.Log(0.5), 0), Logarithm(new AlgebraicInterval(0.5, 1)));
152      //Log([-1, 5]) = [NaN, log(5)]
153      var result = Logarithm(new AlgebraicInterval(-1, 5));
154      AssertAreEqualInterval(new AlgebraicInterval(double.NaN, Math.Log(5)), result);
155
156    }
157
158    private AlgebraicInterval Logarithm(AlgebraicInterval algebraicInterval) {
159      return algebraicInterval.Log();
160    }
161
162    [TestMethod]
163    [TestCategory("Problems.DataAnalysis")]
164    [TestProperty("Time", "short")]
165    public void TestIntervalExpOperator() {
166      //Exp([0, 1]) = [exp(0), exp(1)]
167      AssertAreEqualInterval(new AlgebraicInterval(1, Math.Exp(1)), Exponential(new AlgebraicInterval(0, 1)));
168    }
169
170    private AlgebraicInterval Exponential(AlgebraicInterval algebraicInterval) {
171      return algebraicInterval.Exp();
172    }
173
174    [TestMethod]
175    [TestCategory("Problems.DataAnalysis")]
176    [TestProperty("Time", "short")]
177    public void TestIntervalSqrOperator() {
178      AssertAreEqualInterval(new AlgebraicInterval(1, 4), Square(new AlgebraicInterval(1, 2)));
179      AssertAreEqualInterval(new AlgebraicInterval(1, 4), Square(new AlgebraicInterval(-2, -1)));
180      AssertAreEqualInterval(new AlgebraicInterval(0, 4), Square(new AlgebraicInterval(-2, 2)));
181    }
182
183    private AlgebraicInterval Square(AlgebraicInterval algebraicInterval) {
184      return algebraicInterval.IntPower(2);
185    }
186
187    [TestMethod]
188    [TestCategory("Problems.DataAnalysis")]
189    [TestProperty("Time", "short")]
190    public void TestIntervalSqrtOperator() {
191      AssertAreEqualInterval(new AlgebraicInterval(1, 2), SquareRoot(new AlgebraicInterval(1, 4)));
192      AssertAreEqualInterval(new AlgebraicInterval(double.NaN, double.NaN), SquareRoot(new AlgebraicInterval(-4, -1)));
193    }
194
195    private AlgebraicInterval SquareRoot(AlgebraicInterval algebraicInterval) {
196      return algebraicInterval.IntRoot(2);
197    }
198
199    [TestMethod]
200    [TestCategory("Problems.DataAnalysis")]
201    [TestProperty("Time", "short")]
202    public void TestIntervalCubeOperator() {
203      AssertAreEqualInterval(new AlgebraicInterval(1, 8), Cube(new AlgebraicInterval(1, 2)));
204      AssertAreEqualInterval(new AlgebraicInterval(-8, -1), Cube(new AlgebraicInterval(-2, -1)));
205      AssertAreEqualInterval(new AlgebraicInterval(-8, 8), Cube(new AlgebraicInterval(-2, 2)));
206    }
207
208    private AlgebraicInterval Cube(AlgebraicInterval algebraicInterval) {
209      return algebraicInterval.IntPower(3);
210    }
211
212    [TestMethod]
213    [TestCategory("Problems.DataAnalysis")]
214    [TestProperty("Time", "short")]
215    public void TestIntervalCbrtOperator() {
216      AssertAreEqualInterval(new AlgebraicInterval(1, 2), CubicRoot(new AlgebraicInterval(1, 8)));
217      AssertAreEqualInterval(new AlgebraicInterval(double.NaN, double.NaN), CubicRoot(new AlgebraicInterval(-8, -1)));
218    }
219
220    private AlgebraicInterval CubicRoot(AlgebraicInterval algebraicInterval) {
221      return algebraicInterval.IntRoot(3);
222    }
223  }
224}
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