1 | using System;
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2 | using HeuristicLab.Problems.DataAnalysis.Symbolic;
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3 | using Microsoft.VisualStudio.TestTools.UnitTesting;
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4 |
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5 | namespace HeuristicLab.Problems.DataAnalysis.Tests {
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6 | [TestClass]
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7 | public class AlgebraicIntervalTest {
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8 | private readonly AlgebraicInterval a = new AlgebraicInterval(-1, 1);
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9 | private readonly AlgebraicInterval b = new AlgebraicInterval(-2, 2);
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10 | private readonly AlgebraicInterval c = new AlgebraicInterval(0, 3);
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11 | private readonly AlgebraicInterval d = new AlgebraicInterval(1, 3);
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12 | private readonly AlgebraicInterval e = new AlgebraicInterval(4, 6);
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13 |
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14 | [TestMethod]
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15 | [TestCategory("Problems.DataAnalysis")]
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16 | [TestProperty("Time", "short")]
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17 | public void AlgebraicIntervalAdd() {
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18 | //add [x1,x2] + [y1,y2] = [x1 + y1,x2 + y2]
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19 |
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20 | // [-1,1] + [-2,2] = [-3,3]
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21 | AssertAreEqualInterval(Add(a, b), new AlgebraicInterval(-3, 3));
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22 | //([-1, 1] + [-2, 2]) + [0, 3] = [-3, 6]
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23 | AssertAreEqualInterval(Add(Add(a, b), c), new AlgebraicInterval(-3, 6));
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24 | //([-1, 1] + [0, 3]) + [-2, 2] = [-3, 6]
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25 | AssertAreEqualInterval(Add(Add(a, c), b), new AlgebraicInterval(-3, 6));
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26 | }
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27 |
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28 | private void AssertAreEqualInterval(AlgebraicInterval a, AlgebraicInterval b) {
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29 | if (double.IsNaN(a.LowerBound.Value)) {
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30 | Assert.IsTrue(double.IsNaN(b.LowerBound.Value));
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31 | } else {
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32 | Assert.AreEqual(a.LowerBound.Value.Value, b.LowerBound.Value.Value, Math.Abs(a.LowerBound.Value.Value) * 1e-4); // relative error < 0.1%
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33 | }
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34 |
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35 | if (double.IsNaN(a.UpperBound.Value)) {
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36 | Assert.IsTrue(double.IsNaN(b.UpperBound.Value));
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37 | } else {
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38 | Assert.AreEqual(a.UpperBound.Value.Value, b.UpperBound.Value.Value, Math.Abs(a.UpperBound.Value.Value) * 1e-4);
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39 | }
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40 | }
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41 |
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42 | private static AlgebraicInterval Add(AlgebraicInterval a, AlgebraicInterval b) {
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43 | return a.Clone().Add(b);
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44 | }
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45 |
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46 | [TestMethod]
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47 | [TestCategory("Problems.DataAnalysis")]
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48 | [TestProperty("Time", "short")]
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49 | public void AlgebraicIntervalSub() {
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50 | //subtract [x1,x2] − [y1,y2] = [x1 − y2,x2 − y1]
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51 |
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52 | //[-1, 1] - [-2, 2] = [-3, 3]
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53 | AssertAreEqualInterval(Subtract(a, b), new AlgebraicInterval(-3, 3));
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54 | //([-1, 1] - [-2, 2]) - [0, 3] = [-6, 3]
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55 | AssertAreEqualInterval(Subtract(Subtract(a, b), c), new AlgebraicInterval(-6, 3));
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56 | //([-1, 1] - [0, 3]) - [-2, 2] = [-6, 3]
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57 | AssertAreEqualInterval(Subtract(Subtract(a, c), b), new AlgebraicInterval(-6, 3));
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58 | }
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59 |
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60 | private AlgebraicInterval Subtract(AlgebraicInterval a, AlgebraicInterval b) {
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61 | return a.Clone().Sub(b);
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62 | }
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63 |
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64 | [TestMethod]
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65 | [TestCategory("Problems.DataAnalysis")]
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66 | [TestProperty("Time", "short")]
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67 | public void AlgebraicIntervalMutlipy() {
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68 | //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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69 |
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70 | //[-1, 1] * [-2, 2] = [-2, 2]
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71 | AssertAreEqualInterval(Multiply(a, b), new AlgebraicInterval(-2, 2));
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72 | //([-1, 1] * [-2, 2]) * [0, 3] = [-6, 6]
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73 | AssertAreEqualInterval(Multiply(Multiply(a, b), c), new AlgebraicInterval(-6, 6));
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74 | //([-1, 1] * [0, 3]) * [-2, 2] = [-6, 6]
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75 | AssertAreEqualInterval(Multiply(Multiply(a, c), b), new AlgebraicInterval(-6, 6));
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76 |
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77 | // [-2, 0] * [-2, 0] = [0, 4]
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78 | AssertAreEqualInterval(new AlgebraicInterval(0, 4), Multiply(new AlgebraicInterval(-2, 0), new AlgebraicInterval(-2, 0)));
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79 | }
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80 |
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81 | private AlgebraicInterval Multiply(AlgebraicInterval a, AlgebraicInterval b) {
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82 | return a.Clone().Mul(b);
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83 | }
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84 |
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85 | [TestMethod]
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86 | [TestCategory("Problems.DataAnalysis")]
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87 | [TestProperty("Time", "short")]
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88 | public void AlgebraicIntervalDivide() {
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89 | //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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90 |
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91 | //[4, 6] / [1, 3] = [4/3, 6]
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92 | AssertAreEqualInterval(Divide(e, d), new AlgebraicInterval(4.0 / 3.0, 6));
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93 | //([4, 6] / [1, 3]) / [1, 3] = [4/9, 6]
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94 | AssertAreEqualInterval(Divide(Divide(e, d), d), new AlgebraicInterval(4.0 / 9.0, 6));
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95 | //[4, 6] / [0, 3] = [4/3, +Inf]
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96 | AssertAreEqualInterval(Divide(e, c), new AlgebraicInterval(4.0 / 3.0, double.PositiveInfinity));
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97 | //[-1, 1] / [0, 3] = [+Inf, -Inf]
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98 | AssertAreEqualInterval(Divide(a, c), new AlgebraicInterval(double.NegativeInfinity, double.PositiveInfinity));
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99 |
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100 | //Division by 0 ==> IsInfiniteOrUndefined == true
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101 | AssertAreEqualInterval(Divide(d, b), new AlgebraicInterval(double.NegativeInfinity, double.PositiveInfinity));
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102 |
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103 | // [0, 1] / [0, 1]
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104 | AssertAreEqualInterval(new AlgebraicInterval(0, 1).Div(new AlgebraicInterval(0, 1)), new AlgebraicInterval(1, double.PositiveInfinity)); // returns [NaN, PositiveInfinity]
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105 |
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106 | }
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107 |
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108 | private AlgebraicInterval Divide(AlgebraicInterval e, AlgebraicInterval d) {
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109 | return e.Clone().Div(d);
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110 | }
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111 |
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112 | [TestMethod]
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113 | [TestCategory("Problems.DataAnalysis")]
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114 | [TestProperty("Time", "short")]
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115 | public void AlgebraicIntervalSine() {
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116 | //sine depends on interval
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117 | //sin([0, 2*pi]) = [-1, 1]
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118 | AssertAreEqualInterval(Sine(new AlgebraicInterval(0, 2 * Math.PI)), new AlgebraicInterval(-1, 1));
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119 | //sin([-pi/2, pi/2]) = [sin(-pi/2), sin(pi/2)]
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120 | AssertAreEqualInterval(Sine(new AlgebraicInterval(-1 * Math.PI / 2, Math.PI / 2)), new AlgebraicInterval(-1, 1));
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121 | //sin([0, pi/2]) = [sin(0), sin(pi/2)]
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122 | AssertAreEqualInterval(Sine(new AlgebraicInterval(0, Math.PI / 2)), new AlgebraicInterval(0, 1));
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123 | //sin([pi, 3*pi/2]) = [sin(pi), sin(3*pi/2)]
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124 | AssertAreEqualInterval(Sine(new AlgebraicInterval(Math.PI, 3 * Math.PI / 2)), new AlgebraicInterval(-1, 0));
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125 | AssertAreEqualInterval(Sine(new AlgebraicInterval(1, 2)), new AlgebraicInterval(Math.Min(Math.Sin(1), Math.Sin(2)), 1));
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126 | AssertAreEqualInterval(Sine(new AlgebraicInterval(1, 3)), new AlgebraicInterval(Math.Min(Math.Sin(1), Math.Sin(3)), 1));
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127 | AssertAreEqualInterval(Sine(new AlgebraicInterval(Math.PI, 5 * Math.PI / 2)), new AlgebraicInterval(-1, 1));
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128 | }
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129 |
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130 | private AlgebraicInterval Sine(AlgebraicInterval algebraicInterval) {
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131 | return algebraicInterval.Sin();
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132 | }
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133 |
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134 | [TestMethod]
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135 | [TestCategory("Problems.DataAnalysis")]
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136 | [TestProperty("Time", "short")]
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137 | public void AlgebraicIntervalCosine() {
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138 | //Cosine uses sine Sine(Subtract(a, new AlgebraicInterval(Math.PI / 2, Math.PI / 2)));
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139 | AssertAreEqualInterval(Cosine(new AlgebraicInterval(0, 2 * Math.PI)), new AlgebraicInterval(-1, 1));
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140 | AssertAreEqualInterval(new AlgebraicInterval(-1, 1), Cosine(new AlgebraicInterval(Math.PI, 4 * Math.PI / 2)));
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141 |
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142 | // some random expression that were problematic
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143 | AssertAreEqualInterval(new AlgebraicInterval(-0.0326026961803847, 1), new AlgebraicInterval(1, 2).Scale(1.73269159006613).Add(9.23027422279119).Cos());
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144 | AssertAreEqualInterval(new AlgebraicInterval(0.54030230586814, 1), new AlgebraicInterval(1, 2).Scale(3.39318455754522).Cos().IntPower(2).Cos());
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145 | AssertAreEqualInterval(new AlgebraicInterval(-0.825841274068331, 1), new AlgebraicInterval(1, 2).Scale(-16.7140105366707 * -0.223806041028346).Cos());
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146 | AssertAreEqualInterval(new AlgebraicInterval(0, 1), new AlgebraicInterval(1, 2).Scale(1.03513653909418).Exp().Cos().IntPower(2));
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147 | AssertAreEqualInterval(new AlgebraicInterval(-1, 1), new AlgebraicInterval(1, 2).Scale(0.535386838272755).Exp().IntPower(2).Cos());
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148 | }
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149 |
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150 | private AlgebraicInterval Cosine(AlgebraicInterval algebraicInterval) {
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151 | return algebraicInterval.Cos();
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152 | }
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153 |
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154 | [TestMethod]
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155 | [TestCategory("Problems.DataAnalysis")]
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156 | [TestProperty("Time", "short")]
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157 | public void AlgebraicIntervalLog() {
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158 | //Log([3, 5]) = [log(3), log(5)]
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159 | AssertAreEqualInterval(new AlgebraicInterval(Math.Log(3), Math.Log(5)), Logarithm(new AlgebraicInterval(3, 5)));
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160 | //Log([0.5, 1]) = [log(0.5), log(1)]
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161 | AssertAreEqualInterval(new AlgebraicInterval(Math.Log(0.5), 0), Logarithm(new AlgebraicInterval(0.5, 1)));
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162 | //Log([-1, 5]) = [NaN, log(5)]
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163 | var result = Logarithm(new AlgebraicInterval(-1, 5));
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164 | AssertAreEqualInterval(new AlgebraicInterval(double.NaN, Math.Log(5)), result);
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165 |
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166 | }
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167 |
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168 | private AlgebraicInterval Logarithm(AlgebraicInterval algebraicInterval) {
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169 | return algebraicInterval.Log();
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170 | }
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171 |
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172 | [TestMethod]
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173 | [TestCategory("Problems.DataAnalysis")]
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174 | [TestProperty("Time", "short")]
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175 | public void AlgebraicIntervalExp() {
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176 | //Exp([0, 1]) = [exp(0), exp(1)]
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177 | AssertAreEqualInterval(new AlgebraicInterval(1, Math.Exp(1)), Exponential(new AlgebraicInterval(0, 1)));
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178 | }
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179 |
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180 | private AlgebraicInterval Exponential(AlgebraicInterval algebraicInterval) {
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181 | return algebraicInterval.Exp();
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182 | }
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183 |
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184 | [TestMethod]
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185 | [TestCategory("Problems.DataAnalysis")]
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186 | [TestProperty("Time", "short")]
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187 | public void AlgebraicIntervalSqr() {
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188 | AssertAreEqualInterval(new AlgebraicInterval(1, 4), new AlgebraicInterval(1, 2).IntPower(2));
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189 | AssertAreEqualInterval(new AlgebraicInterval(1, 4), new AlgebraicInterval(-2, -1).IntPower(2));
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190 | AssertAreEqualInterval(new AlgebraicInterval(0, 4), new AlgebraicInterval(-2, 2).IntPower(2));
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191 |
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192 | AssertAreEqualInterval(new AlgebraicInterval(0, 16), new AlgebraicInterval(-2, 2).Mul(new AlgebraicInterval(2, 2)).IntPower(2));
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193 | }
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194 |
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195 | [TestMethod]
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196 | [TestCategory("Problems.DataAnalysis")]
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197 | [TestProperty("Time", "short")]
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198 | public void AlgebraicIntervalSqrt() {
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199 | AssertAreEqualInterval(new AlgebraicInterval(1, 2), new AlgebraicInterval(1, 4).IntRoot(2));
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200 | AssertAreEqualInterval(new AlgebraicInterval(double.NaN, double.NaN), new AlgebraicInterval(-4, -1).IntRoot(2));
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201 | AssertAreEqualInterval(new AlgebraicInterval(0, 1), new AlgebraicInterval(0, 1).IntRoot(2));
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202 | }
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203 |
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204 | [TestMethod]
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205 | [TestCategory("Problems.DataAnalysis")]
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206 | [TestProperty("Time", "short")]
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207 | public void AlgebraicIntervalCube() {
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208 | AssertAreEqualInterval(new AlgebraicInterval(1, 8), new AlgebraicInterval(1, 2).IntPower(3));
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209 | AssertAreEqualInterval(new AlgebraicInterval(-8, -1), new AlgebraicInterval(-2, -1).IntPower(3));
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210 | AssertAreEqualInterval(new AlgebraicInterval(-8, 8), new AlgebraicInterval(-2, 2).IntPower(3));
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211 | }
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212 |
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213 |
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214 | [TestMethod]
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215 | [TestCategory("Problems.DataAnalysis")]
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216 | [TestProperty("Time", "short")]
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217 | public void AlgebraicIntervalAbs() {
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218 | AssertAreEqualInterval(new AlgebraicInterval(1, 2), new AlgebraicInterval(1, 2).Abs());
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219 | AssertAreEqualInterval(new AlgebraicInterval(1, 2), new AlgebraicInterval(-2, -1).Abs());
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220 | AssertAreEqualInterval(new AlgebraicInterval(0, 2), new AlgebraicInterval(-2, 2).Abs());
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221 | AssertAreEqualInterval(new AlgebraicInterval(0, double.PositiveInfinity), new AlgebraicInterval(double.NegativeInfinity, double.PositiveInfinity).Abs());
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222 | AssertAreEqualInterval(new AlgebraicInterval(double.NaN, 1), new AlgebraicInterval(-1, double.NaN).Abs()); // XXX unclear how we should handle NaN
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223 | AssertAreEqualInterval(new AlgebraicInterval(double.NaN, 1), new AlgebraicInterval(double.NaN, -1).Abs());
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224 | }
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225 |
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226 |
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227 | [TestMethod]
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228 | [TestCategory("Problems.DataAnalysis")]
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229 | [TestProperty("Time", "short")]
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230 | public void AlgebraicIntervalCbrt() {
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231 | AssertAreEqualInterval(new AlgebraicInterval(1, 2), new AlgebraicInterval(1, 8).IntRoot(3));
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232 | AssertAreEqualInterval(new AlgebraicInterval(-2, -1), new AlgebraicInterval(-8, -1).IntRoot(3));
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233 | AssertAreEqualInterval(new AlgebraicInterval(0, 1), new AlgebraicInterval(0, 1).IntRoot(3));
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234 | }
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235 | }
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236 | }
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