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Tempus_UnitTest_NumericalUtils.cpp
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1 // @HEADER
2 // ****************************************************************************
3 // Tempus: Copyright (2017) Sandia Corporation
4 //
5 // Distributed under BSD 3-clause license (See accompanying file Copyright.txt)
6 // ****************************************************************************
7 // @HEADER
8 
9 #include "Tempus_UnitTest_Utils.hpp"
10 
11 #include "Tempus_NumericalUtils.hpp"
12 
13 
14 namespace Tempus_Unit_Test {
15 
16 using Tempus::approxEqual;
17 using Tempus::approxEqualAbsTol;
18 using Tempus::approxEqualScale;
19 
20 static double PI = M_PI;
21 static double eps = 1.0e-14;
22 
23 
24 // ************************************************************
25 // ************************************************************
26 TEUCHOS_UNIT_TEST(NumericalUtils, approxEqual)
27 {
28  double zero = 0.0;
29  double one = 1.0;
30 
31  std::vector<double> scales;
32  scales.push_back(1.0);
33  scales.push_back(100.0);
34  scales.push_back(0.01);
35  scales.push_back(1.0e-28);
36  scales.push_back(1.0e+28);
37 
38  std::vector<double> numbers;
39  numbers.push_back(one);
40  numbers.push_back(PI);
41 
42  for(auto& s : scales) {
43 
44  out << " *****************************" << std::endl;
45  out << " s, eps = " << s << ", " << eps << std::endl;
46 
47  TEST_COMPARE(approxEqual(zero*s, (zero-10.0*eps)*s), ==, false);
48  TEST_COMPARE(approxEqual(zero*s, (zero- eps)*s), ==, false);
49  TEST_COMPARE(approxEqual(zero*s, (zero )*s), ==, true );
50  TEST_COMPARE(approxEqual(zero*s, (zero+ eps)*s), ==, false);
51  TEST_COMPARE(approxEqual(zero*s, (zero+10.0*eps)*s), ==, false);
52 
53  // Swap
54  TEST_COMPARE(approxEqual((zero-10.0*eps)*s, zero*s), ==, false);
55  TEST_COMPARE(approxEqual((zero- eps)*s, zero*s), ==, false);
56  TEST_COMPARE(approxEqual((zero )*s, zero*s), ==, true );
57  TEST_COMPARE(approxEqual((zero+ eps)*s, zero*s), ==, false);
58  TEST_COMPARE(approxEqual((zero+10.0*eps)*s, zero*s), ==, false);
59 
60  for(auto& n : numbers) {
61 
62  out << " n = " << n << std::endl;
63 
64  TEST_COMPARE(approxEqual(n*s, (n-10.0*eps)*s), ==, false);
65  TEST_COMPARE(approxEqual(n*s, (n- eps)*s), ==, true );
66  TEST_COMPARE(approxEqual(n*s, (n )*s), ==, true );
67  TEST_COMPARE(approxEqual(n*s, (n+ eps)*s), ==, true );
68  TEST_COMPARE(approxEqual(n*s, (n+10.0*eps)*s), ==, false);
69 
70  // Swap
71  TEST_COMPARE(approxEqual((n-10.0*eps)*s, n*s), ==, false);
72  TEST_COMPARE(approxEqual((n- eps)*s, n*s), ==, true );
73  TEST_COMPARE(approxEqual((n )*s, n*s), ==, true );
74  TEST_COMPARE(approxEqual((n+ eps)*s, n*s), ==, true );
75  TEST_COMPARE(approxEqual((n+10.0*eps)*s, n*s), ==, false);
76 
77  }
78  out << " *****************************" << std::endl;
79  }
80 
81 }
82 
83 
84 // ************************************************************
85 // ************************************************************
86 TEUCHOS_UNIT_TEST(NumericalUtils, approxEqualAbsTol)
87 {
88  double numTol = Tempus::numericalTol<double>();
89  double zero = 0.0;
90  double one = 1.0;
91 
92  std::vector<double> scales;
93  scales.push_back(1.0);
94  scales.push_back(100.0);
95  scales.push_back(0.01);
96  scales.push_back(1.0e-28);
97  scales.push_back(1.0e+28);
98 
99  std::vector<double> numbers;
100  numbers.push_back(zero);
101  numbers.push_back(one);
102  numbers.push_back(PI);
103 
104  for(auto& s : scales) {
105  for(auto& n : numbers) {
106 
107  out << " *****************************" << std::endl;
108  out << " n, s, eps = " << n << ", " << s << ", " << eps << std::endl;
109 
110  TEST_COMPARE(approxEqualAbsTol(n*s, (n-10.0*eps)*s, numTol*s), ==, false);
111  TEST_COMPARE(approxEqualAbsTol(n*s, (n- eps)*s, numTol*s), ==, true );
112  TEST_COMPARE(approxEqualAbsTol(n*s, (n )*s, numTol*s), ==, true );
113  TEST_COMPARE(approxEqualAbsTol(n*s, (n+ eps)*s, numTol*s), ==, true );
114  TEST_COMPARE(approxEqualAbsTol(n*s, (n+10.0*eps)*s, numTol*s), ==, false);
115 
116  // Swap
117  TEST_COMPARE(approxEqualAbsTol((n-10.0*eps)*s, n*s, numTol*s), ==, false);
118  TEST_COMPARE(approxEqualAbsTol((n- eps)*s, n*s, numTol*s), ==, true );
119  TEST_COMPARE(approxEqualAbsTol((n )*s, n*s, numTol*s), ==, true );
120  TEST_COMPARE(approxEqualAbsTol((n+ eps)*s, n*s, numTol*s), ==, true );
121  TEST_COMPARE(approxEqualAbsTol((n+10.0*eps)*s, n*s, numTol*s), ==, false);
122 
123  out << " *****************************" << std::endl;
124  }
125  }
126 
127 }
128 
129 
130 // ************************************************************
131 // ************************************************************
132 TEUCHOS_UNIT_TEST(NumericalUtils, approxEqualScale)
133 {
134  double zero = 0.0;
135  double one = 1.0;
136 
137  std::vector<double> scales;
138  scales.push_back(1.0);
139  scales.push_back(100.0);
140  scales.push_back(0.01);
141  scales.push_back(1.0e-28);
142  scales.push_back(1.0e+28);
143 
144  std::vector<double> numbers;
145  numbers.push_back(zero);
146  numbers.push_back(one);
147  numbers.push_back(PI);
148 
149  for(auto& s : scales) {
150  for(auto& n : numbers) {
151 
152  out << " *****************************" << std::endl;
153  out << " n, s, eps = " << n << ", " << s << ", " << eps << std::endl;
154 
155  TEST_COMPARE(approxEqualScale(n*s, (n-10.0*eps)*s, s), ==, false);
156  TEST_COMPARE(approxEqualScale(n*s, (n- eps)*s, s), ==, true );
157  TEST_COMPARE(approxEqualScale(n*s, (n )*s, s), ==, true );
158  TEST_COMPARE(approxEqualScale(n*s, (n+ eps)*s, s), ==, true );
159  TEST_COMPARE(approxEqualScale(n*s, (n+10.0*eps)*s, s), ==, false);
160 
161  // Swap
162  TEST_COMPARE(approxEqualScale((n-10.0*eps)*s, n*s, s), ==, false);
163  TEST_COMPARE(approxEqualScale((n- eps)*s, n*s, s), ==, true );
164  TEST_COMPARE(approxEqualScale((n )*s, n*s, s), ==, true );
165  TEST_COMPARE(approxEqualScale((n+ eps)*s, n*s, s), ==, true );
166  TEST_COMPARE(approxEqualScale((n+10.0*eps)*s, n*s, s), ==, false);
167 
168  out << " *****************************" << std::endl;
169  }
170  }
171 
172 }
173 
174 
175 } // namespace Tempus_Unit_Test
Tempus_NumericalUtils.hpp
TEST_COMPARE
#define TEST_COMPARE(v1, comp, v2)
Tempus_Unit_Test::PI
static double PI
Definition: Tempus_UnitTest_NumericalUtils.cpp:20
Tempus::approxEqual
bool approxEqual(Scalar a, Scalar b, Scalar relTol=numericalTol< Scalar >())
Test if values are approximately equal within the relative tolerance.
Definition: Tempus_NumericalUtils.hpp:46
Tempus_Unit_Test::eps
static double eps
Definition: Tempus_UnitTest_NumericalUtils.cpp:21
Tempus_UnitTest_Utils.hpp
Tempus_Unit_Test::TEUCHOS_UNIT_TEST
TEUCHOS_UNIT_TEST(BackwardEuler, Default_Construction)
Definition: Tempus_UnitTest_BackwardEuler.cpp:34
Tempus::approxEqualAbsTol
bool approxEqualAbsTol(Scalar a, Scalar b, Scalar absTol)
Test if values are approximately equal within the absolute tolerance.
Definition: Tempus_NumericalUtils.hpp:39
Tempus::approxEqualScale
bool approxEqualScale(Scalar a, Scalar b, Scalar scale, Scalar relTol=numericalTol< Scalar >())
Test if values are approximately equal within the relative tolerance given a scale.
Definition: Tempus_NumericalUtils.hpp:56
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