1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
|
/*
* Copyright Evan Miller, 2020
* Use, modification and distribution are subject to the
* Boost Software License, Version 1.0. (See accompanying file
* LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
*/
#include <pch_light.hpp>
#include <boost/math/concepts/real_concept.hpp>
#include "test_jacobi_theta.hpp"
// Test file for the Jacobi Theta functions, a.k.a the four horsemen of the
// Jacobi elliptic integrals. At the moment only Wolfrma Alpha spot checks are
// used. We should generate extra-precise numbers with NTL::RR or some such.
void expected_results()
{
//
// Define the max and mean errors expected for
// various compilers and platforms.
//
//
add_expected_result(
".*", // compiler
".*", // stdlib
".*", // platform
".*", // test type(s)
".*Small Tau.*", // test data group
".*", 1000, 200); // test function
add_expected_result(
".*", // compiler
".*", // stdlib
".*", // platform
".*", // test type(s)
".*WolframAlpha.*", // test data group
".*", 60, 15); // test function
// Catch all cases come last:
//
add_expected_result(
".*", // compiler
".*", // stdlib
".*", // platform
".*", // test type(s)
".*", // test data group
".*", 20, 5); // test function
//
// Finish off by printing out the compiler/stdlib/platform names,
// we do this to make it easier to mark up expected error rates.
//
std::cout << "Tests run with " << BOOST_COMPILER << ", "
<< BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl;
}
BOOST_AUTO_TEST_CASE( test_main )
{
expected_results();
BOOST_MATH_CONTROL_FP;
BOOST_MATH_STD_USING
using namespace boost::math;
BOOST_CHECK_THROW(jacobi_theta1(0.0, 0.0), std::domain_error);
BOOST_CHECK_THROW(jacobi_theta1(0.0, 1.0), std::domain_error);
BOOST_CHECK_THROW(jacobi_theta2(0.0, 0.0), std::domain_error);
BOOST_CHECK_THROW(jacobi_theta2(0.0, 1.0), std::domain_error);
BOOST_CHECK_THROW(jacobi_theta3(0.0, 0.0), std::domain_error);
BOOST_CHECK_THROW(jacobi_theta3(0.0, 1.0), std::domain_error);
BOOST_CHECK_THROW(jacobi_theta4(0.0, 0.0), std::domain_error);
BOOST_CHECK_THROW(jacobi_theta4(0.0, 1.0), std::domain_error);
BOOST_CHECK_THROW(jacobi_theta1tau(0.0, 0.0), std::domain_error);
BOOST_CHECK_THROW(jacobi_theta1tau(0.0, -1.0), std::domain_error);
BOOST_CHECK_THROW(jacobi_theta2tau(0.0, 0.0), std::domain_error);
BOOST_CHECK_THROW(jacobi_theta2tau(0.0, -1.0), std::domain_error);
BOOST_CHECK_THROW(jacobi_theta3tau(0.0, 0.0), std::domain_error);
BOOST_CHECK_THROW(jacobi_theta3tau(0.0, -1.0), std::domain_error);
BOOST_CHECK_THROW(jacobi_theta4tau(0.0, 0.0), std::domain_error);
BOOST_CHECK_THROW(jacobi_theta4tau(0.0, -1.0), std::domain_error);
double eps = std::numeric_limits<double>::epsilon();
for (double q=0.0078125; q<1.0; q += 0.0078125) { // = 1/128
for (double z=-8.0; z<=8.0; z += 0.125) {
test_periodicity(z, q, 100 * eps);
test_argument_translation(z, q, 100 * eps);
test_sums_of_squares(z, q, 100 * eps);
// The addition formula is complicated, cut it some extra slack
test_addition_formulas(z, constants::ln_two<double>(), q, sqrt(sqrt(eps)));
test_duplication_formula(z, q, 100 * eps);
test_transformations_of_nome(z, q, 100 * eps);
test_watsons_identities(z, 0.5, q, 101 * eps);
test_landen_transformations(z, -log(q)/constants::pi<double>(), sqrt(eps));
test_elliptic_functions(z, q, 5 * sqrt(eps));
}
test_elliptic_integrals(q, 10 * eps);
}
test_special_values(eps);
for (double s=0.125; s<3.0; s+=0.125) {
test_mellin_transforms(2.0 + s, eps, 3 * eps);
test_laplace_transforms(s, eps, 4 * eps);
}
test_spots(0.0F, "float");
test_spots(0.0, "double");
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
test_spots(0.0L, "long double");
#ifndef BOOST_MATH_NO_REAL_CONCEPT_TESTS
test_spots(concepts::real_concept(0), "real_concept");
#endif
#else
std::cout << "<note>The long double tests have been disabled on this platform "
"either because the long double overloads of the usual math functions are "
"not available at all, or because they are too inaccurate for these tests "
"to pass.</note>" << std::endl;
#endif
}
|
