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
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
|
// Copyright John Maddock 2006.
// Copyright Paul A. Bristow 2007, 2009
// 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 <boost/math/concepts/real_concept.hpp>
#define BOOST_TEST_MAIN
#include <boost/test/unit_test.hpp>
#include <boost/test/floating_point_comparison.hpp>
#include <boost/math/special_functions/math_fwd.hpp>
#include <boost/math/constants/constants.hpp>
#include <boost/array.hpp>
#include <boost/random.hpp>
#include "functor.hpp"
#include "handle_test_result.hpp"
#include "table_type.hpp"
#ifndef SC_
#define SC_(x) static_cast<typename table_type<T>::type>(BOOST_JOIN(x, L))
#endif
template <class Real, typename T>
void do_test_ellint_rf(T& data, const char* type_name, const char* test)
{
typedef Real value_type;
std::cout << "Testing: " << test << std::endl;
#if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
value_type (*fp)(value_type, value_type, value_type) = boost::math::ellint_rf<value_type, value_type, value_type>;
#else
value_type (*fp)(value_type, value_type, value_type) = boost::math::ellint_rf;
#endif
boost::math::tools::test_result<value_type> result;
result = boost::math::tools::test_hetero<Real>(
data,
bind_func<Real>(fp, 0, 1, 2),
extract_result<Real>(3));
handle_test_result(result, data[result.worst()], result.worst(),
type_name, "boost::math::ellint_rf", test);
std::cout << std::endl;
}
template <class Real, typename T>
void do_test_ellint_rc(T& data, const char* type_name, const char* test)
{
typedef Real value_type;
std::cout << "Testing: " << test << std::endl;
#if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
value_type (*fp)(value_type, value_type) = boost::math::ellint_rc<value_type, value_type>;
#else
value_type (*fp)(value_type, value_type) = boost::math::ellint_rc;
#endif
boost::math::tools::test_result<value_type> result;
result = boost::math::tools::test_hetero<Real>(
data,
bind_func<Real>(fp, 0, 1),
extract_result<Real>(2));
handle_test_result(result, data[result.worst()], result.worst(),
type_name, "boost::math::ellint_rc", test);
std::cout << std::endl;
}
template <class Real, typename T>
void do_test_ellint_rj(T& data, const char* type_name, const char* test)
{
typedef Real value_type;
std::cout << "Testing: " << test << std::endl;
#if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
value_type (*fp)(value_type, value_type, value_type, value_type) = boost::math::ellint_rj<value_type, value_type, value_type, value_type>;
#else
value_type (*fp)(value_type, value_type, value_type, value_type) = boost::math::ellint_rj;
#endif
boost::math::tools::test_result<value_type> result;
result = boost::math::tools::test_hetero<Real>(
data,
bind_func<Real>(fp, 0, 1, 2, 3),
extract_result<Real>(4));
handle_test_result(result, data[result.worst()], result.worst(),
type_name, "boost::math::ellint_rf", test);
std::cout << std::endl;
}
template <class Real, typename T>
void do_test_ellint_rd(T& data, const char* type_name, const char* test)
{
typedef Real value_type;
std::cout << "Testing: " << test << std::endl;
#if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
value_type (*fp)(value_type, value_type, value_type) = boost::math::ellint_rd<value_type, value_type, value_type>;
#else
value_type (*fp)(value_type, value_type, value_type) = boost::math::ellint_rd;
#endif
boost::math::tools::test_result<value_type> result;
result = boost::math::tools::test_hetero<Real>(
data,
bind_func<Real>(fp, 0, 1, 2),
extract_result<Real>(3));
handle_test_result(result, data[result.worst()], result.worst(),
type_name, "boost::math::ellint_rd", test);
std::cout << std::endl;
}
template <typename T>
void test_spots(T, const char* type_name)
{
#ifndef TEST_UDT
using namespace boost::math;
using namespace std;
// Spot values from Numerical Computation of Real or Complex
// Elliptic Integrals, B. C. Carlson: http://arxiv.org/abs/math.CA/9409227
// RF:
T tolerance = (std::max)(T(1e-13f), tools::epsilon<T>() * 5) * 100; // Note 5eps expressed as a persentage!!!
T eps2 = 2 * tools::epsilon<T>();
BOOST_CHECK_CLOSE(ellint_rf(T(1), T(2), T(0)), T(1.3110287771461), tolerance);
BOOST_CHECK_CLOSE(ellint_rf(T(0.5), T(1), T(0)), T(1.8540746773014), tolerance);
BOOST_CHECK_CLOSE(ellint_rf(T(2), T(3), T(4)), T(0.58408284167715), tolerance);
// RC:
BOOST_CHECK_CLOSE_FRACTION(ellint_rc(T(0), T(1)/4), boost::math::constants::pi<T>(), eps2);
BOOST_CHECK_CLOSE_FRACTION(ellint_rc(T(9)/4, T(2)), log(T(2)), eps2);
BOOST_CHECK_CLOSE_FRACTION(ellint_rc(T(1)/4, T(-2)), log(T(2))/3, eps2);
// RJ:
BOOST_CHECK_CLOSE(ellint_rj(T(0), T(1), T(2), T(3)), T(0.77688623778582), tolerance);
BOOST_CHECK_CLOSE(ellint_rj(T(2), T(3), T(4), T(5)), T(0.14297579667157), tolerance);
BOOST_CHECK_CLOSE(ellint_rj(T(2), T(3), T(4), T(-0.5)), T(0.24723819703052), tolerance);
BOOST_CHECK_CLOSE(ellint_rj(T(2), T(3), T(4), T(-5)), T(-0.12711230042964), tolerance);
// RD:
BOOST_CHECK_CLOSE(ellint_rd(T(0), T(2), T(1)), T(1.7972103521034), tolerance);
BOOST_CHECK_CLOSE(ellint_rd(T(2), T(3), T(4)), T(0.16510527294261), tolerance);
// Sanity/consistency checks from Numerical Computation of Real or Complex
// Elliptic Integrals, B. C. Carlson: http://arxiv.org/abs/math.CA/9409227
boost::mt19937 ran;
boost::uniform_real<float> ur(0, 1000);
T eps40 = 40 * tools::epsilon<T>();
for(unsigned i = 0; i < 1000; ++i)
{
T x = ur(ran);
T y = ur(ran);
T z = ur(ran);
T lambda = ur(ran);
T mu = x * y / lambda;
// RF, eq 49:
T s1 = ellint_rf(x+lambda, y+lambda, lambda) +
ellint_rf(x + mu, y + mu, mu);
T s2 = ellint_rf(x, y, T(0));
BOOST_CHECK_CLOSE_FRACTION(s1, s2, eps40);
// RC is degenerate case of RF:
s1 = ellint_rc(x, y);
s2 = ellint_rf(x, y, y);
BOOST_CHECK_CLOSE_FRACTION(s1, s2, eps40);
// RC, eq 50 (Note have to assume y = x):
T mu2 = x * x / lambda;
s1 = ellint_rc(lambda, x+lambda)
+ ellint_rc(mu2, x + mu2);
s2 = ellint_rc(T(0), x);
BOOST_CHECK_CLOSE_FRACTION(s1, s2, eps40);
/*
T p = ????; // no closed form for a, b and p???
s1 = ellint_rj(x+lambda, y+lambda, lambda, p+lambda)
+ ellint_rj(x+mu, y+mu, mu, p+mu);
s2 = ellint_rj(x, y, T(0), p)
- 3 * ellint_rc(a, b);
*/
// RD, eq 53:
s1 = ellint_rd(lambda, x+lambda, y+lambda)
+ ellint_rd(mu, x+mu, y+mu);
s2 = ellint_rd(T(0), x, y)
- 3 / (y * sqrt(x+y+lambda+mu));
BOOST_CHECK_CLOSE_FRACTION(s1, s2, eps40);
// RD is degenerate case of RJ:
s1 = ellint_rd(x, y, z);
s2 = ellint_rj(x, y, z, z);
BOOST_CHECK_CLOSE_FRACTION(s1, s2, eps40);
}
#endif
//
// Now random spot values:
//
#include "ellint_rf_data.ipp"
do_test_ellint_rf<T>(ellint_rf_data, type_name, "RF: Random data");
#include "ellint_rc_data.ipp"
do_test_ellint_rc<T>(ellint_rc_data, type_name, "RC: Random data");
#include "ellint_rj_data.ipp"
do_test_ellint_rj<T>(ellint_rj_data, type_name, "RJ: Random data");
#include "ellint_rd_data.ipp"
do_test_ellint_rd<T>(ellint_rd_data, type_name, "RD: Random data");
}
|
