1 // Copyright John Maddock 2006.
2 // Copyright Paul A. Bristow 2007, 2009
3 // Use, modification and distribution are subject to the
4 // Boost Software License, Version 1.0. (See accompanying file
5 // LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
6
7 #include <boost/math/concepts/real_concept.hpp>
8 #define BOOST_TEST_MAIN
9 #include <boost/test/unit_test.hpp>
10 #include <boost/test/tools/floating_point_comparison.hpp>
11 #include <boost/math/special_functions/math_fwd.hpp>
12 #include <boost/math/tools/stats.hpp>
13 #include <boost/math/tools/test.hpp>
14 #include <boost/math/constants/constants.hpp>
15 #include <boost/type_traits/is_floating_point.hpp>
16 #include <boost/array.hpp>
17 #include "functor.hpp"
18
19 #include "handle_test_result.hpp"
20 #include "table_type.hpp"
21
22 #ifndef SC_
23 #define SC_(x) static_cast<typename table_type<T>::type>(BOOST_JOIN(x, L))
24 #endif
25
26 template <class Real, class T>
test_inverses(const T & data)27 void test_inverses(const T& data)
28 {
29 using namespace std;
30 //typedef typename T::value_type row_type;
31 typedef Real value_type;
32
33 value_type precision = static_cast<value_type>(ldexp(1.0, 1-boost::math::policies::digits<value_type, boost::math::policies::policy<> >()/2)) * 100;
34 if(boost::math::policies::digits<value_type, boost::math::policies::policy<> >() < 50)
35 precision = 1; // 1% or two decimal digits, all we can hope for when the input is truncated
36
37 for(unsigned i = 0; i < data.size(); ++i)
38 {
39 //
40 // These inverse tests are thrown off if the output of the
41 // incomplete beta is too close to 1: basically there is insuffient
42 // information left in the value we're using as input to the inverse
43 // to be able to get back to the original value.
44 //
45 if(Real(data[i][5]) == 0)
46 BOOST_CHECK_EQUAL(boost::math::ibeta_inv(Real(data[i][0]), Real(data[i][1]), Real(data[i][5])), value_type(0));
47 else if((1 - Real(data[i][5]) > 0.001)
48 && (fabs(Real(data[i][5])) > 2 * boost::math::tools::min_value<value_type>())
49 && (fabs(Real(data[i][5])) > 2 * boost::math::tools::min_value<double>()))
50 {
51 value_type inv = boost::math::ibeta_inv(Real(data[i][0]), Real(data[i][1]), Real(data[i][5]));
52 BOOST_CHECK_CLOSE(Real(data[i][2]), inv, precision);
53 }
54 else if(1 == Real(data[i][5]))
55 BOOST_CHECK_EQUAL(boost::math::ibeta_inv(Real(data[i][0]), Real(data[i][1]), Real(data[i][5])), value_type(1));
56
57 if(Real(data[i][6]) == 0)
58 BOOST_CHECK_EQUAL(boost::math::ibetac_inv(Real(data[i][0]), Real(data[i][1]), Real(data[i][6])), value_type(1));
59 else if((1 - Real(data[i][6]) > 0.001)
60 && (fabs(Real(data[i][6])) > 2 * boost::math::tools::min_value<value_type>())
61 && (fabs(Real(data[i][6])) > 2 * boost::math::tools::min_value<double>()))
62 {
63 value_type inv = boost::math::ibetac_inv(Real(data[i][0]), Real(data[i][1]), Real(data[i][6]));
64 BOOST_CHECK_CLOSE(Real(data[i][2]), inv, precision);
65 }
66 else if(Real(data[i][6]) == 1)
67 BOOST_CHECK_EQUAL(boost::math::ibetac_inv(Real(data[i][0]), Real(data[i][1]), Real(data[i][6])), value_type(0));
68 }
69 }
70
71 template <class Real, class T>
test_inverses2(const T & data,const char * type_name,const char * test_name)72 void test_inverses2(const T& data, const char* type_name, const char* test_name)
73 {
74 #if !(defined(ERROR_REPORTING_MODE) && !defined(IBETA_INV_FUNCTION_TO_TEST))
75 //typedef typename T::value_type row_type;
76 typedef Real value_type;
77
78 typedef value_type (*pg)(value_type, value_type, value_type);
79 #ifdef IBETA_INV_FUNCTION_TO_TEST
80 pg funcp = IBETA_INV_FUNCTION_TO_TEST;
81 #elif defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
82 pg funcp = boost::math::ibeta_inv<value_type, value_type, value_type>;
83 #else
84 pg funcp = boost::math::ibeta_inv;
85 #endif
86
87 boost::math::tools::test_result<value_type> result;
88
89 std::cout << "Testing " << test_name << " with type " << type_name
90 << "\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n";
91
92 //
93 // test ibeta_inv(T, T, T) against data:
94 //
95 result = boost::math::tools::test_hetero<Real>(
96 data,
97 bind_func<Real>(funcp, 0, 1, 2),
98 extract_result<Real>(3));
99 handle_test_result(result, data[result.worst()], result.worst(), type_name, "ibeta_inv", test_name);
100 //
101 // test ibetac_inv(T, T, T) against data:
102 //
103 #ifdef IBETAC_INV_FUNCTION_TO_TEST
104 funcp = IBETAC_INV_FUNCTION_TO_TEST;
105 #elif defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
106 funcp = boost::math::ibetac_inv<value_type, value_type, value_type>;
107 #else
108 funcp = boost::math::ibetac_inv;
109 #endif
110 result = boost::math::tools::test_hetero<Real>(
111 data,
112 bind_func<Real>(funcp, 0, 1, 2),
113 extract_result<Real>(4));
114 handle_test_result(result, data[result.worst()], result.worst(), type_name, "ibetac_inv", test_name);
115 #endif
116 }
117
118
119 template <class T>
test_beta(T,const char * name)120 void test_beta(T, const char* name)
121 {
122 #if !defined(ERROR_REPORTING_MODE)
123 (void)name;
124 //
125 // The actual test data is rather verbose, so it's in a separate file
126 //
127 // The contents are as follows, each row of data contains
128 // five items, input value a, input value b, integration limits x, beta(a, b, x) and ibeta(a, b, x):
129 //
130 #if !defined(TEST_DATA) || (TEST_DATA == 1)
131 # include "ibeta_small_data.ipp"
132
133 test_inverses<T>(ibeta_small_data);
134 #endif
135
136 #if !defined(TEST_DATA) || (TEST_DATA == 2)
137 # include "ibeta_data.ipp"
138
139 test_inverses<T>(ibeta_data);
140 #endif
141
142 #if !defined(TEST_DATA) || (TEST_DATA == 3)
143 # include "ibeta_large_data.ipp"
144
145 test_inverses<T>(ibeta_large_data);
146 #endif
147
148 #endif
149
150 #if !defined(TEST_DATA) || (TEST_DATA == 4)
151 # include "ibeta_inv_data.ipp"
152
153 test_inverses2<T>(ibeta_inv_data, name, "Inverse incomplete beta");
154 #endif
155 }
156
157 template <class T>
test_spots(T)158 void test_spots(T)
159 {
160 BOOST_MATH_STD_USING
161 //
162 // basic sanity checks, tolerance is 100 epsilon expressed as a percentage:
163 //
164 T tolerance = boost::math::tools::epsilon<T>() * 10000;
165 BOOST_CHECK_CLOSE(
166 ::boost::math::ibeta_inv(
167 static_cast<T>(1),
168 static_cast<T>(2),
169 static_cast<T>(0.5)),
170 static_cast<T>(0.29289321881345247559915563789515096071516406231153L), tolerance);
171 BOOST_CHECK_CLOSE(
172 ::boost::math::ibeta_inv(
173 static_cast<T>(3),
174 static_cast<T>(0.5),
175 static_cast<T>(0.5)),
176 static_cast<T>(0.92096723292382700385142816696980724853063433975470L), tolerance);
177 BOOST_CHECK_CLOSE(
178 ::boost::math::ibeta_inv(
179 static_cast<T>(20.125),
180 static_cast<T>(0.5),
181 static_cast<T>(0.5)),
182 static_cast<T>(0.98862133312917003480022776106012775747685870929920L), tolerance);
183 BOOST_CHECK_CLOSE(
184 ::boost::math::ibeta_inv(
185 static_cast<T>(40),
186 static_cast<T>(80),
187 static_cast<T>(0.5)),
188 static_cast<T>(0.33240456430025026300937492802591128972548660643778L), tolerance);
189 BOOST_CHECK_CLOSE(
190 ::boost::math::ibeta_inv(
191 static_cast<T>(40),
192 static_cast<T>(0.5),
193 ldexp(T(1), -30)),
194 static_cast<T>(0.624305407878048788716096298053941618358257550305573588792717L), tolerance);
195 BOOST_CHECK_CLOSE(
196 ::boost::math::ibeta_inv(
197 static_cast<T>(40),
198 static_cast<T>(0.5),
199 static_cast<T>(1 - ldexp(T(1), -30))),
200 static_cast<T>(0.99999999999999999998286262026583217516676792408012252456039L), tolerance);
201 BOOST_CHECK_CLOSE(
202 ::boost::math::ibeta_inv(
203 static_cast<T>(0.5),
204 static_cast<T>(40),
205 static_cast<T>(ldexp(T(1), -30))),
206 static_cast<T>(1.713737973416782483323207591987747543960774485649459249e-20L), tolerance);
207 BOOST_CHECK_CLOSE(
208 ::boost::math::ibeta_inv(
209 static_cast<T>(0.5),
210 static_cast<T>(0.75),
211 static_cast<T>(ldexp(T(1), -30))),
212 static_cast<T>(1.245132488513853853809715434621955746959615015005382639e-18L), tolerance);
213 BOOST_CHECK_CLOSE(
214 ::boost::math::ibeta_inv(
215 static_cast<T>(0.5),
216 static_cast<T>(0.5),
217 static_cast<T>(0.25)),
218 static_cast<T>(0.1464466094067262377995778189475754803575820311557629L), tolerance);
219 BOOST_CHECK_CLOSE(
220 ::boost::math::ibeta_inv(
221 static_cast<T>(0.5),
222 static_cast<T>(0.5),
223 static_cast<T>(0.75)),
224 static_cast<T>(0.853553390593273762200422181052424519642417968844237018294169L), tolerance);
225 BOOST_CHECK_CLOSE(
226 ::boost::math::ibeta_inv(
227 static_cast<T>(1),
228 static_cast<T>(5),
229 static_cast<T>(0.125)),
230 static_cast<T>(0.026352819384831863473794894078665766580641189002729204514544L), tolerance);
231 BOOST_CHECK_CLOSE(
232 ::boost::math::ibeta_inv(
233 static_cast<T>(5),
234 static_cast<T>(1),
235 static_cast<T>(0.125)),
236 static_cast<T>(0.659753955386447129687000985614820066516734506596709340752903L), tolerance);
237 BOOST_CHECK_CLOSE(
238 ::boost::math::ibeta_inv(
239 static_cast<T>(1),
240 static_cast<T>(0.125),
241 static_cast<T>(0.125)),
242 static_cast<T>(0.656391084194183349609374999999999999999999999999999999999999L), tolerance);
243 BOOST_CHECK_CLOSE(
244 ::boost::math::ibeta_inv(
245 static_cast<T>(0.125),
246 static_cast<T>(1),
247 static_cast<T>(0.125)),
248 static_cast<T>(5.960464477539062500000e-8), tolerance);
249 BOOST_CHECK_CLOSE(
250 ::boost::math::ibetac_inv(
251 static_cast<T>(5),
252 static_cast<T>(1),
253 static_cast<T>(0.125)),
254 static_cast<T>(0.973647180615168136526205105921334233419358810997270795485455L), tolerance);
255 BOOST_CHECK_CLOSE(
256 ::boost::math::ibetac_inv(
257 static_cast<T>(1),
258 static_cast<T>(5),
259 static_cast<T>(0.125)),
260 static_cast<T>(0.340246044613552870312999014385179933483265493403290659247096L), tolerance);
261 BOOST_CHECK_CLOSE(
262 ::boost::math::ibetac_inv(
263 static_cast<T>(0.125),
264 static_cast<T>(1),
265 static_cast<T>(0.125)),
266 static_cast<T>(0.343608915805816650390625000000000000000000000000000000000000L), tolerance);
267 BOOST_CHECK_CLOSE(
268 ::boost::math::ibetac_inv(
269 static_cast<T>(1),
270 static_cast<T>(0.125),
271 static_cast<T>(0.125)),
272 static_cast<T>(0.99999994039535522460937500000000000000000000000L), tolerance);
273 }
274
275