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/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 "test_beta_hooks.hpp"
20 #include "handle_test_result.hpp"
21 #include "table_type.hpp"
22 
23 #ifndef SC_
24 #define SC_(x) static_cast<typename table_type<T>::type>(BOOST_JOIN(x, L))
25 #endif
26 
27 template <class Real, class T>
do_test_beta(const T & data,const char * type_name,const char * test_name)28 void do_test_beta(const T& data, const char* type_name, const char* test_name)
29 {
30    typedef Real                   value_type;
31 
32    typedef value_type (*pg)(value_type, value_type, value_type);
33 #if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
34    pg funcp = boost::math::beta<value_type, value_type, value_type>;
35 #else
36    pg funcp = boost::math::beta;
37 #endif
38 
39    boost::math::tools::test_result<value_type> result;
40 
41    std::cout << "Testing " << test_name << " with type " << type_name
42       << "\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n";
43 
44    //
45    // test beta against data:
46    //
47    result = boost::math::tools::test_hetero<Real>(
48       data,
49       bind_func<Real>(funcp, 0, 1, 2),
50       extract_result<Real>(3));
51    handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::beta", test_name);
52 
53 #if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
54    funcp = boost::math::betac<value_type, value_type, value_type>;
55 #else
56    funcp = boost::math::betac;
57 #endif
58    result = boost::math::tools::test_hetero<Real>(
59       data,
60       bind_func<Real>(funcp, 0, 1, 2),
61       extract_result<Real>(4));
62    handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::betac", test_name);
63 
64 #if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
65    funcp = boost::math::ibeta<value_type, value_type, value_type>;
66 #else
67    funcp = boost::math::ibeta;
68 #endif
69    result = boost::math::tools::test_hetero<Real>(
70       data,
71       bind_func<Real>(funcp, 0, 1, 2),
72       extract_result<Real>(5));
73    handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::ibeta", test_name);
74 
75 #if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
76    funcp = boost::math::ibetac<value_type, value_type, value_type>;
77 #else
78    funcp = boost::math::ibetac;
79 #endif
80    result = boost::math::tools::test_hetero<Real>(
81       data,
82       bind_func<Real>(funcp, 0, 1, 2),
83       extract_result<Real>(6));
84    handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::ibetac", test_name);
85 #ifdef TEST_OTHER
86    if(::boost::is_floating_point<value_type>::value){
87       funcp = other::ibeta;
88       result = boost::math::tools::test_hetero<Real>(
89          data,
90          bind_func<Real>(funcp, 0, 1, 2),
91          extract_result<Real>(5));
92       print_test_result(result, data[result.worst()], result.worst(), type_name, "other::ibeta");
93    }
94 #endif
95    std::cout << std::endl;
96 }
97 
98 template <class T>
test_beta(T,const char * name)99 void test_beta(T, const char* name)
100 {
101    //
102    // The actual test data is rather verbose, so it's in a separate file
103    //
104    // The contents are as follows, each row of data contains
105    // five items, input value a, input value b, integration limits x, beta(a, b, x) and ibeta(a, b, x):
106    //
107 #if !defined(TEST_DATA) || (TEST_DATA == 1)
108 #  include "ibeta_small_data.ipp"
109 
110    do_test_beta<T>(ibeta_small_data, name, "Incomplete Beta Function: Small Values");
111 #endif
112 
113 #if !defined(TEST_DATA) || (TEST_DATA == 2)
114 #  include "ibeta_data.ipp"
115 
116    do_test_beta<T>(ibeta_data, name, "Incomplete Beta Function: Medium Values");
117 
118 #endif
119 #if !defined(TEST_DATA) || (TEST_DATA == 3)
120 #  include "ibeta_large_data.ipp"
121 
122    do_test_beta<T>(ibeta_large_data, name, "Incomplete Beta Function: Large and Diverse Values");
123 #endif
124 
125 #if !defined(TEST_DATA) || (TEST_DATA == 4)
126 #  include "ibeta_int_data.ipp"
127 
128    do_test_beta<T>(ibeta_int_data, name, "Incomplete Beta Function: Small Integer Values");
129 #endif
130 }
131 
132 template <class T>
test_spots(T)133 void test_spots(T)
134 {
135    //
136    // basic sanity checks, tolerance is 30 epsilon expressed as a percentage:
137    // Spot values are from http://functions.wolfram.com/webMathematica/FunctionEvaluation.jsp?name=BetaRegularized
138    // using precision of 50 decimal digits.
139    T tolerance = boost::math::tools::epsilon<T>() * 3000;
140    BOOST_CHECK_CLOSE(
141       ::boost::math::ibeta(
142          static_cast<T>(159) / 10000, //(0.015964560210704803L),
143          static_cast<T>(1184) / 1000000000L,//(1.1846856068586931e-005L),
144          static_cast<T>(6917) / 10000),//(0.69176378846168518L)),
145       static_cast<T>(0.000075393541456247525676062058821484095548666733251733L), tolerance);
146    BOOST_CHECK_CLOSE(
147       ::boost::math::ibeta(
148          static_cast<T>(4243) / 100,//(42.434902191162109L),
149          static_cast<T>(3001) / 10000, //(0.30012050271034241L),
150          static_cast<T>(9157) / 10000), //(0.91574394702911377L)),
151       static_cast<T>(0.0028387319012616013434124297160711532419664289474798L), tolerance);
152    BOOST_CHECK_CLOSE(
153       ::boost::math::ibeta(
154          static_cast<T>(9713) / 1000, //(9.7131776809692383L),
155          static_cast<T>(9940) / 100, //(99.406852722167969L),
156          static_cast<T>(8391) / 100000), //(0.083912998437881470L)),
157       static_cast<T>(0.46116895440368248909937863372410093344466819447476L), tolerance);
158    BOOST_CHECK_CLOSE(
159       ::boost::math::ibeta(
160          static_cast<T>(72.5),
161          static_cast<T>(1.125),
162          static_cast<T>(0.75)),
163       static_cast<T>(1.3423066982487051710597194786268004978931316494920e-9L), tolerance*3); // extra tolerance needed on linux X86EM64
164    BOOST_CHECK_CLOSE(
165       ::boost::math::ibeta(
166          static_cast<T>(4985)/1000, //(4.9854421615600586L),
167          static_cast<T>(1066)/1000, //(1.0665277242660522L),
168          static_cast<T>(7599)/10000), //(0.75997146964073181L)),
169       static_cast<T>(0.27533431334486812211032939156910472371928659321347L), tolerance);
170    BOOST_CHECK_CLOSE(
171       ::boost::math::ibeta(
172          static_cast<T>(6813)/1000, //(6.8127136230468750L),
173          static_cast<T>(1056)/1000, //(1.0562920570373535L),
174          static_cast<T>(1741)/10000), //(0.17416560649871826L)),
175       static_cast<T>(7.6736128722762245852815040810349072461658078840945e-6L), tolerance);
176    BOOST_CHECK_CLOSE(
177       ::boost::math::ibeta(
178          static_cast<T>(4898)/10000, //(0.48983201384544373L),
179          static_cast<T>(2251)/10000, //(0.22512593865394592L),
180          static_cast<T>(2003)/10000), //(0.20032680034637451L)),
181       static_cast<T>(0.17089223868046209692215231702890838878342349377008L), tolerance);
182    BOOST_CHECK_CLOSE(
183       ::boost::math::ibeta(
184          static_cast<T>(4049)/1000, //(4.0498137474060059L),
185          static_cast<T>(1540)/10000, //(0.15403440594673157L),
186          static_cast<T>(6537)/10000), //(0.65370121598243713L)),
187       static_cast<T>(0.017273988301528087878279199511703371301647583919670L), tolerance);
188    BOOST_CHECK_CLOSE(
189       ::boost::math::ibeta(
190          static_cast<T>(7269)/1000, //(7.2695474624633789L),
191          static_cast<T>(1190)/10000, //(0.11902070045471191L),
192          static_cast<T>(8003)/10000), //(0.80036874115467072L)),
193       static_cast<T>(0.013334694467796052900138431733772122625376753696347L), tolerance);
194    BOOST_CHECK_CLOSE(
195       ::boost::math::ibeta(
196          static_cast<T>(2726)/1000, //(2.7266697883605957L),
197          static_cast<T>(1151)/100000, //(0.011510574258863926L),
198          static_cast<T>(8665)/100000), //(0.086654007434844971L)),
199       static_cast<T>(5.8218877068298586420691288375690562915515260230173e-6L), tolerance);
200    BOOST_CHECK_CLOSE(
201       ::boost::math::ibeta(
202          static_cast<T>(3431)/10000, //(0.34317314624786377L),
203          static_cast<T>(4634)/100000, //0.046342257410287857L),
204          static_cast<T>(7582)/10000), //(0.75823287665843964L)),
205       static_cast<T>(0.15132819929418661038699397753916091907278005695387L), tolerance);
206 
207    BOOST_CHECK_CLOSE(
208       ::boost::math::ibeta(
209          static_cast<T>(0.34317314624786377L),
210          static_cast<T>(0.046342257410287857L),
211          static_cast<T>(0)),
212       static_cast<T>(0), tolerance);
213    BOOST_CHECK_CLOSE(
214       ::boost::math::ibetac(
215          static_cast<T>(0.34317314624786377L),
216          static_cast<T>(0.046342257410287857L),
217          static_cast<T>(0)),
218       static_cast<T>(1), tolerance);
219    BOOST_CHECK_CLOSE(
220       ::boost::math::ibeta(
221          static_cast<T>(0.34317314624786377L),
222          static_cast<T>(0.046342257410287857L),
223          static_cast<T>(1)),
224       static_cast<T>(1), tolerance);
225    BOOST_CHECK_CLOSE(
226       ::boost::math::ibetac(
227          static_cast<T>(0.34317314624786377L),
228          static_cast<T>(0.046342257410287857L),
229          static_cast<T>(1)),
230       static_cast<T>(0), tolerance);
231    BOOST_CHECK_CLOSE(
232       ::boost::math::ibeta(
233          static_cast<T>(1),
234          static_cast<T>(4634)/100000, //(0.046342257410287857L),
235          static_cast<T>(32)/100),
236       static_cast<T>(0.017712849440718489999419956301675684844663359595318L), tolerance);
237    BOOST_CHECK_CLOSE(
238       ::boost::math::ibeta(
239          static_cast<T>(4634)/100000, //(0.046342257410287857L),
240          static_cast<T>(1),
241          static_cast<T>(32)/100),
242       static_cast<T>(0.94856839398626914764591440181367780660208493234722L), tolerance);
243 
244    // try with some integer arguments:
245    BOOST_CHECK_CLOSE(
246       ::boost::math::ibeta(
247          static_cast<T>(3),
248          static_cast<T>(8),
249          static_cast<T>(0.25)),
250       static_cast<T>(0.474407196044921875000000000000000000000000000000000000000000L), tolerance);
251    BOOST_CHECK_CLOSE(
252       ::boost::math::ibeta(
253          static_cast<T>(6),
254          static_cast<T>(8),
255          static_cast<T>(0.25)),
256       static_cast<T>(0.0802125930786132812500000000000000000000000000000000000000000L), tolerance);
257    BOOST_CHECK_CLOSE(
258       ::boost::math::ibeta(
259          static_cast<T>(12),
260          static_cast<T>(1),
261          static_cast<T>(0.25)),
262       static_cast<T>(5.96046447753906250000000000000000000000000000000000000000000e-8L), tolerance);
263    BOOST_CHECK_CLOSE(
264       ::boost::math::ibeta(
265          static_cast<T>(1),
266          static_cast<T>(8),
267          static_cast<T>(0.25)),
268       static_cast<T>(0.899887084960937500000000000000000000000000000000000000000000L), tolerance);
269 
270    // very naive check on derivative:
271    using namespace std;  // For ADL of std functions
272    tolerance = boost::math::tools::epsilon<T>() * 10000; // 100 eps
273    BOOST_CHECK_CLOSE(
274       ::boost::math::ibeta_derivative(
275          static_cast<T>(2),
276          static_cast<T>(3),
277          static_cast<T>(0.5)),
278          pow(static_cast<T>(0.5), static_cast<T>(2)) * pow(static_cast<T>(0.5), static_cast<T>(1)) / boost::math::beta(static_cast<T>(2), static_cast<T>(3)), tolerance);
279 
280    //
281    // Special cases and error handling:
282    //
283    BOOST_CHECK_EQUAL(::boost::math::ibeta(static_cast<T>(0), static_cast<T>(2), static_cast<T>(0.5)), static_cast<T>(1));
284    BOOST_CHECK_EQUAL(::boost::math::ibeta(static_cast<T>(3), static_cast<T>(0), static_cast<T>(0.5)), static_cast<T>(0));
285    BOOST_CHECK_EQUAL(::boost::math::ibetac(static_cast<T>(0), static_cast<T>(2), static_cast<T>(0.5)), static_cast<T>(0));
286    BOOST_CHECK_EQUAL(::boost::math::ibetac(static_cast<T>(4), static_cast<T>(0), static_cast<T>(0.5)), static_cast<T>(1));
287 
288    BOOST_CHECK_THROW(::boost::math::beta(static_cast<T>(0), static_cast<T>(2), static_cast<T>(0.5)), std::domain_error);
289    BOOST_CHECK_THROW(::boost::math::beta(static_cast<T>(3), static_cast<T>(0), static_cast<T>(0.5)), std::domain_error);
290    BOOST_CHECK_THROW(::boost::math::betac(static_cast<T>(0), static_cast<T>(2), static_cast<T>(0.5)), std::domain_error);
291    BOOST_CHECK_THROW(::boost::math::betac(static_cast<T>(4), static_cast<T>(0), static_cast<T>(0.5)), std::domain_error);
292 
293    BOOST_CHECK_THROW(::boost::math::ibetac(static_cast<T>(0), static_cast<T>(0), static_cast<T>(0.5)), std::domain_error);
294    BOOST_CHECK_THROW(::boost::math::ibetac(static_cast<T>(-1), static_cast<T>(2), static_cast<T>(0.5)), std::domain_error);
295    BOOST_CHECK_THROW(::boost::math::ibetac(static_cast<T>(2), static_cast<T>(-2), static_cast<T>(0.5)), std::domain_error);
296    BOOST_CHECK_THROW(::boost::math::ibetac(static_cast<T>(2), static_cast<T>(2), static_cast<T>(-0.5)), std::domain_error);
297    BOOST_CHECK_THROW(::boost::math::ibetac(static_cast<T>(2), static_cast<T>(2), static_cast<T>(1.5)), std::domain_error);
298 
299    //
300    // a = b = 0.5 is a special case:
301    //
302    BOOST_CHECK_CLOSE(
303       ::boost::math::ibeta(
304          static_cast<T>(0.5f),
305          static_cast<T>(0.5f),
306          static_cast<T>(0.25)),
307       static_cast<T>(1) / 3, tolerance);
308    BOOST_CHECK_CLOSE(
309       ::boost::math::ibetac(
310          static_cast<T>(0.5f),
311          static_cast<T>(0.5f),
312          static_cast<T>(0.25)),
313       static_cast<T>(2) / 3, tolerance);
314    BOOST_CHECK_CLOSE(
315       ::boost::math::ibeta(
316          static_cast<T>(0.5f),
317          static_cast<T>(0.5f),
318          static_cast<T>(0.125)),
319       static_cast<T>(0.230053456162615885213780567705142893009911395270714102055874L), tolerance);
320    BOOST_CHECK_CLOSE(
321       ::boost::math::ibetac(
322          static_cast<T>(0.5f),
323          static_cast<T>(0.5f),
324          static_cast<T>(0.125)),
325       static_cast<T>(0.769946543837384114786219432294857106990088604729285897944125L), tolerance);
326    BOOST_CHECK_CLOSE(
327       ::boost::math::ibeta(
328          static_cast<T>(0.5f),
329          static_cast<T>(0.5f),
330          static_cast<T>(0.825L)),
331       static_cast<T>(0.725231121519469565327291851560156562956885802608457839260161L), tolerance);
332    BOOST_CHECK_CLOSE(
333       ::boost::math::ibetac(
334          static_cast<T>(0.5f),
335          static_cast<T>(0.5f),
336          static_cast<T>(0.825L)),
337       static_cast<T>(0.274768878480530434672708148439843437043114197391542160739838L), tolerance);
338    //
339    // Second argument is 1 is a special case, see http://functions.wolfram.com/GammaBetaErf/BetaRegularized/03/01/01/
340    //
341    BOOST_CHECK_CLOSE(
342       ::boost::math::ibeta(
343          static_cast<T>(0.5f),
344          static_cast<T>(1),
345          static_cast<T>(0.825L)),
346       static_cast<T>(0.908295106229247499626759842915458109758420750043003849691665L), tolerance);
347    BOOST_CHECK_CLOSE(
348       ::boost::math::ibetac(
349          static_cast<T>(0.5f),
350          static_cast<T>(1),
351          static_cast<T>(0.825L)),
352       static_cast<T>(0.091704893770752500373240157084541890241579249956996150308334L), tolerance);
353    BOOST_CHECK_CLOSE(
354       ::boost::math::ibeta(
355          static_cast<T>(30),
356          static_cast<T>(1),
357          static_cast<T>(0.825L)),
358       static_cast<T>(0.003116150729395132012981654047222541793435357905008020740211L), tolerance);
359    BOOST_CHECK_CLOSE(
360       ::boost::math::ibetac(
361          static_cast<T>(30),
362          static_cast<T>(1),
363          static_cast<T>(0.825L)),
364       static_cast<T>(0.996883849270604867987018345952777458206564642094991979259788L), tolerance);
365 
366    //
367    // Bug cases from Rocco Romeo:
368    //
369    BOOST_CHECK_CLOSE(
370       ::boost::math::beta(
371       static_cast<T>(2),
372       static_cast<T>(24),
373       ldexp(static_cast<T>(1), -52)),
374       static_cast<T>(2.46519032881565349871772482100516780410072110983579277754743e-32L), tolerance);
375    BOOST_CHECK_CLOSE(
376       ::boost::math::ibeta(
377       static_cast<T>(2),
378       static_cast<T>(24),
379       ldexp(static_cast<T>(1), -52)),
380       static_cast<T>(1.47911419728939209923063489260310068246043266590147566652846e-29L), tolerance);
381    BOOST_CHECK_CLOSE(
382       ::boost::math::beta(
383       static_cast<T>(3),
384       static_cast<T>(2),
385       ldexp(static_cast<T>(1), -270)),
386       static_cast<T>(4.88182556606650701438035298707052523938789614661168065734809e-245L), tolerance);
387    BOOST_CHECK_CLOSE(
388       ::boost::math::beta(
389       static_cast<T>(2),
390       static_cast<T>(31),
391       ldexp(static_cast<T>(1), -373)),
392       static_cast<T>(1.35080680244581673116149460571129957689952846520037541640260e-225L), tolerance);
393    BOOST_CHECK_CLOSE(
394       ::boost::math::ibeta(
395       static_cast<T>(3),
396       static_cast<T>(2),
397       ldexp(static_cast<T>(1), -270)),
398       static_cast<T>(5.85819067927980841725642358448463028726547537593401678881771e-244L), tolerance);
399    BOOST_CHECK_CLOSE(
400       ::boost::math::ibeta(
401       static_cast<T>(2),
402       static_cast<T>(31),
403       ldexp(static_cast<T>(1), -373)),
404       static_cast<T>(1.34000034802625019731220264886560918028433223747877241307138e-222L), tolerance);
405 }
406 
407