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>
do_test_beta(const T & data,const char * type_name,const char * test_name)27 void do_test_beta(const T& data, const char* type_name, const char* test_name)
28 {
29    typedef Real                   value_type;
30 
31    typedef value_type (*pg)(value_type, value_type, value_type);
32 #ifdef BETA_INC_FUNCTION_TO_TEST
33    pg funcp = BETA_INC_FUNCTION_TO_TEST;
34 #elif defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
35    pg funcp = boost::math::beta<value_type, value_type, value_type>;
36 #else
37    pg funcp = boost::math::beta;
38 #endif
39 
40    boost::math::tools::test_result<value_type> result;
41 
42 #if !(defined(ERROR_REPORTING_MODE) && !defined(BETA_INC_FUNCTION_TO_TEST))
43    std::cout << "Testing " << test_name << " with type " << type_name
44       << "\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n";
45 
46    //
47    // test beta against data:
48    //
49    result = boost::math::tools::test_hetero<Real>(
50       data,
51       bind_func<Real>(funcp, 0, 1, 2),
52       extract_result<Real>(3));
53    handle_test_result(result, data[result.worst()], result.worst(), type_name, "beta (incomplete)", test_name);
54 #endif
55 
56 #ifdef BETAC_INC_FUNCTION_TO_TEST
57    funcp = BETAC_INC_FUNCTION_TO_TEST;
58 #elif defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
59    funcp = boost::math::betac<value_type, value_type, value_type>;
60 #else
61    funcp = boost::math::betac;
62 #endif
63 #if !(defined(ERROR_REPORTING_MODE) && !defined(BETAC_INC_FUNCTION_TO_TEST))
64    result = boost::math::tools::test_hetero<Real>(
65       data,
66       bind_func<Real>(funcp, 0, 1, 2),
67       extract_result<Real>(4));
68    handle_test_result(result, data[result.worst()], result.worst(), type_name, "betac", test_name);
69 #endif
70 #ifdef IBETA_FUNCTION_TO_TEST
71    funcp = IBETA_FUNCTION_TO_TEST;
72 #elif defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
73    funcp = boost::math::ibeta<value_type, value_type, value_type>;
74 #else
75    funcp = boost::math::ibeta;
76 #endif
77 #if !(defined(ERROR_REPORTING_MODE) && !defined(IBETA_FUNCTION_TO_TEST))
78    result = boost::math::tools::test_hetero<Real>(
79       data,
80       bind_func<Real>(funcp, 0, 1, 2),
81       extract_result<Real>(5));
82    handle_test_result(result, data[result.worst()], result.worst(), type_name, "ibeta", test_name);
83 #endif
84 #ifdef IBETAC_FUNCTION_TO_TEST
85    funcp = IBETAC_FUNCTION_TO_TEST;
86 #elif defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
87    funcp = boost::math::ibetac<value_type, value_type, value_type>;
88 #else
89    funcp = boost::math::ibetac;
90 #endif
91 #if !(defined(ERROR_REPORTING_MODE) && !defined(IBETAC_FUNCTION_TO_TEST))
92    result = boost::math::tools::test_hetero<Real>(
93       data,
94       bind_func<Real>(funcp, 0, 1, 2),
95       extract_result<Real>(6));
96    handle_test_result(result, data[result.worst()], result.worst(), type_name, "ibetac", test_name);
97    std::cout << std::endl;
98 #endif
99 }
100 
101 template <class T>
test_beta(T,const char * name)102 void test_beta(T, const char* name)
103 {
104    //
105    // The actual test data is rather verbose, so it's in a separate file
106    //
107    // The contents are as follows, each row of data contains
108    // five items, input value a, input value b, integration limits x, beta(a, b, x) and ibeta(a, b, x):
109    //
110 #if !defined(TEST_DATA) || (TEST_DATA == 1)
111 #  include "ibeta_small_data.ipp"
112 
113    do_test_beta<T>(ibeta_small_data, name, "Incomplete Beta Function: Small Values");
114 #endif
115 
116 #if !defined(TEST_DATA) || (TEST_DATA == 2)
117 #  include "ibeta_data.ipp"
118 
119    do_test_beta<T>(ibeta_data, name, "Incomplete Beta Function: Medium Values");
120 
121 #endif
122 #if !defined(TEST_DATA) || (TEST_DATA == 3)
123 #  include "ibeta_large_data.ipp"
124 
125    do_test_beta<T>(ibeta_large_data, name, "Incomplete Beta Function: Large and Diverse Values");
126 #endif
127 
128 #if !defined(TEST_DATA) || (TEST_DATA == 4)
129 #  include "ibeta_int_data.ipp"
130 
131    do_test_beta<T>(ibeta_int_data, name, "Incomplete Beta Function: Small Integer Values");
132 #endif
133 }
134 
135 template <class T>
test_spots(T)136 void test_spots(T)
137 {
138    //
139    // basic sanity checks, tolerance is 30 epsilon expressed as a percentage:
140    // Spot values are from http://functions.wolfram.com/webMathematica/FunctionEvaluation.jsp?name=BetaRegularized
141    // using precision of 50 decimal digits.
142    T tolerance = boost::math::tools::epsilon<T>() * 3000;
143    BOOST_CHECK_CLOSE(
144       ::boost::math::ibeta(
145          static_cast<T>(159) / 10000, //(0.015964560210704803L),
146          static_cast<T>(1184) / 1000000000L,//(1.1846856068586931e-005L),
147          static_cast<T>(6917) / 10000),//(0.69176378846168518L)),
148       static_cast<T>(0.000075393541456247525676062058821484095548666733251733L), tolerance);
149    BOOST_CHECK_CLOSE(
150       ::boost::math::ibeta(
151          static_cast<T>(4243) / 100,//(42.434902191162109L),
152          static_cast<T>(3001) / 10000, //(0.30012050271034241L),
153          static_cast<T>(9157) / 10000), //(0.91574394702911377L)),
154       static_cast<T>(0.0028387319012616013434124297160711532419664289474798L), tolerance);
155    BOOST_CHECK_CLOSE(
156       ::boost::math::ibeta(
157          static_cast<T>(9713) / 1000, //(9.7131776809692383L),
158          static_cast<T>(9940) / 100, //(99.406852722167969L),
159          static_cast<T>(8391) / 100000), //(0.083912998437881470L)),
160       static_cast<T>(0.46116895440368248909937863372410093344466819447476L), tolerance * 2);
161    BOOST_CHECK_CLOSE(
162       ::boost::math::ibeta(
163          static_cast<T>(72.5),
164          static_cast<T>(1.125),
165          static_cast<T>(0.75)),
166       static_cast<T>(1.3423066982487051710597194786268004978931316494920e-9L), tolerance*3); // extra tolerance needed on linux X86EM64
167    BOOST_CHECK_CLOSE(
168       ::boost::math::ibeta(
169          static_cast<T>(4985)/1000, //(4.9854421615600586L),
170          static_cast<T>(1066)/1000, //(1.0665277242660522L),
171          static_cast<T>(7599)/10000), //(0.75997146964073181L)),
172       static_cast<T>(0.27533431334486812211032939156910472371928659321347L), tolerance);
173    BOOST_CHECK_CLOSE(
174       ::boost::math::ibeta(
175          static_cast<T>(6813)/1000, //(6.8127136230468750L),
176          static_cast<T>(1056)/1000, //(1.0562920570373535L),
177          static_cast<T>(1741)/10000), //(0.17416560649871826L)),
178       static_cast<T>(7.6736128722762245852815040810349072461658078840945e-6L), tolerance);
179    BOOST_CHECK_CLOSE(
180       ::boost::math::ibeta(
181          static_cast<T>(4898)/10000, //(0.48983201384544373L),
182          static_cast<T>(2251)/10000, //(0.22512593865394592L),
183          static_cast<T>(2003)/10000), //(0.20032680034637451L)),
184       static_cast<T>(0.17089223868046209692215231702890838878342349377008L), tolerance);
185    BOOST_CHECK_CLOSE(
186       ::boost::math::ibeta(
187          static_cast<T>(4049)/1000, //(4.0498137474060059L),
188          static_cast<T>(1540)/10000, //(0.15403440594673157L),
189          static_cast<T>(6537)/10000), //(0.65370121598243713L)),
190       static_cast<T>(0.017273988301528087878279199511703371301647583919670L), tolerance);
191    BOOST_CHECK_CLOSE(
192       ::boost::math::ibeta(
193          static_cast<T>(7269)/1000, //(7.2695474624633789L),
194          static_cast<T>(1190)/10000, //(0.11902070045471191L),
195          static_cast<T>(8003)/10000), //(0.80036874115467072L)),
196       static_cast<T>(0.013334694467796052900138431733772122625376753696347L), tolerance);
197    BOOST_CHECK_CLOSE(
198       ::boost::math::ibeta(
199          static_cast<T>(2726)/1000, //(2.7266697883605957L),
200          static_cast<T>(1151)/100000, //(0.011510574258863926L),
201          static_cast<T>(8665)/100000), //(0.086654007434844971L)),
202       static_cast<T>(5.8218877068298586420691288375690562915515260230173e-6L), tolerance);
203    BOOST_CHECK_CLOSE(
204       ::boost::math::ibeta(
205          static_cast<T>(3431)/10000, //(0.34317314624786377L),
206          static_cast<T>(4634)/100000, //0.046342257410287857L),
207          static_cast<T>(7582)/10000), //(0.75823287665843964L)),
208       static_cast<T>(0.15132819929418661038699397753916091907278005695387L), tolerance);
209 
210    BOOST_CHECK_CLOSE(
211       ::boost::math::ibeta(
212          static_cast<T>(0.34317314624786377L),
213          static_cast<T>(0.046342257410287857L),
214          static_cast<T>(0)),
215       static_cast<T>(0), tolerance);
216    BOOST_CHECK_CLOSE(
217       ::boost::math::ibetac(
218          static_cast<T>(0.34317314624786377L),
219          static_cast<T>(0.046342257410287857L),
220          static_cast<T>(0)),
221       static_cast<T>(1), tolerance);
222    BOOST_CHECK_CLOSE(
223       ::boost::math::ibeta(
224          static_cast<T>(0.34317314624786377L),
225          static_cast<T>(0.046342257410287857L),
226          static_cast<T>(1)),
227       static_cast<T>(1), tolerance);
228    BOOST_CHECK_CLOSE(
229       ::boost::math::ibetac(
230          static_cast<T>(0.34317314624786377L),
231          static_cast<T>(0.046342257410287857L),
232          static_cast<T>(1)),
233       static_cast<T>(0), tolerance);
234    BOOST_CHECK_CLOSE(
235       ::boost::math::ibeta(
236          static_cast<T>(1),
237          static_cast<T>(4634)/100000, //(0.046342257410287857L),
238          static_cast<T>(32)/100),
239       static_cast<T>(0.017712849440718489999419956301675684844663359595318L), tolerance);
240    BOOST_CHECK_CLOSE(
241       ::boost::math::ibeta(
242          static_cast<T>(4634)/100000, //(0.046342257410287857L),
243          static_cast<T>(1),
244          static_cast<T>(32)/100),
245       static_cast<T>(0.94856839398626914764591440181367780660208493234722L), tolerance);
246 
247    // try with some integer arguments:
248    BOOST_CHECK_CLOSE(
249       ::boost::math::ibeta(
250          static_cast<T>(3),
251          static_cast<T>(8),
252          static_cast<T>(0.25)),
253       static_cast<T>(0.474407196044921875000000000000000000000000000000000000000000L), tolerance);
254    BOOST_CHECK_CLOSE(
255       ::boost::math::ibeta(
256          static_cast<T>(6),
257          static_cast<T>(8),
258          static_cast<T>(0.25)),
259       static_cast<T>(0.0802125930786132812500000000000000000000000000000000000000000L), tolerance);
260    BOOST_CHECK_CLOSE(
261       ::boost::math::ibeta(
262          static_cast<T>(12),
263          static_cast<T>(1),
264          static_cast<T>(0.25)),
265       static_cast<T>(5.96046447753906250000000000000000000000000000000000000000000e-8L), tolerance);
266    BOOST_CHECK_CLOSE(
267       ::boost::math::ibeta(
268          static_cast<T>(1),
269          static_cast<T>(8),
270          static_cast<T>(0.25)),
271       static_cast<T>(0.899887084960937500000000000000000000000000000000000000000000L), tolerance);
272 
273    // very naive check on derivative:
274    using namespace std;  // For ADL of std functions
275    tolerance = boost::math::tools::epsilon<T>() * 10000; // 100 eps
276    BOOST_CHECK_CLOSE(
277       ::boost::math::ibeta_derivative(
278          static_cast<T>(2),
279          static_cast<T>(3),
280          static_cast<T>(0.5)),
281          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);
282 
283    //
284    // Special cases and error handling:
285    //
286    BOOST_CHECK_EQUAL(::boost::math::ibeta(static_cast<T>(0), static_cast<T>(2), static_cast<T>(0.5)), static_cast<T>(1));
287    BOOST_CHECK_EQUAL(::boost::math::ibeta(static_cast<T>(3), static_cast<T>(0), static_cast<T>(0.5)), static_cast<T>(0));
288    BOOST_CHECK_EQUAL(::boost::math::ibetac(static_cast<T>(0), static_cast<T>(2), static_cast<T>(0.5)), static_cast<T>(0));
289    BOOST_CHECK_EQUAL(::boost::math::ibetac(static_cast<T>(4), static_cast<T>(0), static_cast<T>(0.5)), static_cast<T>(1));
290 
291    BOOST_MATH_CHECK_THROW(::boost::math::beta(static_cast<T>(0), static_cast<T>(2), static_cast<T>(0.5)), std::domain_error);
292    BOOST_MATH_CHECK_THROW(::boost::math::beta(static_cast<T>(3), static_cast<T>(0), static_cast<T>(0.5)), std::domain_error);
293    BOOST_MATH_CHECK_THROW(::boost::math::betac(static_cast<T>(0), static_cast<T>(2), static_cast<T>(0.5)), std::domain_error);
294    BOOST_MATH_CHECK_THROW(::boost::math::betac(static_cast<T>(4), static_cast<T>(0), static_cast<T>(0.5)), std::domain_error);
295 
296    BOOST_MATH_CHECK_THROW(::boost::math::ibetac(static_cast<T>(0), static_cast<T>(0), static_cast<T>(0.5)), std::domain_error);
297    BOOST_MATH_CHECK_THROW(::boost::math::ibetac(static_cast<T>(-1), static_cast<T>(2), static_cast<T>(0.5)), std::domain_error);
298    BOOST_MATH_CHECK_THROW(::boost::math::ibetac(static_cast<T>(2), static_cast<T>(-2), static_cast<T>(0.5)), std::domain_error);
299    BOOST_MATH_CHECK_THROW(::boost::math::ibetac(static_cast<T>(2), static_cast<T>(2), static_cast<T>(-0.5)), std::domain_error);
300    BOOST_MATH_CHECK_THROW(::boost::math::ibetac(static_cast<T>(2), static_cast<T>(2), static_cast<T>(1.5)), std::domain_error);
301 
302    //
303    // a = b = 0.5 is a special case:
304    //
305    BOOST_CHECK_CLOSE(
306       ::boost::math::ibeta(
307          static_cast<T>(0.5f),
308          static_cast<T>(0.5f),
309          static_cast<T>(0.25)),
310       static_cast<T>(1) / 3, tolerance);
311    BOOST_CHECK_CLOSE(
312       ::boost::math::ibetac(
313          static_cast<T>(0.5f),
314          static_cast<T>(0.5f),
315          static_cast<T>(0.25)),
316       static_cast<T>(2) / 3, tolerance);
317    BOOST_CHECK_CLOSE(
318       ::boost::math::ibeta(
319          static_cast<T>(0.5f),
320          static_cast<T>(0.5f),
321          static_cast<T>(0.125)),
322       static_cast<T>(0.230053456162615885213780567705142893009911395270714102055874L), tolerance);
323    BOOST_CHECK_CLOSE(
324       ::boost::math::ibetac(
325          static_cast<T>(0.5f),
326          static_cast<T>(0.5f),
327          static_cast<T>(0.125)),
328       static_cast<T>(0.769946543837384114786219432294857106990088604729285897944125L), tolerance);
329    BOOST_CHECK_CLOSE(
330       ::boost::math::ibeta(
331          static_cast<T>(0.5f),
332          static_cast<T>(0.5f),
333          static_cast<T>(0.825L)),
334       static_cast<T>(0.725231121519469565327291851560156562956885802608457839260161L), tolerance);
335    BOOST_CHECK_CLOSE(
336       ::boost::math::ibetac(
337          static_cast<T>(0.5f),
338          static_cast<T>(0.5f),
339          static_cast<T>(0.825L)),
340       static_cast<T>(0.274768878480530434672708148439843437043114197391542160739838L), tolerance);
341    //
342    // Second argument is 1 is a special case, see http://functions.wolfram.com/GammaBetaErf/BetaRegularized/03/01/01/
343    //
344    BOOST_CHECK_CLOSE(
345       ::boost::math::ibeta(
346          static_cast<T>(0.5f),
347          static_cast<T>(1),
348          static_cast<T>(0.825L)),
349       static_cast<T>(0.908295106229247499626759842915458109758420750043003849691665L), tolerance);
350    BOOST_CHECK_CLOSE(
351       ::boost::math::ibetac(
352          static_cast<T>(0.5f),
353          static_cast<T>(1),
354          static_cast<T>(0.825L)),
355       static_cast<T>(0.091704893770752500373240157084541890241579249956996150308334L), tolerance);
356    BOOST_CHECK_CLOSE(
357       ::boost::math::ibeta(
358          static_cast<T>(30),
359          static_cast<T>(1),
360          static_cast<T>(0.825L)),
361       static_cast<T>(0.003116150729395132012981654047222541793435357905008020740211L), tolerance);
362    BOOST_CHECK_CLOSE(
363       ::boost::math::ibetac(
364          static_cast<T>(30),
365          static_cast<T>(1),
366          static_cast<T>(0.825L)),
367       static_cast<T>(0.996883849270604867987018345952777458206564642094991979259788L), tolerance);
368 
369    //
370    // Bug cases from Rocco Romeo:
371    //
372    BOOST_CHECK_CLOSE(
373       ::boost::math::beta(
374       static_cast<T>(2),
375       static_cast<T>(24),
376       ldexp(static_cast<T>(1), -52)),
377       static_cast<T>(2.46519032881565349871772482100516780410072110983579277754743e-32L), tolerance);
378    BOOST_CHECK_CLOSE(
379       ::boost::math::ibeta(
380       static_cast<T>(2),
381       static_cast<T>(24),
382       ldexp(static_cast<T>(1), -52)),
383       static_cast<T>(1.47911419728939209923063489260310068246043266590147566652846e-29L), tolerance);
384    BOOST_CHECK_CLOSE(
385       ::boost::math::beta(
386       static_cast<T>(3),
387       static_cast<T>(2),
388       ldexp(static_cast<T>(1), -270)),
389       static_cast<T>(4.88182556606650701438035298707052523938789614661168065734809e-245L), tolerance);
390    BOOST_CHECK_CLOSE(
391       ::boost::math::beta(
392       static_cast<T>(2),
393       static_cast<T>(31),
394       ldexp(static_cast<T>(1), -373)),
395       static_cast<T>(1.35080680244581673116149460571129957689952846520037541640260e-225L), tolerance);
396    BOOST_CHECK_CLOSE(
397       ::boost::math::ibeta(
398       static_cast<T>(3),
399       static_cast<T>(2),
400       ldexp(static_cast<T>(1), -270)),
401       static_cast<T>(5.85819067927980841725642358448463028726547537593401678881771e-244L), tolerance);
402    BOOST_CHECK_CLOSE(
403       ::boost::math::ibeta(
404       static_cast<T>(2),
405       static_cast<T>(31),
406       ldexp(static_cast<T>(1), -373)),
407       static_cast<T>(1.34000034802625019731220264886560918028433223747877241307138e-222L), tolerance);
408    //
409    // Bug cases from Rocco Romeo:
410    //
411    BOOST_CHECK_CLOSE(
412       ::boost::math::beta(
413          static_cast<T>(2),
414          static_cast<T>(4),
415          ldexp(static_cast<T>(1 + static_cast<T>(1.0) / 1024), -351)),
416       static_cast<T>(2.381008060978474962211278613067275529112106932635520021e-212L), tolerance);
417       BOOST_CHECK_CLOSE(
418          ::boost::math::beta(
419             static_cast<T>(2),
420             static_cast<T>(4),
421             ldexp(static_cast<T>(1 + static_cast<T>(1.0) / 2048), -351)),
422          static_cast<T>(2.378685692854274898232669682422430136513931911501225435e-212L), tolerance);
423       BOOST_CHECK_CLOSE(
424          ::boost::math::ibeta(
425             static_cast<T>(3),
426             static_cast<T>(5),
427             ldexp(static_cast<T>(1 + static_cast<T>(15) / 16), -268)),
428             static_cast<T>(2.386034198603463687323052353589201848077110231388968865e-240L), tolerance);
429       BOOST_CHECK_CLOSE(
430          ::boost::math::ibeta_derivative(
431             static_cast<T>(2),
432             static_cast<T>(4),
433             ldexp(static_cast<T>(1), -557)),
434          static_cast<T>(4.23957586190238472641508753637420672781472122471791800210e-167L), tolerance * 4);
435       BOOST_CHECK_CLOSE(
436          ::boost::math::ibeta_derivative(
437             static_cast<T>(2),
438             static_cast<T>(4.5),
439             ldexp(static_cast<T>(1), -557)),
440          static_cast<T>(5.24647512910420109893867082626308082567071751558842352760e-167L), tolerance * 20);
441 }
442 
443