ceph/src/boost/libs/math/test/test_ibeta.hpp

   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>
  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>
 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>
 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