ceph/src/boost/libs/math/test/test_autodiff_3.cpp

   1 //           Copyright Matthew Pulver 2018 - 2019.
   2 // Distributed under the Boost Software License, Version 1.0.
   3 //      (See accompanying file LICENSE_1_0.txt or copy at
   4 //           https://www.boost.org/LICENSE_1_0.txt)
   5
   6 #include "test_autodiff.hpp"
   7 #include <boost/utility/identity_type.hpp>
   8
   9 BOOST_AUTO_TEST_SUITE(test_autodiff_3)
  10
  11 BOOST_AUTO_TEST_CASE_TEMPLATE(atanh_test, T, all_float_types) {
  12   const T eps = 3000 * test_constants_t<T>::pct_epsilon(); // percent
  13   constexpr unsigned m = 5;
  14   const T cx = 0.5;
  15   auto x = make_fvar<T, m>(cx);
  16   auto y = atanh(x);
  17   // BOOST_CHECK_EQUAL(y.derivative(0) , atanh(cx)); // fails due to overload
  18   BOOST_CHECK_CLOSE(y.derivative(0u), atanh(static_cast<T>(x)), eps);
  19   BOOST_CHECK_CLOSE(y.derivative(1u), static_cast<T>(4) / 3, eps);
  20   BOOST_CHECK_CLOSE(y.derivative(2u), static_cast<T>(16) / 9, eps);
  21   BOOST_CHECK_CLOSE(y.derivative(3u), static_cast<T>(224) / 27, eps);
  22   BOOST_CHECK_CLOSE(y.derivative(4u), static_cast<T>(1280) / 27, eps);
  23   BOOST_CHECK_CLOSE(y.derivative(5u), static_cast<T>(31232) / 81, eps);
  24 }
  25
  26 BOOST_AUTO_TEST_CASE_TEMPLATE(atan_test, T, all_float_types) {
  27   BOOST_MATH_STD_USING
  28   using namespace boost;
  29
  30   const T cx = 1.0;
  31   constexpr unsigned m = 5;
  32   const auto x = make_fvar<T, m>(cx);
  33   auto y = atan(x);
  34   const auto eps = boost::math::tools::epsilon<T>();
  35   BOOST_CHECK_CLOSE(y.derivative(0u), boost::math::constants::pi<T>() / 4, eps);
  36   BOOST_CHECK_CLOSE(y.derivative(1u), T(0.5), eps);
  37   BOOST_CHECK_CLOSE(y.derivative(2u), T(-0.5), eps);
  38   BOOST_CHECK_CLOSE(y.derivative(3u), T(0.5), eps);
  39   BOOST_CHECK_CLOSE(y.derivative(4u), T(0), eps);
  40   BOOST_CHECK_CLOSE(y.derivative(5u), T(-3), eps);
  41 }
  42
  43 BOOST_AUTO_TEST_CASE_TEMPLATE(erf_test, T, all_float_types) {
  44   BOOST_MATH_STD_USING
  45   using namespace boost;
  46
  47   const T eps = 300 * 100 * boost::math::tools::epsilon<T>(); // percent
  48   const T cx = 1.0;
  49   constexpr unsigned m = 5;
  50   const auto x = make_fvar<T, m>(cx);
  51   auto y = erf(x);
  52   BOOST_CHECK_CLOSE(y.derivative(0u), erf(static_cast<T>(x)), eps);
  53   BOOST_CHECK_CLOSE(
  54       y.derivative(1u),
  55       T(2) / (math::constants::e<T>() * math::constants::root_pi<T>()), eps);
  56   BOOST_CHECK_CLOSE(
  57       y.derivative(2u),
  58       T(-4) / (math::constants::e<T>() * math::constants::root_pi<T>()), eps);
  59   BOOST_CHECK_CLOSE(
  60       y.derivative(3u),
  61       T(4) / (math::constants::e<T>() * math::constants::root_pi<T>()), eps);
  62   BOOST_CHECK_CLOSE(
  63       y.derivative(4u),
  64       T(8) / (math::constants::e<T>() * math::constants::root_pi<T>()), eps);
  65   BOOST_CHECK_CLOSE(
  66       y.derivative(5u),
  67       T(-40) / (math::constants::e<T>() * math::constants::root_pi<T>()), eps);
  68 }
  69
  70 BOOST_AUTO_TEST_CASE_TEMPLATE(sinc_test, T, bin_float_types) {
  71   BOOST_MATH_STD_USING
  72   const T eps = 20000 * boost::math::tools::epsilon<T>(); // percent
  73   const T cx = 1;
  74   constexpr unsigned m = 5;
  75   auto x = make_fvar<T, m>(cx);
  76   auto y = sinc(x);
  77   BOOST_CHECK_CLOSE(y.derivative(0u), sin(cx), eps);
  78   BOOST_CHECK_CLOSE(y.derivative(1u), cos(cx) - sin(cx), eps);
  79   BOOST_CHECK_CLOSE(y.derivative(2u), sin(cx) - 2 * cos(cx), eps);
  80   BOOST_CHECK_CLOSE(y.derivative(3u), T(5) * cos(cx) - T(3) * sin(cx), eps);
  81   BOOST_CHECK_CLOSE(y.derivative(4u), T(13) * sin(cx) - T(20) * cos(cx), eps);
  82   BOOST_CHECK_CLOSE(y.derivative(5u), T(101) * cos(cx) - T(65) * sin(cx), eps);
  83   // Test at x = 0
  84   auto y2 = sinc(make_fvar<T, 10>(0));
  85   BOOST_CHECK_CLOSE(y2.derivative(0u), T(1), eps);
  86   BOOST_CHECK_CLOSE(y2.derivative(1u), T(0), eps);
  87   BOOST_CHECK_CLOSE(y2.derivative(2u), -cx / T(3), eps);
  88   BOOST_CHECK_CLOSE(y2.derivative(3u), T(0), eps);
  89   BOOST_CHECK_CLOSE(y2.derivative(4u), cx / T(5), eps);
  90   BOOST_CHECK_CLOSE(y2.derivative(5u), T(0), eps);
  91   BOOST_CHECK_CLOSE(y2.derivative(6u), -cx / T(7), eps);
  92   BOOST_CHECK_CLOSE(y2.derivative(7u), T(0), eps);
  93   BOOST_CHECK_CLOSE(y2.derivative(8u), cx / T(9), eps);
  94   BOOST_CHECK_CLOSE(y2.derivative(9u), T(0), eps);
  95   BOOST_CHECK_CLOSE(y2.derivative(10u), -cx / T(11), eps);
  96 }
  97
  98 BOOST_AUTO_TEST_CASE_TEMPLATE(sinh_and_cosh, T, bin_float_types) {
  99   BOOST_MATH_STD_USING
 100   const T eps = 300 * boost::math::tools::epsilon<T>(); // percent
 101   const T cx = 1;
 102   constexpr unsigned m = 5;
 103   auto x = make_fvar<T, m>(cx);
 104   auto s = sinh(x);
 105   auto c = cosh(x);
 106   BOOST_CHECK_CLOSE(s.derivative(0u), sinh(static_cast<T>(x)), eps);
 107   BOOST_CHECK_CLOSE(c.derivative(0u), cosh(static_cast<T>(x)), eps);
 108   for (auto i : boost::irange(m + 1)) {
 109     BOOST_CHECK_CLOSE(s.derivative(i), static_cast<T>(i % 2 == 1 ? c : s), eps);
 110     BOOST_CHECK_CLOSE(c.derivative(i), static_cast<T>(i % 2 == 1 ? s : c), eps);
 111   }
 112 }
 113
 114 #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
 115 BOOST_AUTO_TEST_CASE_TEMPLATE(tanh_test, T, all_float_types) {
 116   using bmp::fabs;
 117   using bmp::tanh;
 118   using detail::fabs;
 119   using detail::tanh;
 120   using std::fabs;
 121   using std::tanh;
 122   constexpr std::array<const char *, 6> tanh_derivatives{
 123       {"0."
 124        "76159415595576488811945828260479359041276859725793655159681050012195324"
 125        "457663848345894752167367671442190275970155",
 126        "0."
 127        "41997434161402606939449673904170144491718672823077095471331144024458989"
 128        "95240483056156940088623187260",
 129        "-0."
 130        "63970000844922450018849176930384395321921136306079914494299856318702069"
 131        "34885434644440069533372017992",
 132        "0."
 133        "62162668077129626310653042872222339967572411755445418563968706335816206"
 134        "22188951465548376863495698762",
 135        "0."
 136        "66509104475050167773507148092106234992757132833203125448814929383096463"
 137        "47626843278089998045994094537",
 138        "-5."
 139        "55689355847371979760458290231697200987383372116293456019531342394708989"
 140        "7942786231796317250984197038"}};
 141   const T cx = 1;
 142   constexpr std::size_t m = 5;
 143   auto x = make_fvar<T, m>(cx);
 144   auto t = tanh(x);
 145   for (auto i : boost::irange(tanh_derivatives.size())) {
 146     BOOST_TEST_WARN(isNearZero(t.derivative(i) -
 147                                boost::lexical_cast<T>(tanh_derivatives[i])));
 148   }
 149 }
 150 #endif
 151
 152 BOOST_AUTO_TEST_CASE_TEMPLATE(tan_test, T, bin_float_types) {
 153   BOOST_MATH_STD_USING
 154   const T eps = 800 * boost::math::tools::epsilon<T>(); // percent
 155   const T cx = boost::math::constants::third_pi<T>();
 156   const T root_three = boost::math::constants::root_three<T>();
 157   constexpr unsigned m = 5;
 158   const auto x = make_fvar<T, m>(cx);
 159   auto y = tan(x);
 160   BOOST_CHECK_CLOSE(y.derivative(0u), root_three, eps);
 161   BOOST_CHECK_CLOSE(y.derivative(1u), T(4), eps);
 162   BOOST_CHECK_CLOSE(y.derivative(2u), T(8) * root_three, eps);
 163   BOOST_CHECK_CLOSE(y.derivative(3u), T(80), eps);
 164   BOOST_CHECK_CLOSE(y.derivative(4u), T(352) * root_three, eps);
 165   BOOST_CHECK_CLOSE(y.derivative(5u), T(5824), eps);
 166 }
 167
 168 BOOST_AUTO_TEST_CASE_TEMPLATE(fmod_test, T, bin_float_types) {
 169   BOOST_MATH_STD_USING
 170   constexpr unsigned m = 3;
 171   const T cx = 3.25;
 172   const T cy = 0.5;
 173   auto x = make_fvar<T, m>(cx);
 174   auto y = fmod(x, autodiff_fvar<T, m>(cy));
 175   BOOST_CHECK_EQUAL(y.derivative(0u), T(0.25));
 176   BOOST_CHECK_EQUAL(y.derivative(1u), T(1));
 177   BOOST_CHECK_EQUAL(y.derivative(2u), T(0));
 178   BOOST_CHECK_EQUAL(y.derivative(3u), T(0));
 179 }
 180
 181 BOOST_AUTO_TEST_CASE_TEMPLATE(round_and_trunc, T, all_float_types) {
 182   BOOST_MATH_STD_USING
 183   constexpr unsigned m = 3;
 184   const T cx = 3.25;
 185   auto x = make_fvar<T, m>(cx);
 186   auto y = round(x);
 187   BOOST_CHECK_EQUAL(y.derivative(0u), round(cx));
 188   BOOST_CHECK_EQUAL(y.derivative(1u), T(0));
 189   BOOST_CHECK_EQUAL(y.derivative(2u), T(0));
 190   BOOST_CHECK_EQUAL(y.derivative(3u), T(0));
 191   y = trunc(x);
 192   BOOST_CHECK_EQUAL(y.derivative(0u), trunc(cx));
 193   BOOST_CHECK_EQUAL(y.derivative(1u), T(0));
 194   BOOST_CHECK_EQUAL(y.derivative(2u), T(0));
 195   BOOST_CHECK_EQUAL(y.derivative(3u), T(0));
 196 }
 197
 198 BOOST_AUTO_TEST_CASE_TEMPLATE(iround_and_itrunc, T, all_float_types) {
 199   BOOST_MATH_STD_USING
 200   using namespace boost::math;
 201   constexpr unsigned m = 3;
 202   const T cx = 3.25;
 203   auto x = make_fvar<T, m>(cx);
 204   int y = iround(x);
 205   BOOST_CHECK_EQUAL(y, iround(cx));
 206   y = itrunc(x);
 207   BOOST_CHECK_EQUAL(y, itrunc(cx));
 208 }
 209
 210 BOOST_AUTO_TEST_CASE_TEMPLATE(lambert_w0_test, T, all_float_types) {
 211   const T eps = 1000 * boost::math::tools::epsilon<T>(); // percent
 212   constexpr unsigned m = 10;
 213   const T cx = 3;
 214   // Mathematica: N[Table[D[ProductLog[x], {x, n}], {n, 0, 10}] /. x -> 3, 52]
 215   constexpr std::array<const char *, m + 1> answers{
 216       {"1.049908894964039959988697070552897904589466943706341",
 217        "0.1707244807388472968312949774415522047470762509741737",
 218        "-0.04336545501146252734105411312976167858858970875797718",
 219        "0.02321456264324789334313200360870492961288748451791104",
 220        "-0.01909049778427783072663170526188353869136655225133878",
 221        "0.02122935002563637629500975949987796094687564718834156",
 222        "-0.02979093848448877259041971538394953658978044986784643",
 223        "0.05051290266216717699803334605370337985567016837482099",
 224        "-0.1004503154972645060971099914384090562800544486549660",
 225        "0.2292464437392250211967939182075930820454464472006425",
 226        "-0.5905839053125614593682763387470654123192290838719517"}};
 227   auto x = make_fvar<T, m>(cx);
 228   auto y = lambert_w0(x);
 229   for (auto i : boost::irange(m + 1)) {
 230     const T answer = boost::lexical_cast<T>(answers[i]);
 231     BOOST_CHECK_CLOSE(y.derivative(i), answer, eps);
 232   }
 233   // const T cx0 = -1 / boost::math::constants::e<T>();
 234   // auto edge = lambert_w0(make_fvar<T,m>(cx0));
 235   // std::cout << "edge = " << edge << std::endl;
 236   // edge = depth(1)(-1,inf,-inf,inf,-inf,inf,-inf,inf,-inf,inf,-inf)
 237   // edge = depth(1)(-1,inf,-inf,inf,-inf,inf,-inf,inf,-inf,inf,-inf)
 238   // edge =
 239   // depth(1)(-1,3.68935e+19,-9.23687e+57,4.62519e+96,-2.89497e+135,2.02945e+174,-1.52431e+213,1.19943e+252,-9.75959e+290,8.14489e+329,-6.93329e+368)
 240 }
 241
 242 BOOST_AUTO_TEST_CASE_TEMPLATE(digamma_test, T, all_float_types) {
 243   const T eps = 1000 * boost::math::tools::epsilon<T>(); // percent
 244   constexpr unsigned m = 10;
 245   const T cx = 3;
 246   // Mathematica: N[Table[PolyGamma[n, 3], {n, 0, 10}], 52]
 247   constexpr std::array<const char *, m + 1> answers{
 248     {"0.9227843350984671393934879099175975689578406640600764"
 249     ,"0.3949340668482264364724151666460251892189499012067984"
 250     ,"-0.1541138063191885707994763230228999815299725846809978"
 251     ,"0.1189394022668291490960221792470074166485057115123614"
 252     ,"-0.1362661234408782319527716749688200333699420680459075"
 253     ,"0.2061674381338967657421515749104633482180988039424274"
 254     ,"-0.3864797149844353246542358918536669119017636069718686"
 255     ,"0.8623752376394704685736020836084249051623848752441025"
 256     ,"-2.228398747634885327823655450854278779627928241914664"
 257     ,"6.536422382626807143525565747764891144367614117601463"
 258     ,"-21.4366066287129906188428320541054572790340793874298"}};
 259   auto x = make_fvar<T, m>(cx);
 260   auto y = digamma(x);
 261   for (auto i : boost::irange(m + 1)) {
 262     const T answer = boost::lexical_cast<T>(answers[i]);
 263     BOOST_CHECK_CLOSE(y.derivative(i), answer, eps);
 264   }
 265 }
 266
 267 BOOST_AUTO_TEST_CASE_TEMPLATE(lgamma_test, T, all_float_types) {
 268   const T eps = 1000 * boost::math::tools::epsilon<T>(); // percent
 269   constexpr unsigned m = 10;
 270   const T cx = 3;
 271   // Mathematica: N[Table[D[LogGamma[x],{x,n}] /. x->3, {n, 0, 10}], 52]
 272   constexpr std::array<const char *, m + 1> answers{
 273     {"0.6931471805599453094172321214581765680755001343602553"
 274     ,"0.9227843350984671393934879099175975689578406640600764"
 275     ,"0.3949340668482264364724151666460251892189499012067984"
 276     ,"-0.1541138063191885707994763230228999815299725846809978"
 277     ,"0.1189394022668291490960221792470074166485057115123614"
 278     ,"-0.1362661234408782319527716749688200333699420680459075"
 279     ,"0.2061674381338967657421515749104633482180988039424274"
 280     ,"-0.3864797149844353246542358918536669119017636069718686"
 281     ,"0.8623752376394704685736020836084249051623848752441025"
 282     ,"-2.228398747634885327823655450854278779627928241914664"
 283     ,"6.536422382626807143525565747764891144367614117601463"}};
 284   auto x = make_fvar<T, m>(cx);
 285   auto y = lgamma(x);
 286   for (auto i : boost::irange(m + 1)) {
 287     const T answer = boost::lexical_cast<T>(answers[i]);
 288     BOOST_CHECK_CLOSE(y.derivative(i), answer, eps);
 289   }
 290 }
 291
 292 BOOST_AUTO_TEST_CASE_TEMPLATE(tgamma_test, T, all_float_types) {
 293   const T eps = 1000 * boost::math::tools::epsilon<T>(); // percent
 294   constexpr unsigned m = 10;
 295   const T cx = 3;
 296   // Mathematica: N[Table[D[Gamma[x],{x,n}] /. x->3, {n, 0, 10}], 52]
 297   constexpr std::array<const char *, m + 1> answers{
 298     {"2.0"
 299     ,"1.845568670196934278786975819835195137915681328120153"
 300     ,"2.492929991902693057942510065508124245503778067273315"
 301     ,"3.449965013523673365279327178241708777509009968597547"
 302     ,"5.521798578098737512443417699412265532987916790978887"
 303     ,"8.845805593922864253981346455183370214190789096412155"
 304     ,"15.86959874461221647760760269963155031595848150772695"
 305     ,"27.46172054213435946038727460195592342721862288816812"
 306     ,"54.64250508485402729556251663145824730270508661240771"
 307     ,"96.08542140594972502872131946513104238293824803599579"
 308     ,"222.0936743583156040996433943128676567542497584689499"}};
 309   auto x = make_fvar<T, m>(cx);
 310   auto y = tgamma(x);
 311   for (auto i : boost::irange(m + 1)) {
 312     const T answer = boost::lexical_cast<T>(answers[i]);
 313     BOOST_CHECK_CLOSE(y.derivative(i), answer, eps);
 314   }
 315 }
 316
 317 BOOST_AUTO_TEST_CASE_TEMPLATE(tgamma2_test, T, all_float_types) {
 318   //const T eps = 5000 * boost::math::tools::epsilon<T>(); // ok for non-multiprecision
 319   const T eps = 500000 * boost::math::tools::epsilon<T>(); // percent
 320   constexpr unsigned m = 10;
 321   const T cx = -1.5;
 322   // Mathematica: N[Table[D[Gamma[x],{x,n}] /. x->-3/2, {n, 0, 10}], 52]
 323   constexpr std::array<const char *, m + 1> answers{
 324     {"2.363271801207354703064223311121526910396732608163183"
 325     ,"1.661750260668596505586468565464938761014714509096807"
 326     ,"23.33417984355457252918927856618603412638766668207679"
 327     ,"47.02130025080143055642555842335081335790754507072526"
 328     ,"1148.336052788822231948472800239024335856568111484074"
 329     ,"3831.214710988836934569706027888431190714054814541186"
 330     ,"138190.9008816865362698874238213771413807566436072179"
 331     ,"644956.0066517306036921195893233874126907491308967028"
 332     ,"3.096453684470713902448094810299787572782887316764214e7"
 333     ,"1.857893143852025058151037296906468662709947415219451e8"
 334     ,"1.114762466163487983067783853825224537320312784955935e10"}};
 335   auto x = make_fvar<T, m>(cx);
 336   auto y = tgamma(x);
 337   for (auto i : boost::irange(m + 1)) {
 338     const T answer = boost::lexical_cast<T>(answers[i]);
 339     BOOST_CHECK_CLOSE(y.derivative(i), answer, eps);
 340   }
 341 }
 342
 343 BOOST_AUTO_TEST_SUITE_END()