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

   1 // Copyright Paul Bristow 2006, 2007.
   2 // Copyright John Maddock 2006, 2007.
   3
   4 // Use, modification and distribution are subject to the
   5 // Boost Software License, Version 1.0.
   6 // (See accompanying file LICENSE_1_0.txt
   7 // or copy at http://www.boost.org/LICENSE_1_0.txt)
   8
   9 // test_triangular.cpp
  10
  11 #include <pch.hpp>
  12
  13 #ifdef _MSC_VER
  14 #  pragma warning(disable: 4127) // conditional expression is constant.
  15 #  pragma warning(disable: 4305) // truncation from 'long double' to 'float'
  16 #endif
  17
  18 #include <boost/math/concepts/real_concept.hpp> // for real_concept
  19 #define BOOST_TEST_MAIN
  20 #include <boost/test/unit_test.hpp> // Boost.Test
  21 #include <boost/test/floating_point_comparison.hpp>
  22
  23 #include <boost/math/distributions/triangular.hpp>
  24 using boost::math::triangular_distribution;
  25 #include <boost/math/tools/test.hpp>
  26 #include <boost/math/special_functions/fpclassify.hpp>
  27 #include "test_out_of_range.hpp"
  28
  29 #include <iostream>
  30 #include <iomanip>
  31 using std::cout;
  32 using std::endl;
  33 using std::scientific;
  34 using std::fixed;
  35 using std::left;
  36 using std::right;
  37 using std::setw;
  38 using std::setprecision;
  39 using std::showpos;
  40 #include <limits>
  41 using std::numeric_limits;
  42
  43 template <class RealType>
  44 void check_triangular(RealType lower, RealType mode, RealType upper, RealType x, RealType p, RealType q, RealType tol)
  45 {
  46   BOOST_CHECK_CLOSE_FRACTION(
  47     ::boost::math::cdf(
  48     triangular_distribution<RealType>(lower, mode, upper),   // distribution.
  49     x),  // random variable.
  50     p,    // probability.
  51     tol);   // tolerance.
  52   BOOST_CHECK_CLOSE_FRACTION(
  53     ::boost::math::cdf(
  54     complement(
  55     triangular_distribution<RealType>(lower, mode, upper), // distribution.
  56     x)),    // random variable.
  57     q,    // probability complement.
  58     tol);  // tolerance.
  59   BOOST_CHECK_CLOSE_FRACTION(
  60     ::boost::math::quantile(
  61     triangular_distribution<RealType>(lower,mode, upper),  // distribution.
  62     p),   // probability.
  63     x,  // random variable.
  64     tol);  // tolerance.
  65   BOOST_CHECK_CLOSE_FRACTION(
  66     ::boost::math::quantile(
  67     complement(
  68     triangular_distribution<RealType>(lower, mode, upper),  // distribution.
  69     q)),     // probability complement.
  70     x,                                             // random variable.
  71     tol);  // tolerance.
  72 } // void check_triangular
  73
  74 template <class RealType>
  75 void test_spots(RealType)
  76 {
  77   // Basic sanity checks:
  78   //
  79   // Some test values were generated for the triangular distribution
  80   // using the online calculator at
  81   // http://espse.ed.psu.edu/edpsych/faculty/rhale/hale/507Mat/statlets/free/pdist.htm
  82   //
  83   // Tolerance is just over 5 epsilon expressed as a fraction:
  84   RealType tolerance = boost::math::tools::epsilon<RealType>() * 5; // 5 eps as a fraction.
  85   RealType tol5eps = boost::math::tools::epsilon<RealType>() * 5; // 5 eps as a fraction.
  86
  87   cout << "Tolerance for type " << typeid(RealType).name()  << " is " << tolerance << "." << endl;
  88
  89   using namespace std; // for ADL of std::exp;
  90
  91   // Tests on construction
  92   // Default should be 0, 0, 1
  93   BOOST_CHECK_EQUAL(triangular_distribution<RealType>().lower(), -1);
  94   BOOST_CHECK_EQUAL(triangular_distribution<RealType>().mode(), 0);
  95   BOOST_CHECK_EQUAL(triangular_distribution<RealType>().upper(), 1);
  96   BOOST_CHECK_EQUAL(support(triangular_distribution<RealType>()).first, triangular_distribution<RealType>().lower());
  97   BOOST_CHECK_EQUAL(support(triangular_distribution<RealType>()).second, triangular_distribution<RealType>().upper());
  98
  99   if (std::numeric_limits<RealType>::has_quiet_NaN == true)
 100   {
 101   BOOST_MATH_CHECK_THROW( // duff parameter lower.
 102     triangular_distribution<RealType>(static_cast<RealType>(std::numeric_limits<RealType>::quiet_NaN()), 0, 0),
 103     std::domain_error);
 104
 105   BOOST_MATH_CHECK_THROW( // duff parameter mode.
 106     triangular_distribution<RealType>(0, static_cast<RealType>(std::numeric_limits<RealType>::quiet_NaN()), 0),
 107     std::domain_error);
 108
 109   BOOST_MATH_CHECK_THROW( // duff parameter upper.
 110     triangular_distribution<RealType>(0, 0, static_cast<RealType>(std::numeric_limits<RealType>::quiet_NaN())),
 111     std::domain_error);
 112   } // quiet_NaN tests.
 113
 114   BOOST_MATH_CHECK_THROW( // duff parameters upper < lower.
 115     triangular_distribution<RealType>(1, 0, -1),
 116     std::domain_error);
 117
 118   BOOST_MATH_CHECK_THROW( // duff parameters upper == lower.
 119     triangular_distribution<RealType>(0, 0, 0),
 120     std::domain_error);
 121   BOOST_MATH_CHECK_THROW( // duff parameters mode < lower.
 122     triangular_distribution<RealType>(0, -1, 1),
 123     std::domain_error);
 124
 125   BOOST_MATH_CHECK_THROW( // duff parameters mode > upper.
 126     triangular_distribution<RealType>(0, 2, 1),
 127     std::domain_error);
 128
 129   // Tests for PDF
 130   // // triangular_distribution<RealType>() default is (0, 0, 1), mode == lower.
 131   BOOST_CHECK_CLOSE_FRACTION( // x == lower == mode
 132     pdf(triangular_distribution<RealType>(0, 0, 1), static_cast<RealType>(0)),
 133     static_cast<RealType>(2),
 134     tolerance);
 135
 136   BOOST_CHECK_CLOSE_FRACTION( // x == upper
 137     pdf(triangular_distribution<RealType>(0, 0, 1), static_cast<RealType>(1)),
 138     static_cast<RealType>(0),
 139     tolerance);
 140
 141   BOOST_CHECK_CLOSE_FRACTION( // x > upper
 142     pdf(triangular_distribution<RealType>(0, 0, 1), static_cast<RealType>(-1)),
 143     static_cast<RealType>(0),
 144     tolerance);
 145   BOOST_CHECK_CLOSE_FRACTION( // x < lower
 146     pdf(triangular_distribution<RealType>(0, 0, 1), static_cast<RealType>(2)),
 147     static_cast<RealType>(0),
 148     tolerance);
 149
 150   BOOST_CHECK_CLOSE_FRACTION( // x < lower
 151     pdf(triangular_distribution<RealType>(0, 0, 1), static_cast<RealType>(2)),
 152     static_cast<RealType>(0),
 153     tolerance);
 154
 155   // triangular_distribution<RealType>() (0, 1, 1) mode == upper
 156   BOOST_CHECK_CLOSE_FRACTION( // x == lower
 157     pdf(triangular_distribution<RealType>(0, 1, 1), static_cast<RealType>(0)),
 158     static_cast<RealType>(0),
 159     tolerance);
 160
 161   BOOST_CHECK_CLOSE_FRACTION( // x == upper
 162     pdf(triangular_distribution<RealType>(0, 1, 1), static_cast<RealType>(1)),
 163     static_cast<RealType>(2),
 164     tolerance);
 165
 166   BOOST_CHECK_CLOSE_FRACTION( // x > upper
 167     pdf(triangular_distribution<RealType>(0, 1, 1), static_cast<RealType>(-1)),
 168     static_cast<RealType>(0),
 169     tolerance);
 170   BOOST_CHECK_CLOSE_FRACTION( // x < lower
 171     pdf(triangular_distribution<RealType>(0, 1, 1), static_cast<RealType>(2)),
 172     static_cast<RealType>(0),
 173     tolerance);
 174
 175   BOOST_CHECK_CLOSE_FRACTION( // x < middle so Wiki says special case pdf = 2 * x
 176     pdf(triangular_distribution<RealType>(0, 1, 1), static_cast<RealType>(0.25)),
 177     static_cast<RealType>(0.5),
 178     tolerance);
 179
 180   BOOST_CHECK_CLOSE_FRACTION( // x < middle so Wiki says special case cdf = x * x
 181     cdf(triangular_distribution<RealType>(0, 1, 1), static_cast<RealType>(0.25)),
 182     static_cast<RealType>(0.25 * 0.25),
 183     tolerance);
 184
 185   // triangular_distribution<RealType>() (0, 0.5, 1) mode == middle.
 186   BOOST_CHECK_CLOSE_FRACTION( // x == lower
 187     pdf(triangular_distribution<RealType>(0, 0.5, 1), static_cast<RealType>(0)),
 188     static_cast<RealType>(0),
 189     tolerance);
 190
 191   BOOST_CHECK_CLOSE_FRACTION( // x == upper
 192     pdf(triangular_distribution<RealType>(0, 0.5, 1), static_cast<RealType>(1)),
 193     static_cast<RealType>(0),
 194     tolerance);
 195
 196   BOOST_CHECK_CLOSE_FRACTION( // x > upper
 197     pdf(triangular_distribution<RealType>(0, 0.5, 1), static_cast<RealType>(-1)),
 198     static_cast<RealType>(0),
 199     tolerance);
 200   BOOST_CHECK_CLOSE_FRACTION( // x < lower
 201     pdf(triangular_distribution<RealType>(0, 0.5, 1), static_cast<RealType>(2)),
 202     static_cast<RealType>(0),
 203     tolerance);
 204
 205   BOOST_CHECK_CLOSE_FRACTION( // x == mode
 206     pdf(triangular_distribution<RealType>(0, 0.5, 1), static_cast<RealType>(0.5)),
 207     static_cast<RealType>(2),
 208     tolerance);
 209
 210   BOOST_CHECK_CLOSE_FRACTION( // x == half mode
 211     pdf(triangular_distribution<RealType>(0, 0.5, 1), static_cast<RealType>(0.25)),
 212     static_cast<RealType>(1),
 213     tolerance);
 214   BOOST_CHECK_CLOSE_FRACTION( // x == half mode
 215     pdf(triangular_distribution<RealType>(0, 0.5, 1), static_cast<RealType>(0.75)),
 216     static_cast<RealType>(1),
 217     tolerance);
 218
 219   if(std::numeric_limits<RealType>::has_infinity)
 220   { // BOOST_CHECK tests for infinity using std::numeric_limits<>::infinity()
 221     // Note that infinity is not implemented for real_concept, so these tests
 222     // are only done for types, like built-in float, double.. that have infinity.
 223     // Note that these assume that  BOOST_MATH_OVERFLOW_ERROR_POLICY is NOT throw_on_error.
 224     // #define BOOST_MATH_OVERFLOW_ERROR_POLICY == throw_on_error would give a throw here.
 225     // #define BOOST_MATH_DOMAIN_ERROR_POLICY == throw_on_error IS defined, so the throw path
 226     // of error handling is tested below with BOOST_MATH_CHECK_THROW tests.
 227
 228     BOOST_MATH_CHECK_THROW( // x == infinity NOT OK.
 229       pdf(triangular_distribution<RealType>(0, 0, 1), static_cast<RealType>(std::numeric_limits<RealType>::infinity())),
 230       std::domain_error);
 231
 232     BOOST_MATH_CHECK_THROW( // x == minus infinity not OK too.
 233       pdf(triangular_distribution<RealType>(0, 0, 1), static_cast<RealType>(-std::numeric_limits<RealType>::infinity())),
 234       std::domain_error);
 235   }
 236   if(std::numeric_limits<RealType>::has_quiet_NaN)
 237   { // BOOST_CHECK tests for NaN using std::numeric_limits<>::has_quiet_NaN() - should throw.
 238     BOOST_MATH_CHECK_THROW(
 239       pdf(triangular_distribution<RealType>(0, 0, 1), static_cast<RealType>(std::numeric_limits<RealType>::quiet_NaN())),
 240       std::domain_error);
 241     BOOST_MATH_CHECK_THROW(
 242       pdf(triangular_distribution<RealType>(0, 0, 1), static_cast<RealType>(-std::numeric_limits<RealType>::quiet_NaN())),
 243       std::domain_error);
 244   } // test for x = NaN using std::numeric_limits<>::quiet_NaN()
 245
 246   // cdf
 247   BOOST_CHECK_EQUAL( // x < lower
 248     cdf(triangular_distribution<RealType>(0, 1, 1), static_cast<RealType>(-1)),
 249     static_cast<RealType>(0) );
 250   BOOST_CHECK_CLOSE_FRACTION( // x == lower
 251     cdf(triangular_distribution<RealType>(0, 1, 1), static_cast<RealType>(0)),
 252     static_cast<RealType>(0),
 253     tolerance);
 254   BOOST_CHECK_CLOSE_FRACTION( // x == upper
 255     cdf(triangular_distribution<RealType>(0, 1, 1), static_cast<RealType>(1)),
 256     static_cast<RealType>(1),
 257     tolerance);
 258    BOOST_CHECK_EQUAL( // x > upper
 259     cdf(triangular_distribution<RealType>(0, 1, 1), static_cast<RealType>(2)),
 260     static_cast<RealType>(1));
 261
 262   BOOST_CHECK_CLOSE_FRACTION( // x == mode
 263     cdf(triangular_distribution<RealType>(-1, 0, 1), static_cast<RealType>(0)),
 264     //static_cast<RealType>((mode - lower) / (upper - lower)),
 265     static_cast<RealType>(0.5),    // (0 --1) / (1 -- 1) = 0.5
 266     tolerance);
 267   BOOST_CHECK_CLOSE_FRACTION(
 268     cdf(triangular_distribution<RealType>(0, 1, 1), static_cast<RealType>(0.9L)),
 269     static_cast<RealType>(0.81L),
 270     tolerance);
 271
 272   BOOST_CHECK_CLOSE_FRACTION(
 273     cdf(triangular_distribution<RealType>(-1, 0, 1), static_cast<RealType>(-1)),
 274     static_cast<RealType>(0),
 275     tolerance);
 276   BOOST_CHECK_CLOSE_FRACTION(
 277     cdf(triangular_distribution<RealType>(-1, 0, 1), static_cast<RealType>(-0.5L)),
 278     static_cast<RealType>(0.125L),
 279     tolerance);
 280   BOOST_CHECK_CLOSE_FRACTION(
 281     cdf(triangular_distribution<RealType>(-1, 0, 1), static_cast<RealType>(0)),
 282     static_cast<RealType>(0.5),
 283     tolerance);
 284   BOOST_CHECK_CLOSE_FRACTION(
 285     cdf(triangular_distribution<RealType>(-1, 0, 1), static_cast<RealType>(+0.5L)),
 286     static_cast<RealType>(0.875L),
 287     tolerance);
 288   BOOST_CHECK_CLOSE_FRACTION(
 289     cdf(triangular_distribution<RealType>(-1, 0, 1), static_cast<RealType>(1)),
 290     static_cast<RealType>(1),
 291     tolerance);
 292
 293    // cdf complement
 294   BOOST_CHECK_EQUAL( // x < lower
 295     cdf(complement(triangular_distribution<RealType>(0, 0, 1), static_cast<RealType>(-1))),
 296     static_cast<RealType>(1));
 297   BOOST_CHECK_EQUAL( // x == lower
 298     cdf(complement(triangular_distribution<RealType>(0, 0, 1), static_cast<RealType>(0))),
 299     static_cast<RealType>(1));
 300
 301   BOOST_CHECK_EQUAL( // x == mode
 302     cdf(complement(triangular_distribution<RealType>(-1, 0, 1), static_cast<RealType>(0))),
 303     static_cast<RealType>(0.5));
 304
 305   BOOST_CHECK_EQUAL( // x == mode
 306     cdf(complement(triangular_distribution<RealType>(0, 0, 1), static_cast<RealType>(0))),
 307     static_cast<RealType>(1));
 308   BOOST_CHECK_EQUAL( // x == mode
 309     cdf(complement(triangular_distribution<RealType>(0, 1, 1), static_cast<RealType>(1))),
 310     static_cast<RealType>(0));
 311
 312   BOOST_CHECK_EQUAL( // x > upper
 313     cdf(complement(triangular_distribution<RealType>(0, 0, 1), static_cast<RealType>(2))),
 314     static_cast<RealType>(0));
 315   BOOST_CHECK_EQUAL( // x == upper
 316     cdf(complement(triangular_distribution<RealType>(0, 0, 1), static_cast<RealType>(1))),
 317     static_cast<RealType>(0));
 318
 319   BOOST_CHECK_CLOSE_FRACTION( // x = -0.5
 320     cdf(complement(triangular_distribution<RealType>(-1, 0, 1), static_cast<RealType>(-0.5))),
 321     static_cast<RealType>(0.875L),
 322     tolerance);
 323
 324   BOOST_CHECK_CLOSE_FRACTION( // x = +0.5
 325     cdf(complement(triangular_distribution<RealType>(-1, 0, 1), static_cast<RealType>(0.5))),
 326     static_cast<RealType>(0.125),
 327     tolerance);
 328
 329   triangular_distribution<RealType> triang; // Using typedef == triangular_distribution<double> tristd;
 330   triangular_distribution<RealType> tristd(0, 0.5, 1); // 'Standard' triangular distribution.
 331
 332   BOOST_CHECK_CLOSE_FRACTION( // median of Standard triangular is sqrt(mode/2) if c > 1/2 else 1 - sqrt((1-c)/2)
 333     median(tristd),
 334     static_cast<RealType>(0.5),
 335     tolerance);
 336   triangular_distribution<RealType> tri011(0, 1, 1); // Using default RealType double.
 337   triangular_distribution<RealType> tri0q1(0, 0.25, 1); // mode is near bottom.
 338   triangular_distribution<RealType> tri0h1(0, 0.5, 1); // Equilateral triangle - mode is the middle.
 339   triangular_distribution<RealType> trim12(-1, -0.5, 2); // mode is negative.
 340
 341   BOOST_CHECK_CLOSE_FRACTION(cdf(tri0q1, 0.02L), static_cast<RealType>(0.0016L), tolerance);
 342   BOOST_CHECK_CLOSE_FRACTION(cdf(tri0q1, 0.5L), static_cast<RealType>(0.66666666666666666666666666666666666666666666667L), tolerance);
 343   BOOST_CHECK_CLOSE_FRACTION(cdf(tri0q1, 0.98L), static_cast<RealType>(0.9994666666666666666666666666666666666666666666L), tolerance);
 344
 345   // quantile
 346   BOOST_CHECK_CLOSE_FRACTION(quantile(tri0q1, static_cast<RealType>(0.0016L)), static_cast<RealType>(0.02L), tol5eps);
 347   BOOST_CHECK_CLOSE_FRACTION(quantile(tri0q1, static_cast<RealType>(0.66666666666666666666666666666666666666666666667L)), static_cast<RealType>(0.5), tol5eps);
 348   BOOST_CHECK_CLOSE_FRACTION(quantile(complement(tri0q1, static_cast<RealType>(0.3333333333333333333333333333333333333333333333333L))), static_cast<RealType>(0.5), tol5eps);
 349   BOOST_CHECK_CLOSE_FRACTION(quantile(tri0q1, static_cast<RealType>(0.999466666666666666666666666666666666666666666666666L)), static_cast<RealType>(98) / 100, 10 * tol5eps);
 350
 351   BOOST_CHECK_CLOSE_FRACTION(pdf(trim12, 0), static_cast<RealType>(0.533333333333333333333333333333333333333333333L), tol5eps);
 352   BOOST_CHECK_CLOSE_FRACTION(cdf(trim12, 0), static_cast<RealType>(0.466666666666666666666666666666666666666666667L), tol5eps);
 353   BOOST_CHECK_CLOSE_FRACTION(cdf(complement(trim12, 0)), static_cast<RealType>(1 - 0.466666666666666666666666666666666666666666667L), tol5eps);
 354
 355   BOOST_CHECK_CLOSE_FRACTION(quantile(complement(tri0q1, static_cast<RealType>(1 - 0.999466666666666666666666666666666666666666666666L))), static_cast<RealType>(0.98L), 10 * tol5eps);
 356   BOOST_CHECK_CLOSE_FRACTION(quantile(complement(tri0h1, static_cast<RealType>(1))), static_cast<RealType>(0), tol5eps);
 357   BOOST_CHECK_CLOSE_FRACTION(quantile(complement(tri0h1, static_cast<RealType>(0.5))), static_cast<RealType>(0.5), tol5eps); // OK
 358   BOOST_CHECK_CLOSE_FRACTION(quantile(complement(tri0h1, static_cast<RealType>(1 - 0.02L))), static_cast<RealType>(0.1L), tol5eps);
 359   BOOST_CHECK_CLOSE_FRACTION(quantile(complement(tri0h1, static_cast<RealType>(1 - 0.98L))), static_cast<RealType>(0.9L), tol5eps);
 360   BOOST_CHECK_CLOSE_FRACTION(quantile(complement(tri0h1, 0)), static_cast<RealType>(1), tol5eps);
 361
 362   RealType xs [] = {0, 0.01L, 0.02L, 0.05L, 0.1L, 0.2L, 0.3L, 0.4L, 0.5L, 0.6L, 0.7L, 0.8L, 0.9L, 0.95L, 0.98L, 0.99L, 1};
 363
 364   const triangular_distribution<RealType>& distr = triang;
 365   BOOST_CHECK_CLOSE_FRACTION(quantile(complement(distr, 1.)), static_cast<RealType>(-1), tol5eps);
 366   const triangular_distribution<RealType>* distp = &triang;
 367   BOOST_CHECK_CLOSE_FRACTION(quantile(complement(*distp, 1.)), static_cast<RealType>(-1), tol5eps);
 368
 369   const triangular_distribution<RealType>* dists [] = {&tristd, &tri011, &tri0q1, &tri0h1, &trim12};
 370   BOOST_CHECK_CLOSE_FRACTION(quantile(complement(*dists[1], 1.)), static_cast<RealType>(0), tol5eps);
 371
 372    for (int i = 0; i < 5; i++)
 373   {
 374     const triangular_distribution<RealType>* const dist = dists[i];
 375     // cout << "Distribution " << i << endl;
 376     BOOST_CHECK_CLOSE_FRACTION(quantile(*dists[i], 0.5L), quantile(complement(*dist, 0.5L)),  tol5eps);
 377     BOOST_CHECK_CLOSE_FRACTION(quantile(*dists[i], 0.98L), quantile(complement(*dist, 1.L - 0.98L)),tol5eps);
 378     BOOST_CHECK_CLOSE_FRACTION(quantile(*dists[i], 0.98L), quantile(complement(*dist, 1.L - 0.98L)),tol5eps);
 379   } // for i
 380
 381    // quantile complement
 382   for (int i = 0; i < 5; i++)
 383   {
 384     const triangular_distribution<RealType>* const dist = dists[i];
 385     //cout << "Distribution " << i << endl;
 386     BOOST_CHECK_EQUAL(quantile(complement(*dists[i], 1.)), quantile(*dists[i], 0.));
 387     for (unsigned j = 0; j < sizeof(xs) /sizeof(RealType); j++)
 388     {
 389       RealType x = xs[j];
 390       BOOST_CHECK_CLOSE_FRACTION(quantile(*dists[i], x), quantile(complement(*dist, 1 - x)),  tol5eps);
 391     } // for j
 392   } // for i
 393
 394
 395   check_triangular(
 396     static_cast<RealType>(0),       // lower
 397     static_cast<RealType>(0.5),     // mode
 398     static_cast<RealType>(1),       // upper
 399     static_cast<RealType>(0.5),     // x
 400     static_cast<RealType>(0.5),     // p
 401     static_cast<RealType>(1 - 0.5), // q
 402     tolerance);
 403
 404   // Some Not-standard triangular tests.
 405   check_triangular(
 406     static_cast<RealType>(-1),    // lower
 407     static_cast<RealType>(0),     // mode
 408     static_cast<RealType>(1),     // upper
 409     static_cast<RealType>(0),     // x
 410     static_cast<RealType>(0.5),   // p
 411     static_cast<RealType>(1 - 0.5), // q = 1 - p
 412     tolerance);
 413
 414   check_triangular(
 415     static_cast<RealType>(1),       // lower
 416     static_cast<RealType>(1),       // mode
 417     static_cast<RealType>(3),       // upper
 418     static_cast<RealType>(2),    // x
 419     static_cast<RealType>(0.75),     // p
 420     static_cast<RealType>(1 - 0.75), // q = 1 - p
 421     tolerance);
 422
 423   check_triangular(
 424     static_cast<RealType>(-1),    // lower
 425     static_cast<RealType>(1),       // mode
 426     static_cast<RealType>(2),     // upper
 427     static_cast<RealType>(1),     // x
 428     static_cast<RealType>(0.66666666666666666666666666666666666666666667L),   // p
 429     static_cast<RealType>(0.33333333333333333333333333333333333333333333L), // q = 1 - p
 430     tolerance);
 431   tolerance = (std::max)(
 432     boost::math::tools::epsilon<RealType>(),
 433     static_cast<RealType>(boost::math::tools::epsilon<double>())) * 10; // 10 eps as a fraction.
 434   cout << "Tolerance (as fraction) for type " << typeid(RealType).name()  << " is " << tolerance << "." << endl;
 435
 436     triangular_distribution<RealType> tridef; // (-1, 0, 1) // Default distribution.
 437     RealType x = static_cast<RealType>(0.5);
 438     using namespace std; // ADL of std names.
 439     // mean:
 440     BOOST_CHECK_CLOSE_FRACTION(
 441       mean(tridef), static_cast<RealType>(0), tolerance);
 442     // variance:
 443     BOOST_CHECK_CLOSE_FRACTION(
 444       variance(tridef), static_cast<RealType>(0.16666666666666666666666666666666666666666667L), tolerance);
 445     // was 0.0833333333333333333333333333333333333333333L
 446
 447     // std deviation:
 448     BOOST_CHECK_CLOSE_FRACTION(
 449       standard_deviation(tridef), sqrt(variance(tridef)), tolerance);
 450     // hazard:
 451     BOOST_CHECK_CLOSE_FRACTION(
 452       hazard(tridef, x), pdf(tridef, x) / cdf(complement(tridef, x)), tolerance);
 453     // cumulative hazard:
 454     BOOST_CHECK_CLOSE_FRACTION(
 455       chf(tridef, x), -log(cdf(complement(tridef, x))), tolerance);
 456     // coefficient_of_variation:
 457     if (mean(tridef) != 0)
 458     {
 459       BOOST_CHECK_CLOSE_FRACTION(
 460         coefficient_of_variation(tridef), standard_deviation(tridef) / mean(tridef), tolerance);
 461     }
 462     // mode:
 463     BOOST_CHECK_CLOSE_FRACTION(
 464       mode(tridef), static_cast<RealType>(0), tolerance);
 465     // skewness:
 466     BOOST_CHECK_CLOSE_FRACTION(
 467       median(tridef), static_cast<RealType>(0), tolerance);
 468     // https://reference.wolfram.com/language/ref/Skewness.html  skewness{-1, 0, +1} = 0
 469     // skewness[triangulardistribution{-1, 0, +1}] does not compute a result.
 470     // skewness[triangulardistribution{0, +1}] result == 0
 471     // skewness[normaldistribution{0,1}] result == 0
 472
 473     BOOST_CHECK_EQUAL(
 474       skewness(tridef), static_cast<RealType>(0));
 475     // kurtosis:
 476     BOOST_CHECK_CLOSE_FRACTION(
 477       kurtosis_excess(tridef), kurtosis(tridef) - static_cast<RealType>(3L), tolerance);
 478     // kurtosis excess = kurtosis - 3;
 479     BOOST_CHECK_CLOSE_FRACTION(
 480       kurtosis_excess(tridef), static_cast<RealType>(-0.6), tolerance); // Constant value of -3/5 for all distributions.
 481
 482   {
 483     triangular_distribution<RealType> tri01(0, 1, 1); //  Asymmetric 0, 1, 1 distribution.
 484     RealType x = static_cast<RealType>(0.5);
 485     using namespace std; // ADL of std names.
 486                          // mean:
 487     BOOST_CHECK_CLOSE_FRACTION(
 488       mean(tri01), static_cast<RealType>(0.66666666666666666666666666666666666666666666666667L), tolerance);
 489     // variance: N[variance[triangulardistribution{0, 1}, 1], 50]
 490     BOOST_CHECK_CLOSE_FRACTION(
 491       variance(tri01), static_cast<RealType>(0.055555555555555555555555555555555555555555555555556L), tolerance);
 492     // std deviation:
 493     BOOST_CHECK_CLOSE_FRACTION(
 494       standard_deviation(tri01), sqrt(variance(tri01)), tolerance);
 495     // hazard:
 496     BOOST_CHECK_CLOSE_FRACTION(
 497       hazard(tri01, x), pdf(tri01, x) / cdf(complement(tri01, x)), tolerance);
 498     // cumulative hazard:
 499     BOOST_CHECK_CLOSE_FRACTION(
 500       chf(tri01, x), -log(cdf(complement(tri01, x))), tolerance);
 501     // coefficient_of_variation:
 502     if (mean(tri01) != 0)
 503     {
 504       BOOST_CHECK_CLOSE_FRACTION(
 505         coefficient_of_variation(tri01), standard_deviation(tri01) / mean(tri01), tolerance);
 506     }
 507     // mode:
 508     BOOST_CHECK_CLOSE_FRACTION(
 509       mode(tri01), static_cast<RealType>(1), tolerance);
 510     // skewness:
 511     BOOST_CHECK_CLOSE_FRACTION(
 512       median(tri01), static_cast<RealType>(0.70710678118654752440084436210484903928483593768847L), tolerance);
 513
 514     // https://reference.wolfram.com/language/ref/Skewness.html
 515     // N[skewness[triangulardistribution{0, 1}, 1], 50]
 516     BOOST_CHECK_CLOSE_FRACTION(
 517       skewness(tri01), static_cast<RealType>(-0.56568542494923801952067548968387923142786875015078L), tolerance);
 518     // kurtosis:
 519     BOOST_CHECK_CLOSE_FRACTION(
 520       kurtosis_excess(tri01), kurtosis(tri01) - static_cast<RealType>(3L), tolerance);
 521     // kurtosis excess = kurtosis - 3;
 522     BOOST_CHECK_CLOSE_FRACTION(
 523       kurtosis_excess(tri01), static_cast<RealType>(-0.6), tolerance); // Constant value of -3/5 for all distributions.
 524   } // tri01 tests
 525
 526   if(std::numeric_limits<RealType>::has_infinity)
 527   { // BOOST_CHECK tests for infinity using std::numeric_limits<>::infinity()
 528     // Note that infinity is not implemented for real_concept, so these tests
 529     // are only done for types, like built-in float, double.. that have infinity.
 530     // Note that these assume that BOOST_MATH_OVERFLOW_ERROR_POLICY is NOT throw_on_error.
 531     // #define BOOST_MATH_OVERFLOW_ERROR_POLICY == throw_on_error would give a throw here.
 532     // #define BOOST_MATH_DOMAIN_ERROR_POLICY == throw_on_error IS defined, so the throw path
 533     // of error handling is tested below with BOOST_MATH_CHECK_THROW tests.
 534
 535     using boost::math::policies::policy;
 536     using boost::math::policies::domain_error;
 537     using boost::math::policies::ignore_error;
 538
 539     // Define a (bad?) policy to ignore domain errors ('bad' arguments):
 540     typedef policy<domain_error<ignore_error> > inf_policy; // domain error returns infinity.
 541     triangular_distribution<RealType, inf_policy> tridef_inf(-1, 0., 1);
 542     // But can't use BOOST_CHECK_EQUAL(?, quiet_NaN)
 543     using boost::math::isnan;
 544     BOOST_CHECK((isnan)(pdf(tridef_inf, std::numeric_limits<RealType>::infinity())));
 545   } // test for infinity using std::numeric_limits<>::infinity()
 546   else
 547   { // real_concept case, does has_infinfity == false, so can't check it throws.
 548     // cout << std::numeric_limits<RealType>::infinity() << ' '
 549     // << (boost::math::fpclassify)(std::numeric_limits<RealType>::infinity()) << endl;
 550     // value of std::numeric_limits<RealType>::infinity() is zero, so FPclassify is zero,
 551     // so (boost::math::isfinite)(std::numeric_limits<RealType>::infinity()) does not detect infinity.
 552     // so these tests would never throw.
 553     //BOOST_MATH_CHECK_THROW(pdf(tridef, std::numeric_limits<RealType>::infinity()),  std::domain_error);
 554     //BOOST_MATH_CHECK_THROW(pdf(tridef, std::numeric_limits<RealType>::quiet_NaN()),  std::domain_error);
 555     // BOOST_MATH_CHECK_THROW(pdf(tridef, boost::math::tools::max_value<RealType>() * 2),  std::domain_error); // Doesn't throw.
 556     BOOST_CHECK_EQUAL(pdf(tridef, boost::math::tools::max_value<RealType>()), 0);
 557   }
 558   // Special cases:
 559   BOOST_CHECK(pdf(tridef, -1) == 0);
 560   BOOST_CHECK(pdf(tridef, 1) == 0);
 561   BOOST_CHECK(cdf(tridef, 0) == 0.5);
 562   BOOST_CHECK(pdf(tridef, 1) == 0);
 563   BOOST_CHECK(cdf(tridef, 1) == 1);
 564   BOOST_CHECK(cdf(complement(tridef, -1)) == 1);
 565   BOOST_CHECK(cdf(complement(tridef, 1)) == 0);
 566   BOOST_CHECK(quantile(tridef, 1) == 1);
 567   BOOST_CHECK(quantile(complement(tridef, 1)) == -1);
 568
 569   BOOST_CHECK_EQUAL(support(trim12).first, trim12.lower());
 570   BOOST_CHECK_EQUAL(support(trim12).second, trim12.upper());
 571
 572   // Error checks:
 573   if(std::numeric_limits<RealType>::has_quiet_NaN)
 574   { // BOOST_CHECK tests for quiet_NaN (not for real_concept, for example - see notes above).
 575     BOOST_MATH_CHECK_THROW(triangular_distribution<RealType>(0, std::numeric_limits<RealType>::quiet_NaN()), std::domain_error);
 576     BOOST_MATH_CHECK_THROW(triangular_distribution<RealType>(0, -std::numeric_limits<RealType>::quiet_NaN()), std::domain_error);
 577   }
 578   BOOST_MATH_CHECK_THROW(triangular_distribution<RealType>(1, 0), std::domain_error); // lower > upper!
 579
 580   check_out_of_range<triangular_distribution<RealType> >(-1, 0, 1);
 581 } // template <class RealType>void test_spots(RealType)
 582
 583 BOOST_AUTO_TEST_CASE( test_main )
 584 {
 585   //  double toleps = std::numeric_limits<double>::epsilon(); // 5 eps as a fraction.
 586   double tol5eps = std::numeric_limits<double>::epsilon() * 5; // 5 eps as a fraction.
 587   // double tol50eps = std::numeric_limits<double>::epsilon() * 50; // 50 eps as a fraction.
 588   double tol500eps = std::numeric_limits<double>::epsilon() * 500; // 500 eps as a fraction.
 589
 590   // Check that can construct triangular distribution using the two convenience methods:
 591   using namespace boost::math;
 592   triangular triang; // Using typedef
 593   // == triangular_distribution<double> triang;
 594
 595   BOOST_CHECK_EQUAL(triang.lower(), -1); // Check default.
 596   BOOST_CHECK_EQUAL(triang.mode(), 0);
 597   BOOST_CHECK_EQUAL(triang.upper(), 1);
 598
 599   triangular tristd (0, 0.5, 1); // Using typedef
 600
 601   BOOST_CHECK_EQUAL(tristd.lower(), 0);
 602   BOOST_CHECK_EQUAL(tristd.mode(), 0.5);
 603   BOOST_CHECK_EQUAL(tristd.upper(), 1);
 604
 605   //cout << "X range from " << range(tristd).first << " to " << range(tristd).second << endl;
 606   //cout << "Supported from "<< support(tristd).first << ' ' << support(tristd).second << endl;
 607
 608   BOOST_CHECK_EQUAL(support(tristd).first, tristd.lower());
 609   BOOST_CHECK_EQUAL(support(tristd).second, tristd.upper());
 610
 611   triangular_distribution<> tri011(0, 1, 1); // Using default RealType double.
 612   // mode is upper
 613   BOOST_CHECK_EQUAL(tri011.lower(), 0); // Check defaults again.
 614   BOOST_CHECK_EQUAL(tri011.mode(), 1); // Check defaults again.
 615   BOOST_CHECK_EQUAL(tri011.upper(), 1);
 616   BOOST_CHECK_EQUAL(mode(tri011), 1);
 617
 618   BOOST_CHECK_EQUAL(pdf(tri011, 0), 0);
 619   BOOST_CHECK_EQUAL(pdf(tri011, 0.1), 0.2);
 620   BOOST_CHECK_EQUAL(pdf(tri011, 0.5), 1);
 621   BOOST_CHECK_EQUAL(pdf(tri011, 0.9), 1.8);
 622   BOOST_CHECK_EQUAL(pdf(tri011, 1), 2);
 623
 624   BOOST_CHECK_EQUAL(cdf(tri011, 0), 0);
 625   BOOST_CHECK_CLOSE_FRACTION(cdf(tri011, 0.1), 0.01, tol5eps);
 626   BOOST_CHECK_EQUAL(cdf(tri011, 0.5), 0.25);
 627   BOOST_CHECK_EQUAL(cdf(tri011, 0.9), 0.81);
 628   BOOST_CHECK_EQUAL(cdf(tri011, 1), 1);
 629   BOOST_CHECK_EQUAL(cdf(tri011, 9), 1);
 630   BOOST_CHECK_EQUAL(mean(tri011), 0.666666666666666666666666666666666666666666666666667);
 631   BOOST_CHECK_EQUAL(variance(tri011), 1./18.);
 632
 633   triangular tri0h1(0, 0.5, 1); // Equilateral triangle - mode is the middle.
 634   BOOST_CHECK_EQUAL(tri0h1.lower(), 0);
 635   BOOST_CHECK_EQUAL(tri0h1.mode(), 0.5);
 636   BOOST_CHECK_EQUAL(tri0h1.upper(), 1);
 637   BOOST_CHECK_EQUAL(mean(tri0h1), 0.5);
 638   BOOST_CHECK_EQUAL(mode(tri0h1), 0.5);
 639   BOOST_CHECK_EQUAL(pdf(tri0h1, -1), 0);
 640   BOOST_CHECK_EQUAL(cdf(tri0h1, -1), 0);
 641   BOOST_CHECK_EQUAL(pdf(tri0h1, 1), 0);
 642   BOOST_CHECK_EQUAL(pdf(tri0h1, 999), 0);
 643   BOOST_CHECK_EQUAL(cdf(tri0h1, 999), 1);
 644   BOOST_CHECK_EQUAL(cdf(tri0h1, 1), 1);
 645   BOOST_CHECK_CLOSE_FRACTION(cdf(tri0h1, 0.1), 0.02, tol5eps);
 646   BOOST_CHECK_EQUAL(cdf(tri0h1, 0.5), 0.5);
 647   BOOST_CHECK_CLOSE_FRACTION(cdf(tri0h1, 0.9), 0.98, tol5eps);
 648
 649   BOOST_CHECK_CLOSE_FRACTION(quantile(tri0h1, 0.), 0., tol5eps);
 650   BOOST_CHECK_CLOSE_FRACTION(quantile(tri0h1, 0.02), 0.1, tol5eps);
 651   BOOST_CHECK_CLOSE_FRACTION(quantile(tri0h1, 0.5), 0.5, tol5eps);
 652   BOOST_CHECK_CLOSE_FRACTION(quantile(tri0h1, 0.98), 0.9, tol5eps);
 653   BOOST_CHECK_CLOSE_FRACTION(quantile(tri0h1, 1.), 1., tol5eps);
 654
 655   triangular tri0q1(0, 0.25, 1); // mode is near bottom.
 656   BOOST_CHECK_CLOSE_FRACTION(cdf(tri0q1, 0.02), 0.0016, tol5eps);
 657   BOOST_CHECK_CLOSE_FRACTION(cdf(tri0q1, 0.5), 0.66666666666666666666666666666666666666666666667, tol5eps);
 658   BOOST_CHECK_CLOSE_FRACTION(cdf(tri0q1, 0.98), 0.99946666666666661, tol5eps);
 659
 660   BOOST_CHECK_CLOSE_FRACTION(quantile(tri0q1, 0.0016), 0.02, tol5eps);
 661   BOOST_CHECK_CLOSE_FRACTION(quantile(tri0q1, 0.66666666666666666666666666666666666666666666667), 0.5, tol5eps);
 662   BOOST_CHECK_CLOSE_FRACTION(quantile(complement(tri0q1, 0.3333333333333333333333333333333333333333333333333)), 0.5, tol5eps);
 663   BOOST_CHECK_CLOSE_FRACTION(quantile(tri0q1, 0.99946666666666661), 0.98, 10 * tol5eps);
 664
 665   triangular trim12(-1, -0.5, 2); // mode is negative.
 666   BOOST_CHECK_CLOSE_FRACTION(pdf(trim12, 0), 0.533333333333333333333333333333333333333333333, tol5eps);
 667   BOOST_CHECK_CLOSE_FRACTION(cdf(trim12, 0), 0.466666666666666666666666666666666666666666667, tol5eps);
 668   BOOST_CHECK_CLOSE_FRACTION(cdf(complement(trim12, 0)), 1 - 0.466666666666666666666666666666666666666666667, tol5eps);
 669
 670   BOOST_CHECK_CLOSE_FRACTION(quantile(complement(tri0q1, 1 - 0.99946666666666661)), 0.98, 10 * tol5eps);
 671   BOOST_CHECK_CLOSE_FRACTION(quantile(complement(tri0h1, 1.)), 0., tol5eps);
 672   BOOST_CHECK_CLOSE_FRACTION(quantile(complement(tri0h1, 0.5)), 0.5, tol5eps); // OK
 673   BOOST_CHECK_CLOSE_FRACTION(quantile(complement(tri0h1, 1. - 0.02)), 0.1, tol5eps);
 674   BOOST_CHECK_CLOSE_FRACTION(quantile(complement(tri0h1, 1. - 0.98)), 0.9, tol5eps);
 675   BOOST_CHECK_CLOSE_FRACTION(quantile(complement(tri0h1, 0)), 1., tol5eps);
 676
 677   double xs [] = {0., 0.01, 0.02, 0.05, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 0.95, 0.98, 0.99, 1.};
 678
 679   const triangular_distribution<double>& distr = tristd;
 680   BOOST_CHECK_CLOSE_FRACTION(quantile(complement(distr, 1.)), 0., tol5eps);
 681   const triangular_distribution<double>* distp = &tristd;
 682   BOOST_CHECK_CLOSE_FRACTION(quantile(complement(*distp, 1.)), 0., tol5eps);
 683
 684   const triangular_distribution<double>* dists [] = {&tristd, &tri011, &tri0q1, &tri0h1, &trim12};
 685   BOOST_CHECK_CLOSE_FRACTION(quantile(complement(*dists[1], 1.)), 0., tol5eps);
 686
 687   for (int i = 0; i < 5; i++)
 688   {
 689     const triangular_distribution<double>* const dist = dists[i];
 690     cout << "Distribution " << i << endl;
 691     BOOST_CHECK_EQUAL(quantile(complement(*dists[i], 1.)), quantile(*dists[i], 0.));
 692     BOOST_CHECK_CLOSE_FRACTION(quantile(*dists[i], 0.5), quantile(complement(*dist, 0.5)),  tol5eps); // OK
 693     BOOST_CHECK_CLOSE_FRACTION(quantile(*dists[i], 0.98), quantile(complement(*dist, 1. - 0.98)),tol5eps);
 694     // cout << setprecision(17) <<  median(*dist) << endl;
 695   }
 696
 697   cout << showpos << setprecision(2) << endl;
 698
 699   //triangular_distribution<double>& dist = trim12;
 700   for (unsigned i = 0; i < sizeof(xs) /sizeof(double); i++)
 701   {
 702     double x = xs[i] * (trim12.upper() - trim12.lower()) + trim12.lower();
 703     double dx = cdf(trim12, x);
 704     double cx = cdf(complement(trim12, x));
 705     //cout << fixed << showpos << setprecision(3)
 706     //  << xs[i] << ", " << x << ",  " << pdf(trim12, x) << ",  " << dx << ",  " << cx << ",, " ;
 707
 708     BOOST_CHECK_CLOSE_FRACTION(cx, 1 - dx, tol500eps); // cx == 1 - dx
 709
 710     // << setprecision(2) << scientific << cr - x << ", " // difference x - quan(cdf)
 711     // << setprecision(3) << fixed
 712     // << quantile(trim12, dx) << ", "
 713     // << quantile(complement(trim12, 1 - dx)) << ", "
 714     // << quantile(complement(trim12, cx)) << ", "
 715     // << endl;
 716     BOOST_CHECK_CLOSE_FRACTION(quantile(trim12, dx), quantile(complement(trim12, 1 - dx)), tol500eps);
 717   }
 718   cout << endl;
 719   // Basic sanity-check spot values.
 720   // (Parameter value, arbitrarily zero, only communicates the floating point type).
 721   test_spots(0.0F); // Test float. OK at decdigits = 0 tolerance = 0.0001 %
 722   test_spots(0.0); // Test double. OK at decdigits 7, tolerance = 1e07 %
 723   #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
 724     test_spots(0.0L); // Test long double.
 725   #if !BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x0582))
 726     test_spots(boost::math::concepts::real_concept(0.)); // Test real concept.
 727   #endif
 728   #else
 729      std::cout << "<note>The long double tests have been disabled on this platform "
 730         "either because the long double overloads of the usual math functions are "
 731         "not available at all, or because they are too inaccurate for these tests "
 732         "to pass.</note>" << std::endl;
 733   #endif
 734
 735
 736 } // BOOST_AUTO_TEST_CASE( test_main )
 737
 738 /*
 739
 740 Output:
 741
 742 Autorun "i:\boost-06-05-03-1300\libs\math\test\Math_test\debug\test_triangular.exe"
 743 Running 1 test case...
 744 Distribution 0
 745 Distribution 1
 746 Distribution 2
 747 Distribution 3
 748 Distribution 4
 749 Tolerance for type float is 5.96046e-007.
 750 Tolerance for type double is 1.11022e-015.
 751 Tolerance for type long double is 1.11022e-015.
 752 Tolerance for type class boost::math::concepts::real_concept is 1.11022e-015.
 753 *** No errors detected
 754
 755
 756
 757 */
 758
 759
 760
 761