libs/math/test/test_normal.cpp

   1 // Copyright Paul A. Bristow 2010.
   2 // Copyright John Maddock 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_normal.cpp
  10
  11 // http://en.wikipedia.org/wiki/Normal_distribution
  12 // http://www.itl.nist.gov/div898/handbook/eda/section3/eda3661.htm
  13 // Also:
  14 // Weisstein, Eric W. "Normal Distribution."
  15 // From MathWorld--A Wolfram Web Resource.
  16 // http://mathworld.wolfram.com/NormalDistribution.html
  17
  18 #include <pch.hpp> // include directory /libs/math/src/tr1/ is needed.
  19
  20 #ifdef _MSC_VER
  21 #  pragma warning (disable: 4127) // conditional expression is constant
  22 // caused by using   if(std::numeric_limits<RealType>::has_infinity)
  23 // and   if (std::numeric_limits<RealType>::has_quiet_NaN)
  24 #endif
  25
  26 #include <boost/math/tools/test.hpp>
  27 #include <boost/math/concepts/real_concept.hpp> // for real_concept
  28 #define BOOST_TEST_MAIN
  29 #include <boost/test/unit_test.hpp> // Boost.Test
  30 #include <boost/test/tools/floating_point_comparison.hpp>
  31
  32 #include <boost/math/distributions/normal.hpp>
  33     using boost::math::normal_distribution;
  34 #include <boost/math/tools/test.hpp>
  35 #include "test_out_of_range.hpp"
  36
  37 #include <iostream>
  38 #include <iomanip>
  39    using std::cout;
  40    using std::endl;
  41    using std::setprecision;
  42 #include <limits>
  43   using std::numeric_limits;
  44
  45 template <class RealType>
  46 RealType NaivePDF(RealType mean, RealType sd, RealType x)
  47 {
  48    // Deliberately naive PDF calculator again which
  49    // we'll compare our pdf function.  However some
  50    // published values to compare against would be better....
  51    using namespace std;
  52    return exp(-(x-mean)*(x-mean)/(2*sd*sd))/(sd * sqrt(2*boost::math::constants::pi<RealType>()));
  53 }
  54
  55 template <class RealType>
  56 void check_normal(RealType mean, RealType sd, RealType x, RealType p, RealType q, RealType tol)
  57 {
  58    BOOST_CHECK_CLOSE(
  59       ::boost::math::cdf(
  60          normal_distribution<RealType>(mean, sd),       // distribution.
  61          x),                                            // random variable.
  62          p,                                             // probability.
  63          tol);                                          // %tolerance.
  64    BOOST_CHECK_CLOSE(
  65       ::boost::math::cdf(
  66          complement(
  67             normal_distribution<RealType>(mean, sd),    // distribution.
  68             x)),                                        // random variable.
  69          q,                                             // probability complement.
  70          tol);                                          // %tolerance.
  71    BOOST_CHECK_CLOSE(
  72       ::boost::math::quantile(
  73          normal_distribution<RealType>(mean, sd),       // distribution.
  74          p),                                            // probability.
  75          x,                                             // random variable.
  76          tol);                                          // %tolerance.
  77    BOOST_CHECK_CLOSE(
  78       ::boost::math::quantile(
  79          complement(
  80             normal_distribution<RealType>(mean, sd),    // distribution.
  81             q)),                                        // probability complement.
  82          x,                                             // random variable.
  83          tol);                                          // %tolerance.
  84 }
  85
  86 template <class RealType>
  87 void test_spots(RealType)
  88 {
  89    // Basic sanity checks
  90    RealType tolerance = 1e-2f; // 1e-4 (as %)
  91    // Some tests only pass at 1e-4 because values generated by
  92    // http://faculty.vassar.edu/lowry/VassarStats.html
  93    // give only 5 or 6 *fixed* places, so small values have fewer digits.
  94
  95   // Check some bad parameters to the distribution,
  96 #ifndef BOOST_NO_EXCEPTIONS
  97    BOOST_MATH_CHECK_THROW(boost::math::normal_distribution<RealType> nbad1(0, 0), std::domain_error); // zero sd
  98    BOOST_MATH_CHECK_THROW(boost::math::normal_distribution<RealType> nbad1(0, -1), std::domain_error); // negative sd
  99 #else
 100    BOOST_MATH_CHECK_THROW(boost::math::normal_distribution<RealType>(0, 0), std::domain_error); // zero sd
 101    BOOST_MATH_CHECK_THROW(boost::math::normal_distribution<RealType>(0, -1), std::domain_error); // negative sd
 102 #endif
 103
 104   // Tests on extreme values of random variate x, if has std::numeric_limits infinity etc.
 105     normal_distribution<RealType> N01;
 106   if(std::numeric_limits<RealType>::has_infinity)
 107   {
 108     BOOST_CHECK_EQUAL(pdf(N01, +std::numeric_limits<RealType>::infinity()), 0); // x = + infinity, pdf = 0
 109     BOOST_CHECK_EQUAL(pdf(N01, -std::numeric_limits<RealType>::infinity()), 0); // x = - infinity, pdf = 0
 110     BOOST_CHECK_EQUAL(cdf(N01, +std::numeric_limits<RealType>::infinity()), 1); // x = + infinity, cdf = 1
 111     BOOST_CHECK_EQUAL(cdf(N01, -std::numeric_limits<RealType>::infinity()), 0); // x = - infinity, cdf = 0
 112     BOOST_CHECK_EQUAL(cdf(complement(N01, +std::numeric_limits<RealType>::infinity())), 0); // x = + infinity, c cdf = 0
 113     BOOST_CHECK_EQUAL(cdf(complement(N01, -std::numeric_limits<RealType>::infinity())), 1); // x = - infinity, c cdf = 1
 114 #ifndef BOOST_NO_EXCEPTIONS
 115     BOOST_MATH_CHECK_THROW(boost::math::normal_distribution<RealType> nbad1(std::numeric_limits<RealType>::infinity(), static_cast<RealType>(1)), std::domain_error); // +infinite mean
 116      BOOST_MATH_CHECK_THROW(boost::math::normal_distribution<RealType> nbad1(-std::numeric_limits<RealType>::infinity(),  static_cast<RealType>(1)), std::domain_error); // -infinite mean
 117      BOOST_MATH_CHECK_THROW(boost::math::normal_distribution<RealType> nbad1(static_cast<RealType>(0), std::numeric_limits<RealType>::infinity()), std::domain_error); // infinite sd
 118 #else
 119     BOOST_MATH_CHECK_THROW(boost::math::normal_distribution<RealType>(std::numeric_limits<RealType>::infinity(), static_cast<RealType>(1)), std::domain_error); // +infinite mean
 120      BOOST_MATH_CHECK_THROW(boost::math::normal_distribution<RealType>(-std::numeric_limits<RealType>::infinity(),  static_cast<RealType>(1)), std::domain_error); // -infinite mean
 121      BOOST_MATH_CHECK_THROW(boost::math::normal_distribution<RealType>(static_cast<RealType>(0), std::numeric_limits<RealType>::infinity()), std::domain_error); // infinite sd
 122 #endif
 123   }
 124
 125   if (std::numeric_limits<RealType>::has_quiet_NaN)
 126   {
 127     // No longer allow x to be NaN, then these tests should throw.
 128     BOOST_MATH_CHECK_THROW(pdf(N01, +std::numeric_limits<RealType>::quiet_NaN()), std::domain_error); // x = NaN
 129     BOOST_MATH_CHECK_THROW(cdf(N01, +std::numeric_limits<RealType>::quiet_NaN()), std::domain_error); // x = NaN
 130     BOOST_MATH_CHECK_THROW(cdf(complement(N01, +std::numeric_limits<RealType>::quiet_NaN())), std::domain_error); // x = + infinity
 131     BOOST_MATH_CHECK_THROW(quantile(N01, +std::numeric_limits<RealType>::quiet_NaN()), std::domain_error); // p = + infinity
 132     BOOST_MATH_CHECK_THROW(quantile(complement(N01, +std::numeric_limits<RealType>::quiet_NaN())), std::domain_error); // p = + infinity
 133   }
 134
 135    cout << "Tolerance for type " << typeid(RealType).name()  << " is " << tolerance << " %" << endl;
 136
 137    check_normal(
 138       static_cast<RealType>(5),
 139       static_cast<RealType>(2),
 140       static_cast<RealType>(4.8),
 141       static_cast<RealType>(0.46017),
 142       static_cast<RealType>(1 - 0.46017),
 143       tolerance);
 144
 145    check_normal(
 146       static_cast<RealType>(5),
 147       static_cast<RealType>(2),
 148       static_cast<RealType>(5.2),
 149       static_cast<RealType>(1 - 0.46017),
 150       static_cast<RealType>(0.46017),
 151       tolerance);
 152
 153    check_normal(
 154       static_cast<RealType>(5),
 155       static_cast<RealType>(2),
 156       static_cast<RealType>(2.2),
 157       static_cast<RealType>(0.08076),
 158       static_cast<RealType>(1 - 0.08076),
 159       tolerance);
 160
 161    check_normal(
 162       static_cast<RealType>(5),
 163       static_cast<RealType>(2),
 164       static_cast<RealType>(7.8),
 165       static_cast<RealType>(1 - 0.08076),
 166       static_cast<RealType>(0.08076),
 167       tolerance);
 168
 169    check_normal(
 170       static_cast<RealType>(-3),
 171       static_cast<RealType>(5),
 172       static_cast<RealType>(-4.5),
 173       static_cast<RealType>(0.38209),
 174       static_cast<RealType>(1 - 0.38209),
 175       tolerance);
 176
 177    check_normal(
 178       static_cast<RealType>(-3),
 179       static_cast<RealType>(5),
 180       static_cast<RealType>(-1.5),
 181       static_cast<RealType>(1 - 0.38209),
 182       static_cast<RealType>(0.38209),
 183       tolerance);
 184
 185    check_normal(
 186       static_cast<RealType>(-3),
 187       static_cast<RealType>(5),
 188       static_cast<RealType>(-8.5),
 189       static_cast<RealType>(0.13567),
 190       static_cast<RealType>(1 - 0.13567),
 191       tolerance);
 192
 193    check_normal(
 194       static_cast<RealType>(-3),
 195       static_cast<RealType>(5),
 196       static_cast<RealType>(2.5),
 197       static_cast<RealType>(1 - 0.13567),
 198       static_cast<RealType>(0.13567),
 199       tolerance);
 200
 201    //
 202    // Tests for PDF: we know that the peak value is at 1/sqrt(2*pi)
 203    //
 204    tolerance = boost::math::tools::epsilon<RealType>() * 5 * 100; // 5 eps as a percentage
 205    BOOST_CHECK_CLOSE(
 206       pdf(normal_distribution<RealType>(), static_cast<RealType>(0)),
 207       static_cast<RealType>(0.3989422804014326779399460599343818684759L), // 1/sqrt(2*pi)
 208       tolerance);
 209    BOOST_CHECK_CLOSE(
 210       pdf(normal_distribution<RealType>(3), static_cast<RealType>(3)),
 211       static_cast<RealType>(0.3989422804014326779399460599343818684759L),
 212       tolerance);
 213    BOOST_CHECK_CLOSE(
 214       pdf(normal_distribution<RealType>(3, 5), static_cast<RealType>(3)),
 215       static_cast<RealType>(0.3989422804014326779399460599343818684759L / 5),
 216       tolerance);
 217
 218    //
 219    // Spot checks for mean = -5, sd = 6:
 220    //
 221    for(RealType x = -15; x < 5; x += 0.125)
 222    {
 223       BOOST_CHECK_CLOSE(
 224          pdf(normal_distribution<RealType>(-5, 6), x),
 225          NaivePDF(RealType(-5), RealType(6), x),
 226          tolerance);
 227    }
 228
 229     RealType tol2 = boost::math::tools::epsilon<RealType>() * 5;
 230     normal_distribution<RealType> dist(8, 3);
 231     RealType x = static_cast<RealType>(0.125);
 232
 233     BOOST_MATH_STD_USING // ADL of std math lib names
 234
 235     // mean:
 236     BOOST_CHECK_CLOSE(
 237        mean(dist)
 238        , static_cast<RealType>(8), tol2);
 239     // variance:
 240     BOOST_CHECK_CLOSE(
 241        variance(dist)
 242        , static_cast<RealType>(9), tol2);
 243     // std deviation:
 244     BOOST_CHECK_CLOSE(
 245        standard_deviation(dist)
 246        , static_cast<RealType>(3), tol2);
 247     // hazard:
 248     BOOST_CHECK_CLOSE(
 249        hazard(dist, x)
 250        , pdf(dist, x) / cdf(complement(dist, x)), tol2);
 251     // cumulative hazard:
 252     BOOST_CHECK_CLOSE(
 253        chf(dist, x)
 254        , -log(cdf(complement(dist, x))), tol2);
 255     // coefficient_of_variation:
 256     BOOST_CHECK_CLOSE(
 257        coefficient_of_variation(dist)
 258        , standard_deviation(dist) / mean(dist), tol2);
 259     // mode:
 260     BOOST_CHECK_CLOSE(
 261        mode(dist)
 262        , static_cast<RealType>(8), tol2);
 263
 264     BOOST_CHECK_CLOSE(
 265        median(dist)
 266        , static_cast<RealType>(8), tol2);
 267
 268     // skewness:
 269     BOOST_CHECK_CLOSE(
 270        skewness(dist)
 271        , static_cast<RealType>(0), tol2);
 272     // kertosis:
 273     BOOST_CHECK_CLOSE(
 274        kurtosis(dist)
 275        , static_cast<RealType>(3), tol2);
 276     // kertosis excess:
 277     BOOST_CHECK_CLOSE(
 278        kurtosis_excess(dist)
 279        , static_cast<RealType>(0), tol2);
 280
 281     normal_distribution<RealType> norm01(0, 1); // Test default (0, 1)
 282     BOOST_CHECK_CLOSE(
 283        mean(norm01),
 284        static_cast<RealType>(0), 0); // Mean == zero
 285
 286     normal_distribution<RealType> defsd_norm01(0); // Test default (0, sd = 1)
 287     BOOST_CHECK_CLOSE(
 288        mean(defsd_norm01),
 289        static_cast<RealType>(0), 0); // Mean == zero
 290
 291     normal_distribution<RealType> def_norm01; // Test default (0, sd = 1)
 292     BOOST_CHECK_CLOSE(
 293        mean(def_norm01),
 294        static_cast<RealType>(0), 0); // Mean == zero
 295
 296     BOOST_CHECK_CLOSE(
 297        standard_deviation(def_norm01),
 298        static_cast<RealType>(1), 0); // Mean == zero
 299
 300     // Error tests:
 301     check_out_of_range<boost::math::normal_distribution<RealType> >(0, 1); // (All) valid constructor parameter values.
 302
 303     BOOST_MATH_CHECK_THROW(pdf(normal_distribution<RealType>(0, 0), 0), std::domain_error);
 304     BOOST_MATH_CHECK_THROW(pdf(normal_distribution<RealType>(0, -1), 0), std::domain_error);
 305     BOOST_MATH_CHECK_THROW(quantile(normal_distribution<RealType>(0, 1), -1), std::domain_error);
 306     BOOST_MATH_CHECK_THROW(quantile(normal_distribution<RealType>(0, 1), 2), std::domain_error);
 307 } // template <class RealType>void test_spots(RealType)
 308
 309 BOOST_AUTO_TEST_CASE( test_main )
 310 {
 311     // Check that can generate normal distribution using the two convenience methods:
 312    boost::math::normal myf1(1., 2); // Using typedef
 313    normal_distribution<> myf2(1., 2); // Using default RealType double.
 314   boost::math::normal myn01; // Use default values.
 315   // Note NOT myn01() as the compiler will interpret as a function!
 316
 317   // Check the synonyms, provided to allow generic use of find_location and find_scale.
 318   BOOST_CHECK_EQUAL(myn01.mean(), myn01.location());
 319   BOOST_CHECK_EQUAL(myn01.standard_deviation(), myn01.scale());
 320
 321     // Basic sanity-check spot values.
 322    // (Parameter value, arbitrarily zero, only communicates the floating point type).
 323   test_spots(0.0F); // Test float. OK at decdigits = 0 tolerance = 0.0001 %
 324   test_spots(0.0); // Test double. OK at decdigits 7, tolerance = 1e07 %
 325 #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
 326   test_spots(0.0L); // Test long double.
 327 #if !BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x0582))
 328   test_spots(boost::math::concepts::real_concept(0.)); // Test real concept.
 329 #endif
 330 #else
 331    std::cout << "<note>The long double tests have been disabled on this platform "
 332       "either because the long double overloads of the usual math functions are "
 333       "not available at all, or because they are too inaccurate for these tests "
 334       "to pass.</note>" << std::endl;
 335 #endif
 336
 337
 338 } // BOOST_AUTO_TEST_CASE( test_main )
 339
 340 /*
 341
 342 Output:
 343
 344 Autorun "i:\boost-06-05-03-1300\libs\math\test\Math_test\debug\test_normal.exe"
 345 Running 1 test case...
 346 Tolerance for type float is 0.01 %
 347 Tolerance for type double is 0.01 %
 348 Tolerance for type long double is 0.01 %
 349 Tolerance for type class boost::math::concepts::real_concept is 0.01 %
 350 *** No errors detected
 351
 352
 353
 354
 355 ------ Build started: Project: test_normal, Configuration: Release Win32 ------
 356   test_normal.cpp
 357   Generating code
 358   Finished generating code
 359   test_normal.vcxproj -> J:\Cpp\MathToolkit\test\Math_test\Release\test_normal.exe
 360   Running 1 test case...
 361   Tolerance for type float is 0.01 %
 362   Tolerance for type double is 0.01 %
 363   Tolerance for type long double is 0.01 %
 364   Tolerance for type class boost::math::concepts::real_concept is 0.01 %
 365
 366   *** No errors detected
 367   Detected memory leaks!
 368   Dumping objects ->
 369   {2413} normal block at 0x00321190, 42 bytes long.
 370    Data: <class boost::mat> 63 6C 61 73 73 20 62 6F 6F 73 74 3A 3A 6D 61 74
 371   {2412} normal block at 0x003231F0, 8 bytes long.
 372    Data: <  2  22 > 90 11 32 00 98 32 32 00
 373   {1824} normal block at 0x00323180, 12 bytes long.
 374    Data: <long double > 6C 6F 6E 67 20 64 6F 75 62 6C 65 00
 375   {1823} normal block at 0x00323298, 8 bytes long.
 376    Data: < 12 `22 > 80 31 32 00 60 32 32 00
 377   {1227} normal block at 0x00323148, 7 bytes long.
 378    Data: <double > 64 6F 75 62 6C 65 00
 379   {1226} normal block at 0x00323260, 8 bytes long.
 380    Data: <H12  02 > 48 31 32 00 A0 30 32 00
 381   {633} normal block at 0x003230D8, 6 bytes long.
 382    Data: <float > 66 6C 6F 61 74 00
 383   {632} normal block at 0x003230A0, 8 bytes long.
 384    Data: < 02     > D8 30 32 00 00 00 00 00
 385   Object dump complete.
 386 ========== Build: 1 succeeded, 0 failed, 0 up-to-date, 0 skipped ==========
 387
 388
 389 */
 390
 391