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