[ceph.git] / ceph / src / boost / libs / math / test / test_normal.cpp

// Copyright Paul A. Bristow 2010.
// Copyright John Maddock 2007.

// Use, modification and distribution are subject to the
// Boost Software License, Version 1.0.
// (See accompanying file LICENSE_1_0.txt
// or copy at http://www.boost.org/LICENSE_1_0.txt)

// test_normal.cpp

// http://en.wikipedia.org/wiki/Normal_distribution
// http://www.itl.nist.gov/div898/handbook/eda/section3/eda3661.htm
// Also:
// Weisstein, Eric W. "Normal Distribution."
// From MathWorld--A Wolfram Web Resource.
// http://mathworld.wolfram.com/NormalDistribution.html

#include <pch.hpp> // include directory /libs/math/src/tr1/ is needed.

#ifdef _MSC_VER
#  pragma warning (disable: 4127) // conditional expression is constant
// caused by using   if(std::numeric_limits<RealType>::has_infinity)
// and   if (std::numeric_limits<RealType>::has_quiet_NaN)
#endif

#include <boost/math/tools/test.hpp>
#include <boost/math/concepts/real_concept.hpp> // for real_concept
#define BOOST_TEST_MAIN
#include <boost/test/unit_test.hpp> // Boost.Test
#include <boost/test/tools/floating_point_comparison.hpp>

#include <boost/math/distributions/normal.hpp>
    using boost::math::normal_distribution;
#include <boost/math/tools/test.hpp>
#include "test_out_of_range.hpp"

#include <iostream>
#include <iomanip>
   using std::cout;
   using std::endl;
   using std::setprecision;
#include <limits>
  using std::numeric_limits;

template <class RealType>
RealType NaivePDF(RealType mean, RealType sd, RealType x)
{
   // Deliberately naive PDF calculator again which
   // we'll compare our pdf function.  However some
   // published values to compare against would be better....
   using namespace std;
   return exp(-(x-mean)*(x-mean)/(2*sd*sd))/(sd * sqrt(2*boost::math::constants::pi<RealType>()));
}

template <class RealType>
void check_normal(RealType mean, RealType sd, RealType x, RealType p, RealType q, RealType tol)
{
   BOOST_CHECK_CLOSE(
      ::boost::math::cdf(
         normal_distribution<RealType>(mean, sd),       // distribution.
         x),                                            // random variable.
         p,                                             // probability.
         tol);                                          // %tolerance.
   BOOST_CHECK_CLOSE(
      ::boost::math::cdf(
         complement(
            normal_distribution<RealType>(mean, sd),    // distribution.
            x)),                                        // random variable.
         q,                                             // probability complement.
         tol);                                          // %tolerance.
   BOOST_CHECK_CLOSE(
      ::boost::math::quantile(
         normal_distribution<RealType>(mean, sd),       // distribution.
         p),                                            // probability.
         x,                                             // random variable.
         tol);                                          // %tolerance.
   BOOST_CHECK_CLOSE(
      ::boost::math::quantile(
         complement(
            normal_distribution<RealType>(mean, sd),    // distribution.
            q)),                                        // probability complement.
         x,                                             // random variable.
         tol);                                          // %tolerance.
}

template <class RealType>
void test_spots(RealType)
{
   // Basic sanity checks
   RealType tolerance = 1e-2f; // 1e-4 (as %)
   // Some tests only pass at 1e-4 because values generated by
   // http://faculty.vassar.edu/lowry/VassarStats.html
   // give only 5 or 6 *fixed* places, so small values have fewer digits.

  // Check some bad parameters to the distribution,
#ifndef BOOST_NO_EXCEPTIONS
   BOOST_MATH_CHECK_THROW(boost::math::normal_distribution<RealType> nbad1(0, 0), std::domain_error); // zero sd
   BOOST_MATH_CHECK_THROW(boost::math::normal_distribution<RealType> nbad1(0, -1), std::domain_error); // negative sd
#else
   BOOST_MATH_CHECK_THROW(boost::math::normal_distribution<RealType>(0, 0), std::domain_error); // zero sd
   BOOST_MATH_CHECK_THROW(boost::math::normal_distribution<RealType>(0, -1), std::domain_error); // negative sd
#endif

  // Tests on extreme values of random variate x, if has std::numeric_limits infinity etc.
    normal_distribution<RealType> N01;
  if(std::numeric_limits<RealType>::has_infinity)
  {
    BOOST_CHECK_EQUAL(pdf(N01, +std::numeric_limits<RealType>::infinity()), 0); // x = + infinity, pdf = 0
    BOOST_CHECK_EQUAL(pdf(N01, -std::numeric_limits<RealType>::infinity()), 0); // x = - infinity, pdf = 0
    BOOST_CHECK_EQUAL(cdf(N01, +std::numeric_limits<RealType>::infinity()), 1); // x = + infinity, cdf = 1
    BOOST_CHECK_EQUAL(cdf(N01, -std::numeric_limits<RealType>::infinity()), 0); // x = - infinity, cdf = 0
    BOOST_CHECK_EQUAL(cdf(complement(N01, +std::numeric_limits<RealType>::infinity())), 0); // x = + infinity, c cdf = 0
    BOOST_CHECK_EQUAL(cdf(complement(N01, -std::numeric_limits<RealType>::infinity())), 1); // x = - infinity, c cdf = 1
#ifndef BOOST_NO_EXCEPTIONS
    BOOST_MATH_CHECK_THROW(boost::math::normal_distribution<RealType> nbad1(std::numeric_limits<RealType>::infinity(), static_cast<RealType>(1)), std::domain_error); // +infinite mean
     BOOST_MATH_CHECK_THROW(boost::math::normal_distribution<RealType> nbad1(-std::numeric_limits<RealType>::infinity(),  static_cast<RealType>(1)), std::domain_error); // -infinite mean
     BOOST_MATH_CHECK_THROW(boost::math::normal_distribution<RealType> nbad1(static_cast<RealType>(0), std::numeric_limits<RealType>::infinity()), std::domain_error); // infinite sd
#else
    BOOST_MATH_CHECK_THROW(boost::math::normal_distribution<RealType>(std::numeric_limits<RealType>::infinity(), static_cast<RealType>(1)), std::domain_error); // +infinite mean
     BOOST_MATH_CHECK_THROW(boost::math::normal_distribution<RealType>(-std::numeric_limits<RealType>::infinity(),  static_cast<RealType>(1)), std::domain_error); // -infinite mean
     BOOST_MATH_CHECK_THROW(boost::math::normal_distribution<RealType>(static_cast<RealType>(0), std::numeric_limits<RealType>::infinity()), std::domain_error); // infinite sd
#endif
  }

  if (std::numeric_limits<RealType>::has_quiet_NaN)
  {
    // No longer allow x to be NaN, then these tests should throw.
    BOOST_MATH_CHECK_THROW(pdf(N01, +std::numeric_limits<RealType>::quiet_NaN()), std::domain_error); // x = NaN
    BOOST_MATH_CHECK_THROW(cdf(N01, +std::numeric_limits<RealType>::quiet_NaN()), std::domain_error); // x = NaN
    BOOST_MATH_CHECK_THROW(cdf(complement(N01, +std::numeric_limits<RealType>::quiet_NaN())), std::domain_error); // x = + infinity
    BOOST_MATH_CHECK_THROW(quantile(N01, +std::numeric_limits<RealType>::quiet_NaN()), std::domain_error); // p = + infinity
    BOOST_MATH_CHECK_THROW(quantile(complement(N01, +std::numeric_limits<RealType>::quiet_NaN())), std::domain_error); // p = + infinity
  }

   cout << "Tolerance for type " << typeid(RealType).name()  << " is " << tolerance << " %" << endl;

   check_normal(
      static_cast<RealType>(5),
      static_cast<RealType>(2),
      static_cast<RealType>(4.8),
      static_cast<RealType>(0.46017),
      static_cast<RealType>(1 - 0.46017),
      tolerance);

   check_normal(
      static_cast<RealType>(5),
      static_cast<RealType>(2),
      static_cast<RealType>(5.2),
      static_cast<RealType>(1 - 0.46017),
      static_cast<RealType>(0.46017),
      tolerance);

   check_normal(
      static_cast<RealType>(5),
      static_cast<RealType>(2),
      static_cast<RealType>(2.2),
      static_cast<RealType>(0.08076),
      static_cast<RealType>(1 - 0.08076),
      tolerance);

   check_normal(
      static_cast<RealType>(5),
      static_cast<RealType>(2),
      static_cast<RealType>(7.8),
      static_cast<RealType>(1 - 0.08076),
      static_cast<RealType>(0.08076),
      tolerance);

   check_normal(
      static_cast<RealType>(-3),
      static_cast<RealType>(5),
      static_cast<RealType>(-4.5),
      static_cast<RealType>(0.38209),
      static_cast<RealType>(1 - 0.38209),
      tolerance);

   check_normal(
      static_cast<RealType>(-3),
      static_cast<RealType>(5),
      static_cast<RealType>(-1.5),
      static_cast<RealType>(1 - 0.38209),
      static_cast<RealType>(0.38209),
      tolerance);

   check_normal(
      static_cast<RealType>(-3),
      static_cast<RealType>(5),
      static_cast<RealType>(-8.5),
      static_cast<RealType>(0.13567),
      static_cast<RealType>(1 - 0.13567),
      tolerance);

   check_normal(
      static_cast<RealType>(-3),
      static_cast<RealType>(5),
      static_cast<RealType>(2.5),
      static_cast<RealType>(1 - 0.13567),
      static_cast<RealType>(0.13567),
      tolerance);

   //
   // Tests for PDF: we know that the peak value is at 1/sqrt(2*pi)
   //
   tolerance = boost::math::tools::epsilon<RealType>() * 5 * 100; // 5 eps as a percentage
   BOOST_CHECK_CLOSE(
      pdf(normal_distribution<RealType>(), static_cast<RealType>(0)),
      static_cast<RealType>(0.3989422804014326779399460599343818684759L), // 1/sqrt(2*pi)
      tolerance);
   BOOST_CHECK_CLOSE(
      pdf(normal_distribution<RealType>(3), static_cast<RealType>(3)),
      static_cast<RealType>(0.3989422804014326779399460599343818684759L),
      tolerance);
   BOOST_CHECK_CLOSE(
      pdf(normal_distribution<RealType>(3, 5), static_cast<RealType>(3)),
      static_cast<RealType>(0.3989422804014326779399460599343818684759L / 5),
      tolerance);

   //
   // Spot checks for mean = -5, sd = 6:
   //
   for(RealType x = -15; x < 5; x += 0.125)
   {
      BOOST_CHECK_CLOSE(
         pdf(normal_distribution<RealType>(-5, 6), x),
         NaivePDF(RealType(-5), RealType(6), x),
         tolerance);
   }

    RealType tol2 = boost::math::tools::epsilon<RealType>() * 5;
    normal_distribution<RealType> dist(8, 3);
    RealType x = static_cast<RealType>(0.125);

    BOOST_MATH_STD_USING // ADL of std math lib names

    // mean:
    BOOST_CHECK_CLOSE(
       mean(dist)
       , static_cast<RealType>(8), tol2);
    // variance:
    BOOST_CHECK_CLOSE(
       variance(dist)
       , static_cast<RealType>(9), tol2);
    // std deviation:
    BOOST_CHECK_CLOSE(
       standard_deviation(dist)
       , static_cast<RealType>(3), tol2);
    // hazard:
    BOOST_CHECK_CLOSE(
       hazard(dist, x)
       , pdf(dist, x) / cdf(complement(dist, x)), tol2);
    // cumulative hazard:
    BOOST_CHECK_CLOSE(
       chf(dist, x)
       , -log(cdf(complement(dist, x))), tol2);
    // coefficient_of_variation:
    BOOST_CHECK_CLOSE(
       coefficient_of_variation(dist)
       , standard_deviation(dist) / mean(dist), tol2);
    // mode:
    BOOST_CHECK_CLOSE(
       mode(dist)
       , static_cast<RealType>(8), tol2);

    BOOST_CHECK_CLOSE(
       median(dist)
       , static_cast<RealType>(8), tol2);

    // skewness:
    BOOST_CHECK_CLOSE(
       skewness(dist)
       , static_cast<RealType>(0), tol2);
    // kertosis:
    BOOST_CHECK_CLOSE(
       kurtosis(dist)
       , static_cast<RealType>(3), tol2);
    // kertosis excess:
    BOOST_CHECK_CLOSE(
       kurtosis_excess(dist)
       , static_cast<RealType>(0), tol2);

    normal_distribution<RealType> norm01(0, 1); // Test default (0, 1)
    BOOST_CHECK_CLOSE(
       mean(norm01),
       static_cast<RealType>(0), 0); // Mean == zero

    normal_distribution<RealType> defsd_norm01(0); // Test default (0, sd = 1)
    BOOST_CHECK_CLOSE(
       mean(defsd_norm01),
       static_cast<RealType>(0), 0); // Mean == zero

    normal_distribution<RealType> def_norm01; // Test default (0, sd = 1)
    BOOST_CHECK_CLOSE(
       mean(def_norm01),
       static_cast<RealType>(0), 0); // Mean == zero

    BOOST_CHECK_CLOSE(
       standard_deviation(def_norm01),
       static_cast<RealType>(1), 0); // Mean == zero

    // Error tests:
    check_out_of_range<boost::math::normal_distribution<RealType> >(0, 1); // (All) valid constructor parameter values.
    
    BOOST_MATH_CHECK_THROW(pdf(normal_distribution<RealType>(0, 0), 0), std::domain_error);
    BOOST_MATH_CHECK_THROW(pdf(normal_distribution<RealType>(0, -1), 0), std::domain_error);
    BOOST_MATH_CHECK_THROW(quantile(normal_distribution<RealType>(0, 1), -1), std::domain_error);
    BOOST_MATH_CHECK_THROW(quantile(normal_distribution<RealType>(0, 1), 2), std::domain_error);
} // template <class RealType>void test_spots(RealType)

BOOST_AUTO_TEST_CASE( test_main )
{
    // Check that can generate normal distribution using the two convenience methods:
   boost::math::normal myf1(1., 2); // Using typedef
   normal_distribution<> myf2(1., 2); // Using default RealType double.
  boost::math::normal myn01; // Use default values.
  // Note NOT myn01() as the compiler will interpret as a function!

  // Check the synonyms, provided to allow generic use of find_location and find_scale.
  BOOST_CHECK_EQUAL(myn01.mean(), myn01.location());
  BOOST_CHECK_EQUAL(myn01.standard_deviation(), myn01.scale());

    // Basic sanity-check spot values.
   // (Parameter value, arbitrarily zero, only communicates the floating point type).
  test_spots(0.0F); // Test float. OK at decdigits = 0 tolerance = 0.0001 %
  test_spots(0.0); // Test double. OK at decdigits 7, tolerance = 1e07 %
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
  test_spots(0.0L); // Test long double.
#if !BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x0582))
  test_spots(boost::math::concepts::real_concept(0.)); // Test real concept.
#endif
#else
   std::cout << "<note>The long double tests have been disabled on this platform "
      "either because the long double overloads of the usual math functions are "
      "not available at all, or because they are too inaccurate for these tests "
      "to pass.</note>" << std::endl;
#endif

   
} // BOOST_AUTO_TEST_CASE( test_main )

/*

Output:

Autorun "i:\boost-06-05-03-1300\libs\math\test\Math_test\debug\test_normal.exe"
Running 1 test case...
Tolerance for type float is 0.01 %
Tolerance for type double is 0.01 %
Tolerance for type long double is 0.01 %
Tolerance for type class boost::math::concepts::real_concept is 0.01 %
*** No errors detected


------ Build started: Project: test_normal, Configuration: Release Win32 ------
  test_normal.cpp
  Generating code
  Finished generating code
  test_normal.vcxproj -> J:\Cpp\MathToolkit\test\Math_test\Release\test_normal.exe
  Running 1 test case...
  Tolerance for type float is 0.01 %
  Tolerance for type double is 0.01 %
  Tolerance for type long double is 0.01 %
  Tolerance for type class boost::math::concepts::real_concept is 0.01 %
  
  *** No errors detected
  Detected memory leaks!
  Dumping objects ->
  {2413} normal block at 0x00321190, 42 bytes long.
   Data: <class boost::mat> 63 6C 61 73 73 20 62 6F 6F 73 74 3A 3A 6D 61 74 
  {2412} normal block at 0x003231F0, 8 bytes long.
   Data: <  2  22 > 90 11 32 00 98 32 32 00 
  {1824} normal block at 0x00323180, 12 bytes long.
   Data: <long double > 6C 6F 6E 67 20 64 6F 75 62 6C 65 00 
  {1823} normal block at 0x00323298, 8 bytes long.
   Data: < 12 `22 > 80 31 32 00 60 32 32 00 
  {1227} normal block at 0x00323148, 7 bytes long.
   Data: <double > 64 6F 75 62 6C 65 00 
  {1226} normal block at 0x00323260, 8 bytes long.
   Data: <H12  02 > 48 31 32 00 A0 30 32 00 
  {633} normal block at 0x003230D8, 6 bytes long.
   Data: <float > 66 6C 6F 61 74 00 
  {632} normal block at 0x003230A0, 8 bytes long.
   Data: < 02     > D8 30 32 00 00 00 00 00 
  Object dump complete.
========== Build: 1 succeeded, 0 failed, 0 up-to-date, 0 skipped ==========


*/
Commit	Line	Data
7c673cae FG	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
92f5a8d4	30	#include <boost/test/tools/floating_point_comparison.hpp>
7c673cae FG	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)/(2sdsd))/(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