WSJT-X/boost/libs/math/test/test_uniform.cpp

// Copyright Paul Bristow 2007.
// Copyright John Maddock 2006.

// 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_uniform.cpp

#include <pch.hpp>

#ifdef _MSC_VER
#  pragma warning(disable: 4127) // conditional expression is constant.
#  pragma warning(disable: 4100) // unreferenced formal parameter.
#endif

#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/floating_point_comparison.hpp>

#include <boost/math/distributions/uniform.hpp>
    using boost::math::uniform_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>
void check_uniform(RealType lower, RealType upper, RealType x, RealType p, RealType q, RealType tol)
{
   BOOST_CHECK_CLOSE_FRACTION(
      ::boost::math::cdf(
         uniform_distribution<RealType>(lower, upper),   // distribution.
         x),  // random variable.
         p,    // probability.
         tol);   // tolerance.
   BOOST_CHECK_CLOSE_FRACTION(
      ::boost::math::cdf(
         complement(
            uniform_distribution<RealType>(lower, upper), // distribution.
            x)),    // random variable.
         q,    // probability complement.
         tol);  // tolerance.
   BOOST_CHECK_CLOSE_FRACTION(
      ::boost::math::quantile(
         uniform_distribution<RealType>(lower, upper),  // distribution.
         p),   // probability.
         x,  // random variable.
         tol);  // tolerance.
   BOOST_CHECK_CLOSE_FRACTION(
      ::boost::math::quantile(
         complement(
            uniform_distribution<RealType>(lower, upper),  // distribution.
            q)),     // probability complement.
         x,                                             // random variable.
         tol);  // tolerance.
} // void check_uniform

template <class RealType>
void test_spots(RealType)
{
   // Basic sanity checks
   //
   // These test values were generated for the normal distribution
   // using the online calculator at 
   // http://espse.ed.psu.edu/edpsych/faculty/rhale/hale/507Mat/statlets/free/pdist.htm
   //
   // Tolerance is just over 5 decimal digits expressed as a fraction:
   // that's the limit of the test data.
   RealType tolerance = 2e-5f;  
   cout << "Tolerance for type " << typeid(RealType).name()  << " is " << tolerance << "." << endl;

   using std::exp;

   // Tests for PDF
   //
   BOOST_CHECK_CLOSE_FRACTION( // x == upper
      pdf(uniform_distribution<RealType>(0, 1), static_cast<RealType>(0)), 
      static_cast<RealType>(1), 
      tolerance);
   BOOST_CHECK_CLOSE_FRACTION( // x == lower
      pdf(uniform_distribution<RealType>(0, 1), static_cast<RealType>(1)), 
      static_cast<RealType>(1), 
      tolerance);
   BOOST_CHECK_CLOSE_FRACTION( // x > upper
      pdf(uniform_distribution<RealType>(0, 1), static_cast<RealType>(-1)), 
      static_cast<RealType>(0), 
      tolerance); 
   BOOST_CHECK_CLOSE_FRACTION( // x < lower
      pdf(uniform_distribution<RealType>(0, 1), static_cast<RealType>(2)), 
      static_cast<RealType>(0), 
      tolerance);

   if(std::numeric_limits<RealType>::has_infinity)
    { // BOOST_CHECK tests for infinity using std::numeric_limits<>::infinity()
      // Note that infinity is not implemented for real_concept, so these tests
      // are only done for types, like built-in float, double.. that have infinity.
    // Note that these assume that  BOOST_MATH_OVERFLOW_ERROR_POLICY is NOT throw_on_error.
    // #define BOOST_MATH_OVERFLOW_ERROR_POLICY == throw_on_error would give a throw here.
    // #define BOOST_MATH_DOMAIN_ERROR_POLICY == throw_on_error IS defined, so the throw path
    // of error handling is tested below with BOOST_MATH_CHECK_THROW tests.

     BOOST_MATH_CHECK_THROW( // x == infinity should NOT be OK.
       pdf(uniform_distribution<RealType>(0, 1), static_cast<RealType>(std::numeric_limits<RealType>::infinity())), 
       std::domain_error);

     BOOST_MATH_CHECK_THROW( // x == minus infinity should be OK too.
       pdf(uniform_distribution<RealType>(0, 1), static_cast<RealType>(-std::numeric_limits<RealType>::infinity())), 
       std::domain_error);
   }
   if(std::numeric_limits<RealType>::has_quiet_NaN)
   { // BOOST_CHECK tests for NaN using std::numeric_limits<>::has_quiet_NaN() - should throw.
     BOOST_MATH_CHECK_THROW(
       pdf(uniform_distribution<RealType>(0, 1), static_cast<RealType>(std::numeric_limits<RealType>::quiet_NaN())), 
       std::domain_error);
     BOOST_MATH_CHECK_THROW(
       pdf(uniform_distribution<RealType>(0, 1), static_cast<RealType>(-std::numeric_limits<RealType>::quiet_NaN())), 
       std::domain_error);
   } // test for x = NaN using std::numeric_limits<>::quiet_NaN()

   // cdf
   BOOST_CHECK_EQUAL( // x < lower
      cdf(uniform_distribution<RealType>(0, 1), static_cast<RealType>(-1)), 
      static_cast<RealType>(0) );
   BOOST_CHECK_CLOSE_FRACTION(
      cdf(uniform_distribution<RealType>(0, 1), static_cast<RealType>(0)), 
      static_cast<RealType>(0), 
      tolerance);
   BOOST_CHECK_CLOSE_FRACTION(
      cdf(uniform_distribution<RealType>(0, 1), static_cast<RealType>(0.5)), 
      static_cast<RealType>(0.5), 
      tolerance);
   BOOST_CHECK_CLOSE_FRACTION(
      cdf(uniform_distribution<RealType>(0, 1), static_cast<RealType>(0.1)), 
      static_cast<RealType>(0.1), 
      tolerance);
   BOOST_CHECK_CLOSE_FRACTION(
      cdf(uniform_distribution<RealType>(0, 1), static_cast<RealType>(0.9)), 
      static_cast<RealType>(0.9), 
      tolerance);
   BOOST_CHECK_EQUAL( // x > upper
      cdf(uniform_distribution<RealType>(0, 1), static_cast<RealType>(2)), 
      static_cast<RealType>(1));

  // cdf complement
   BOOST_CHECK_EQUAL( // x < lower
      cdf(complement(uniform_distribution<RealType>(0, 1), static_cast<RealType>(0))), 
      static_cast<RealType>(1));
   BOOST_CHECK_EQUAL( // x == 0
      cdf(complement(uniform_distribution<RealType>(0, 1), static_cast<RealType>(0))), 
      static_cast<RealType>(1));
   BOOST_CHECK_CLOSE_FRACTION( // x = 0.1
      cdf(complement(uniform_distribution<RealType>(0, 1), static_cast<RealType>(0.1))), 
      static_cast<RealType>(0.9), 
      tolerance);
   BOOST_CHECK_CLOSE_FRACTION( // x = 0.5
      cdf(complement(uniform_distribution<RealType>(0, 1), static_cast<RealType>(0.5))), 
      static_cast<RealType>(0.5), 
      tolerance);
   BOOST_CHECK_EQUAL( // x == 1
      cdf(complement(uniform_distribution<RealType>(0, 1), static_cast<RealType>(1))), 
      static_cast<RealType>(0));
   BOOST_CHECK_EQUAL( // x > upper
      cdf(complement(uniform_distribution<RealType>(0, 1), static_cast<RealType>(2))), 
      static_cast<RealType>(0));

   // quantile

   BOOST_CHECK_CLOSE_FRACTION(
      quantile(uniform_distribution<RealType>(0, 1), static_cast<RealType>(0.9)), 
      static_cast<RealType>(0.9), 
      tolerance);
   BOOST_CHECK_CLOSE_FRACTION(
      quantile(uniform_distribution<RealType>(0, 1), static_cast<RealType>(0.1)), 
      static_cast<RealType>(0.1), 
      tolerance);
   BOOST_CHECK_CLOSE_FRACTION(
      quantile(uniform_distribution<RealType>(0, 1), static_cast<RealType>(0.5)), 
      static_cast<RealType>(0.5), 
      tolerance);
   BOOST_CHECK_CLOSE_FRACTION(
      quantile(uniform_distribution<RealType>(0, 1), static_cast<RealType>(0)), 
      static_cast<RealType>(0), 
      tolerance);
   BOOST_CHECK_CLOSE_FRACTION(
      quantile(uniform_distribution<RealType>(0, 1), static_cast<RealType>(1)), 
      static_cast<RealType>(1), 
      tolerance);

   // quantile complement

   BOOST_CHECK_CLOSE_FRACTION(
      quantile(complement(uniform_distribution<RealType>(0, 1), static_cast<RealType>(0.1))), 
      static_cast<RealType>(0.9), 
      tolerance);
   BOOST_CHECK_CLOSE_FRACTION(
      quantile(complement(uniform_distribution<RealType>(0, 1), static_cast<RealType>(0.9))), 
      static_cast<RealType>(0.1), 
      tolerance);
   BOOST_CHECK_CLOSE_FRACTION(
      quantile(complement(uniform_distribution<RealType>(0, 1), static_cast<RealType>(0.5))), 
      static_cast<RealType>(0.5), 
      tolerance);
   BOOST_CHECK_CLOSE_FRACTION(
      quantile(complement(uniform_distribution<RealType>(0, 1), static_cast<RealType>(0))), 
      static_cast<RealType>(1), 
      tolerance);
   BOOST_CHECK_CLOSE_FRACTION(
      quantile(complement(uniform_distribution<RealType>(0, 1), static_cast<RealType>(1))), 
      static_cast<RealType>(0), 
      tolerance);

   // Some tests using a different location & scale, neight zero or unity.
   BOOST_CHECK_CLOSE_FRACTION( // x == mid
      pdf(uniform_distribution<RealType>(-1, 2), static_cast<RealType>(1)), 
      static_cast<RealType>(0.3333333333333333333333333333333333333333333333333333), 
      tolerance);

   BOOST_CHECK_CLOSE_FRACTION( // x == upper
      pdf(uniform_distribution<RealType>(-1, 2), static_cast<RealType>(+2)), 
      static_cast<RealType>(0.3333333333333333333333333333333333333333333333333333),  // 1 / (2 - -1) = 1/3
      tolerance);

   BOOST_CHECK_CLOSE_FRACTION( // x == lower
      cdf(uniform_distribution<RealType>(-1, 2), static_cast<RealType>(-1)), 
      static_cast<RealType>(0), 
      tolerance);
   BOOST_CHECK_CLOSE_FRACTION( // x == upper
      cdf(uniform_distribution<RealType>(-1, 2), static_cast<RealType>(0)), 
      static_cast<RealType>(0.3333333333333333333333333333333333333333333333333333), 
      tolerance);

   BOOST_CHECK_CLOSE_FRACTION( // x == upper
      cdf(uniform_distribution<RealType>(-1, 2), static_cast<RealType>(1)), 
      static_cast<RealType>(0.6666666666666666666666666666666666666666666666666667), 
      tolerance);

   BOOST_CHECK_CLOSE_FRACTION( // x == lower
      cdf(uniform_distribution<RealType>(-1, 2), static_cast<RealType>(2)), 
      static_cast<RealType>(1), 
      tolerance);

   BOOST_CHECK_CLOSE_FRACTION( // x == upper
      quantile(uniform_distribution<RealType>(-1, 2), static_cast<RealType>(0.6666666666666666666666666666666666666666666666666667)), 
      static_cast<RealType>(1),
      tolerance);

      check_uniform(
      static_cast<RealType>(0),       // lower
      static_cast<RealType>(1),       // upper
      static_cast<RealType>(0.5),     // x
      static_cast<RealType>(0.5),     // p
      static_cast<RealType>(1 - 0.5), // q
      tolerance);

      // Some Not-standard uniform tests.
      check_uniform(
      static_cast<RealType>(-1),    // lower
      static_cast<RealType>(1),     // upper
      static_cast<RealType>(0),     // x
      static_cast<RealType>(0.5),   // p
      static_cast<RealType>(1 - 0.5), // q = 1 - p
      tolerance);

      check_uniform(
      static_cast<RealType>(1),    // lower
      static_cast<RealType>(3),     // upper
      static_cast<RealType>(2),     // x
      static_cast<RealType>(0.5),   // p
      static_cast<RealType>(1 - 0.5), // q = 1 - p
      tolerance);

      check_uniform(
      static_cast<RealType>(-1),    // lower
      static_cast<RealType>(2),     // upper
      static_cast<RealType>(1),     // x
      static_cast<RealType>(0.66666666666666666666666666666666666666666667),   // p
      static_cast<RealType>(0.33333333333333333333333333333333333333333333), // q = 1 - p
      tolerance);
   tolerance = (std::max)(
      boost::math::tools::epsilon<RealType>(),
      static_cast<RealType>(boost::math::tools::epsilon<double>())) * 5; // 5 eps as a fraction.
    cout << "Tolerance (as fraction) for type " << typeid(RealType).name()  << " is " << tolerance << "." << endl;
   uniform_distribution<RealType> distu01(0, 1);
   RealType x = static_cast<RealType>(0.5);
   using namespace std; // ADL of std names.
   // mean:
   BOOST_CHECK_CLOSE_FRACTION(
      mean(distu01), static_cast<RealType>(0.5), tolerance);
   // variance:
   BOOST_CHECK_CLOSE_FRACTION(
      variance(distu01), static_cast<RealType>(0.0833333333333333333333333333333333333333333), tolerance);
   // std deviation:
   BOOST_CHECK_CLOSE_FRACTION(
    standard_deviation(distu01), sqrt(variance(distu01)), tolerance);
   // hazard:
   BOOST_CHECK_CLOSE_FRACTION(
    hazard(distu01, x), pdf(distu01, x) / cdf(complement(distu01, x)), tolerance);
   // cumulative hazard:
   BOOST_CHECK_CLOSE_FRACTION(
    chf(distu01, x), -log(cdf(complement(distu01, x))), tolerance);
   // coefficient_of_variation:
   BOOST_CHECK_CLOSE_FRACTION(
    coefficient_of_variation(distu01), standard_deviation(distu01) / mean(distu01), tolerance);
   // mode:
   BOOST_CHECK_CLOSE_FRACTION(
    mode(distu01), static_cast<RealType>(0), tolerance);
   BOOST_CHECK_CLOSE_FRACTION(
      median(distu01), static_cast<RealType>(0.5), tolerance);
   // skewness:
   BOOST_CHECK_EQUAL(
    skewness(distu01), static_cast<RealType>(0));
   // kertosis:
   BOOST_CHECK_CLOSE_FRACTION(
    kurtosis(distu01), kurtosis_excess(distu01) + static_cast<RealType>(3), tolerance);
   // kertosis excess:
   BOOST_CHECK_CLOSE_FRACTION(
    kurtosis_excess(distu01), static_cast<RealType>(-1.2), tolerance);

   if(std::numeric_limits<RealType>::has_infinity)
  { // BOOST_CHECK tests for infinity using std::numeric_limits<>::infinity()
    // Note that infinity is not implemented for real_concept, so these tests
    // are only done for types, like built-in float, double, long double, that have infinity.
    // Note that these assume that  BOOST_MATH_OVERFLOW_ERROR_POLICY is NOT throw_on_error.
    // #define BOOST_MATH_OVERFLOW_ERROR_POLICY == throw_on_error would give a throw here.
    // #define BOOST_MATH_DOMAIN_ERROR_POLICY == throw_on_error IS defined, so the throw path
    // of error handling is tested below with BOOST_MATH_CHECK_THROW tests.

    BOOST_MATH_CHECK_THROW(pdf(distu01, std::numeric_limits<RealType>::infinity()),  std::domain_error);
    BOOST_MATH_CHECK_THROW(pdf(distu01, -std::numeric_limits<RealType>::infinity()),  std::domain_error);
   } // test for infinity using std::numeric_limits<>::infinity()
   else
   { // real_concept case, does has_infinfity == false, so can't check it throws.
     // cout << std::numeric_limits<RealType>::infinity() << ' '
     // << (boost::math::fpclassify)(std::numeric_limits<RealType>::infinity()) << endl;
     // value of std::numeric_limits<RealType>::infinity() is zero, so FPclassify is zero,
     // so (boost::math::isfinite)(std::numeric_limits<RealType>::infinity()) does not detect infinity.
     // so these tests would never throw.
     //BOOST_MATH_CHECK_THROW(pdf(distu01, std::numeric_limits<RealType>::infinity()),  std::domain_error);
     //BOOST_MATH_CHECK_THROW(pdf(distu01, std::numeric_limits<RealType>::quiet_NaN()),  std::domain_error);
     // BOOST_MATH_CHECK_THROW(pdf(distu01, boost::math::tools::max_value<RealType>() * 2),  std::domain_error); // Doesn't throw.
     BOOST_CHECK_EQUAL(pdf(distu01, boost::math::tools::max_value<RealType>()), 0); 
   }
   // Special cases:
   BOOST_CHECK(pdf(distu01, 0) == 1);
   BOOST_CHECK(cdf(distu01, 0) == 0);
   BOOST_CHECK(pdf(distu01, 1) == 1);
   BOOST_CHECK(cdf(distu01, 1) == 1);
   BOOST_CHECK(cdf(complement(distu01, 0)) == 1);
   BOOST_CHECK(cdf(complement(distu01, 1)) == 0);
   BOOST_CHECK(quantile(distu01, 0) == 0);
   BOOST_CHECK(quantile(complement(distu01, 0)) == 1);
   BOOST_CHECK(quantile(distu01, 1) == 1);
   BOOST_CHECK(quantile(complement(distu01, 1)) == 0);

   // Error checks:
   if(std::numeric_limits<RealType>::has_quiet_NaN)
   { // BOOST_CHECK tests for constructing with quiet_NaN (not for real_concept, for example - see notes above).
     BOOST_MATH_CHECK_THROW(uniform_distribution<RealType>(0, std::numeric_limits<RealType>::quiet_NaN()), std::domain_error);
     BOOST_MATH_CHECK_THROW(uniform_distribution<RealType>(0, -std::numeric_limits<RealType>::quiet_NaN()), std::domain_error);
   }
   BOOST_MATH_CHECK_THROW(uniform_distribution<RealType>(1, 0), std::domain_error); // lower > upper!
   BOOST_MATH_CHECK_THROW(uniform_distribution<RealType>(1, 1), std::domain_error); // lower == upper!

   check_out_of_range<uniform_distribution<RealType> >(1, 5);
} // template <class RealType>void test_spots(RealType)

BOOST_AUTO_TEST_CASE( test_main )
{
  // Check that can construct uniform distribution using the two convenience methods:
  using namespace boost::math;
  uniform unistd; // Using typedef
  // == uniform_distribution<double> unistd;
  BOOST_CHECK_EQUAL(unistd.lower(), 0); // Check defaults.
  BOOST_CHECK_EQUAL(unistd.upper(), 1);
   uniform_distribution<> myu01(0, 1); // Using default RealType double.
  BOOST_CHECK_EQUAL(myu01.lower(), 0); // Check defaults again.
  BOOST_CHECK_EQUAL(myu01.upper(), 1);

  // Test on extreme values of random variate x, using just double because it has numeric_limit infinity etc..
  // No longer allow x to be + or - infinity, then these tests should throw.
  BOOST_MATH_CHECK_THROW(pdf(unistd, +std::numeric_limits<double>::infinity()), std::domain_error); // x = + infinity
  BOOST_MATH_CHECK_THROW(pdf(unistd, -std::numeric_limits<double>::infinity()), std::domain_error); // x = - infinity
  BOOST_MATH_CHECK_THROW(cdf(unistd, +std::numeric_limits<double>::infinity()), std::domain_error); // x = + infinity
  BOOST_MATH_CHECK_THROW(cdf(unistd, -std::numeric_limits<double>::infinity()), std::domain_error); // x = - infinity

  BOOST_CHECK_EQUAL(pdf(unistd, +(std::numeric_limits<double>::max)()), 0); // x = + max
  BOOST_CHECK_EQUAL(pdf(unistd, -(std::numeric_limits<double>::min)()), 0); // x = - min
  BOOST_CHECK_EQUAL(cdf(unistd, +(std::numeric_limits<double>::max)()), 1); // x = + max
  BOOST_CHECK_EQUAL(cdf(unistd, -(std::numeric_limits<double>::min)()), 0); // x = - min
#ifndef BOOST_NO_EXCEPTIONS
  BOOST_MATH_CHECK_THROW(uniform_distribution<> zinf(0, +std::numeric_limits<double>::infinity()), std::domain_error); // zero to infinity using default RealType double.
#else
  BOOST_MATH_CHECK_THROW(uniform_distribution<>(0, +std::numeric_limits<double>::infinity()), std::domain_error); // zero to infinity using default RealType double.
#endif
   uniform_distribution<> zmax(0, +(std::numeric_limits<double>::max)()); // zero to max using default RealType double.
  BOOST_CHECK_EQUAL(zmax.lower(), 0); // Check defaults again.
  BOOST_CHECK_EQUAL(zmax.upper(), +(std::numeric_limits<double>::max)());

  BOOST_CHECK_EQUAL(pdf(zmax, -1), 0); // pdf is 1/(0 - max) = almost zero for all x
  BOOST_CHECK_EQUAL(pdf(zmax, 0), (std::numeric_limits<double>::min)()/4); // x = 
  BOOST_CHECK_EQUAL(pdf(zmax, 1), (std::numeric_limits<double>::min)()/4); // x = 
  BOOST_MATH_CHECK_THROW(pdf(zmax, +std::numeric_limits<double>::infinity()), std::domain_error); // pdf is 1/(0 - infinity) = zero for all x
  BOOST_MATH_CHECK_THROW(pdf(zmax, -std::numeric_limits<double>::infinity()), std::domain_error); 
  BOOST_CHECK_EQUAL(pdf(zmax, +(std::numeric_limits<double>::max)()), (std::numeric_limits<double>::min)()/4); // x = 
  BOOST_CHECK_EQUAL(pdf(zmax, -(std::numeric_limits<double>::max)()), 0); // x = 
#ifndef BOOST_NO_EXCEPTIONS
  // Ensure NaN throws an exception.
  BOOST_MATH_CHECK_THROW(uniform_distribution<> zNaN(0, std::numeric_limits<double>::quiet_NaN()), std::domain_error);
  BOOST_MATH_CHECK_THROW(pdf(unistd, std::numeric_limits<double>::quiet_NaN()), std::domain_error);
#else
  BOOST_MATH_CHECK_THROW(uniform_distribution<>(0, std::numeric_limits<double>::quiet_NaN()), std::domain_error);
  BOOST_MATH_CHECK_THROW(pdf(unistd, std::numeric_limits<double>::quiet_NaN()), std::domain_error);
#endif
    // 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_uniform.exe"
Running 1 test case...
Tolerance for type float is 2e-005.
Tolerance (as fraction) for type float is 5.96046e-007.
Tolerance for type double is 2e-005.
Tolerance (as fraction) for type double is 1.11022e-015.
Tolerance for type long double is 2e-005.
Tolerance (as fraction) for type long double is 1.11022e-015.
Tolerance for type class boost::math::concepts::real_concept is 2e-005.
Tolerance (as fraction) for type class boost::math::concepts::real_concept is 1.11022e-015.
*** No errors detected

*/