test_uniform.cpp

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// 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

#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
#include <boost/test/included/test_exec_monitor.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 <iostream>
   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_CHECK_THROW tests.

     BOOST_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_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_CHECK_THROW(
       pdf(uniform_distribution<RealType>(0, 1), static_cast<RealType>(std::numeric_limits<RealType>::quiet_NaN())), 
       std::domain_error);
     BOOST_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>(1));

   // 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>(1), 
      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);