test_cauchy.cpp

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// Copyright John Maddock 2006, 2007.
// Copyright Paul A. Bristow 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_cauchy.cpp Test Cauchy distribution

#ifdef _MSC_VER
#  pragma warning(disable: 4100) // unreferenced formal parameter.
// Seems an entirely spurious warning - formal parameter T IS used - get error if /* T */
//#  pragma warning(disable: 4535) // calling _set_se_translator() requires /EHa (in Boost.test)
// Enable C++ Exceptions Yes With SEH Exceptions (/EHa) prevents warning 4535.
#  pragma warning(disable: 4127) // conditional expression is constant
#endif

// #define BOOST_MATH_ASSERT_UNDEFINED_POLICY false 
// To compile even if Cauchy mean is used.

#include <boost/math/concepts/real_concept.hpp> // for real_concept
#include <boost/math/distributions/cauchy.hpp>
    using boost::math::cauchy_distribution;

#include <boost/test/included/test_exec_monitor.hpp> // Boost.Test
#include <boost/test/floating_point_comparison.hpp>

#include <iostream>
   using std::cout;
   using std::endl;

template <class RealType>
void test_spots(RealType T)
{
  // Check some bad parameters to the distribution,
   BOOST_CHECK_THROW(boost::math::cauchy_distribution<RealType> nbad1(0, 0), std::domain_error); // zero sd
   BOOST_CHECK_THROW(boost::math::cauchy_distribution<RealType> nbad1(0, -1), std::domain_error); // negative scale (shape)
  cauchy_distribution<RealType> C01;

  BOOST_CHECK_EQUAL(C01.location(), 0); // Check standard values.
  BOOST_CHECK_EQUAL(C01.scale(), 1);

  // Tests on extreme values of random variate x, if has numeric_limit infinity etc.
  if(std::numeric_limits<RealType>::has_infinity)
  {
    BOOST_CHECK_EQUAL(pdf(C01, +std::numeric_limits<RealType>::infinity()), 0); // x = + infinity, pdf = 0
    BOOST_CHECK_EQUAL(pdf(C01, -std::numeric_limits<RealType>::infinity()), 0); // x = - infinity, pdf = 0
    BOOST_CHECK_EQUAL(cdf(C01, +std::numeric_limits<RealType>::infinity()), 1); // x = + infinity, cdf = 1
    BOOST_CHECK_EQUAL(cdf(C01, -std::numeric_limits<RealType>::infinity()), 0); // x = - infinity, cdf = 0
    BOOST_CHECK_EQUAL(cdf(complement(C01, +std::numeric_limits<RealType>::infinity())), 0); // x = + infinity, cdf = 0
    BOOST_CHECK_EQUAL(cdf(complement(C01, -std::numeric_limits<RealType>::infinity())), 1); // x = - infinity, cdf = 1
    BOOST_CHECK_THROW(boost::math::cauchy_distribution<RealType> nbad1(std::numeric_limits<RealType>::infinity(), static_cast<RealType>(1)), std::domain_error); // +infinite mean
     BOOST_CHECK_THROW(boost::math::cauchy_distribution<RealType> nbad1(-std::numeric_limits<RealType>::infinity(),  static_cast<RealType>(1)), std::domain_error); // -infinite mean
     BOOST_CHECK_THROW(boost::math::cauchy_distribution<RealType> nbad1(static_cast<RealType>(0), std::numeric_limits<RealType>::infinity()), std::domain_error); // infinite sd
  }

  if (std::numeric_limits<RealType>::has_quiet_NaN)
  { // No longer allow x to be NaN, so these tests should throw.
    BOOST_CHECK_THROW(pdf(C01, +std::numeric_limits<RealType>::quiet_NaN()), std::domain_error); // x = NaN
    BOOST_CHECK_THROW(cdf(C01, +std::numeric_limits<RealType>::quiet_NaN()), std::domain_error); // x = NaN
    BOOST_CHECK_THROW(cdf(complement(C01, +std::numeric_limits<RealType>::quiet_NaN())), std::domain_error); // x = + infinity
    BOOST_CHECK_THROW(quantile(C01, +std::numeric_limits<RealType>::quiet_NaN()), std::domain_error); // p = + infinity
    BOOST_CHECK_THROW(quantile(complement(C01, +std::numeric_limits<RealType>::quiet_NaN())), std::domain_error); // p = + infinity
  }

  // Basic sanity checks.
  // 50eps as a percentage, up to a maximum of double precision
  // (that's the limit of our test data).
  RealType tolerance = (std::max)(
     static_cast<RealType>(boost::math::tools::epsilon<double>()),
     boost::math::tools::epsilon<RealType>());
  tolerance *= 50 * 100;

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

   // These first sets of test values were calculated by punching numbers
   // into a calculator, and using the formulas on the Mathworld website:
   // http://mathworld.wolfram.com/CauchyDistribution.html
   // and values from MathCAD 200 Professional, 
   // CDF:
   //
   BOOST_CHECK_CLOSE(
      ::boost::math::cdf(
         cauchy_distribution<RealType>(),
         static_cast<RealType>(0.125)),              // x
         static_cast<RealType>(0.53958342416056554201085167134004L),                // probability.
         tolerance); // %
   BOOST_CHECK_CLOSE(
      ::boost::math::cdf(
         cauchy_distribution<RealType>(),
         static_cast<RealType>(-0.125)),              // x
         static_cast<RealType>(0.46041657583943445798914832865996L),                // probability.
         tolerance); // %
   BOOST_CHECK_CLOSE(
      ::boost::math::cdf(
         cauchy_distribution<RealType>(),
         static_cast<RealType>(0.5)),              // x
         static_cast<RealType>(0.64758361765043327417540107622474L),                // probability.
         tolerance); // %
   BOOST_CHECK_CLOSE(
      ::boost::math::cdf(
         cauchy_distribution<RealType>(),
         static_cast<RealType>(-0.5)),              // x
         static_cast<RealType>(0.35241638234956672582459892377526L),                // probability.
         tolerance); // %
   BOOST_CHECK_CLOSE(
      ::boost::math::cdf(
         cauchy_distribution<RealType>(),
         static_cast<RealType>(1.0)),              // x
         static_cast<RealType>(0.75),                // probability.
         tolerance); // %
   BOOST_CHECK_CLOSE(
      ::boost::math::cdf(
         cauchy_distribution<RealType>(),
         static_cast<RealType>(-1.0)),              // x
         static_cast<RealType>(0.25),                // probability.
         tolerance); // %
   BOOST_CHECK_CLOSE(
      ::boost::math::cdf(
         cauchy_distribution<RealType>(),
         static_cast<RealType>(2.0)),              // x
         static_cast<RealType>(0.85241638234956672582459892377526L),                // probability.
         tolerance); // %
   BOOST_CHECK_CLOSE(
      ::boost::math::cdf(
         cauchy_distribution<RealType>(),
         static_cast<RealType>(-2.0)),              // x
         static_cast<RealType>(0.14758361765043327417540107622474L),                // probability.
         tolerance); // %
   BOOST_CHECK_CLOSE(
      ::boost::math::cdf(
         cauchy_distribution<RealType>(),
         static_cast<RealType>(10.0)),              // x
         static_cast<RealType>(0.9682744825694464304850228813987L),                // probability.
         tolerance); // %
   BOOST_CHECK_CLOSE(
      ::boost::math::cdf(
         cauchy_distribution<RealType>(),
         static_cast<RealType>(-10.0)),              // x
         static_cast<RealType>(0.031725517430553569514977118601302L),                // probability.
         tolerance); // %

   //
   // Complements:
   //
   BOOST_CHECK_CLOSE(
      ::boost::math::cdf(
         complement(cauchy_distribution<RealType>(),
         static_cast<RealType>(0.125))),              // x
         static_cast<RealType>(0.46041657583943445798914832865996L),                // probability.
         tolerance); // %
   BOOST_CHECK_CLOSE(
      ::boost::math::cdf(
         complement(cauchy_distribution<RealType>(),
         static_cast<RealType>(-0.125))),              // x
         static_cast<RealType>(0.53958342416056554201085167134004L),                // probability.
         tolerance); // %
   BOOST_CHECK_CLOSE(
      ::boost::math::cdf(
         complement(cauchy_distribution<RealType>(),
         static_cast<RealType>(0.5))),              // x
         static_cast<RealType>(0.35241638234956672582459892377526L),                // probability.
         tolerance); // %
   BOOST_CHECK_CLOSE(
      ::boost::math::cdf(
         complement(cauchy_distribution<RealType>(),
         static_cast<RealType>(-0.5))),              // x
         static_cast<RealType>(0.64758361765043327417540107622474L),                // probability.
         tolerance); // %
   BOOST_CHECK_CLOSE(
      ::boost::math::cdf(
         complement(cauchy_distribution<RealType>(),
         static_cast<RealType>(1.0))),              // x
         static_cast<RealType>(0.25),                // probability.
         tolerance); // %
   BOOST_CHECK_CLOSE(
      ::boost::math::cdf(
         complement(cauchy_distribution<RealType>(),
         static_cast<RealType>(-1.0))),              // x
         static_cast<RealType>(0.75),                // probability.
         tolerance); // %
   BOOST_CHECK_CLOSE(
      ::boost::math::cdf(
         complement(cauchy_distribution<RealType>(),
         static_cast<RealType>(2.0))),              // x
         static_cast<RealType>(0.14758361765043327417540107622474L),                // probability.
         tolerance); // %
   BOOST_CHECK_CLOSE(
      ::boost::math::cdf(
         complement(cauchy_distribution<RealType>(),
         static_cast<RealType>(-2.0))),              // x
         static_cast<RealType>(0.85241638234956672582459892377526L),                // probability.
         tolerance); // %
   BOOST_CHECK_CLOSE(
      ::boost::math::cdf(
         complement(cauchy_distribution<RealType>(),
         static_cast<RealType>(10.0))),              // x
         static_cast<RealType>(0.031725517430553569514977118601302L),                // probability.
         tolerance); // %
   BOOST_CHECK_CLOSE(
      ::boost::math::cdf(
         complement(cauchy_distribution<RealType>(),
         static_cast<RealType>(-10.0))),              // x
         static_cast<RealType>(0.9682744825694464304850228813987L),                // probability.
         tolerance); // %

   //
   // Quantiles:
   //
   BOOST_CHECK_CLOSE(
      ::boost::math::quantile(
         cauchy_distribution<RealType>(),
         static_cast<RealType>(0.53958342416056554201085167134004L)),
         static_cast<RealType>(0.125),
         tolerance); // %
   BOOST_CHECK_CLOSE(
      ::boost::math::quantile(
         cauchy_distribution<RealType>(),
         static_cast<RealType>(0.46041657583943445798914832865996L)),
         static_cast<RealType>(-0.125),
         tolerance); // %
   BOOST_CHECK_CLOSE(
      ::boost::math::quantile(
         cauchy_distribution<RealType>(),
         static_cast<RealType>(0.64758361765043327417540107622474L)),
         static_cast<RealType>(0.5),
         tolerance); // %
   BOOST_CHECK_CLOSE(
      ::boost::math::quantile(
         cauchy_distribution<RealType>(),
         static_cast<RealType>(0.35241638234956672582459892377526)),
         static_cast<RealType>(-0.5),
         tolerance); // %
   BOOST_CHECK_CLOSE(
      ::boost::math::quantile(
         cauchy_distribution<RealType>(),
         static_cast<RealType>(0.75)),
         static_cast<RealType>(1.0),
         tolerance); // %
   BOOST_CHECK_CLOSE(
      ::boost::math::quantile(
         cauchy_distribution<RealType>(),
         static_cast<RealType>(0.25)),
         static_cast<RealType>(-1.0),
         tolerance); // %
   BOOST_CHECK_CLOSE(
      ::boost::math::quantile(
         cauchy_distribution<RealType>(),
         static_cast<RealType>(0.85241638234956672582459892377526L)),
         static_cast<RealType>(2.0),
         tolerance); // %
   BOOST_CHECK_CLOSE(