SV platform dependency builds

// 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)

#ifndef BOOST_STATS_CAUCHY_HPP

#define BOOST_STATS_CAUCHY_HPP

#ifdef _MSC_VER

#pragma warning(push)

#pragma warning(disable : 4127) // conditional expression is constant

#endif

#include <boost/math/distributions/fwd.hpp>

#include <boost/math/constants/constants.hpp>

#include <boost/math/distributions/complement.hpp>

#include <boost/math/distributions/detail/common_error_handling.hpp>

#include <boost/config/no_tr1/cmath.hpp>

#include <utility>

namespace boost{ namespace math

{

template <class RealType, class Policy>

class cauchy_distribution;

namespace detail

{

template <class RealType, class Policy>

RealType cdf_imp(const cauchy_distribution<RealType, Policy>& dist, const RealType& x, bool complement)

{

   //

   // This calculates the cdf of the Cauchy distribution and/or its complement.

   //

   // The usual formula for the Cauchy cdf is:

   //

   // cdf = 0.5 + atan(x)/pi

   //

   // But that suffers from cancellation error as x -> -INF.

   //

   // Recall that for x < 0:

   //

   // atan(x) = -pi/2 - atan(1/x)

   //

   // Substituting into the above we get:

   //

   // CDF = -atan(1/x)  ; x < 0

   //

   // So the proceedure is to calculate the cdf for -fabs(x)

   // using the above formula, and then subtract from 1 when required

   // to get the result.

   //

   BOOST_MATH_STD_USING // for ADL of std functions

   static const char* function = "boost::math::cdf(cauchy<%1%>&, %1%)";

   RealType result = 0;

   RealType location = dist.location();

   RealType scale = dist.scale();

   if(false == detail::check_location(function, location, &result, Policy()))

   {

     return result;

   }

   if(false == detail::check_scale(function, scale, &result, Policy()))

   {

      return result;

   }

   if(std::numeric_limits<RealType>::has_infinity && x == std::numeric_limits<RealType>::infinity())

   { // cdf +infinity is unity.

     return static_cast<RealType>((complement) ? 0 : 1);

   }

   if(std::numeric_limits<RealType>::has_infinity && x == -std::numeric_limits<RealType>::infinity())

   { // cdf -infinity is zero.

     return static_cast<RealType>((complement) ? 1 : 0);

   }

   if(false == detail::check_x(function, x, &result, Policy()))

   { // Catches x == NaN

      return result;

   }

   RealType mx = -fabs((x - location) / scale); // scale is > 0

   if(mx > -tools::epsilon<RealType>() / 8)

   {  // special case first: x extremely close to location.

      return 0.5;

   }

   result = -atan(1 / mx) / constants::pi<RealType>();

   return (((x > location) != complement) ? 1 - result : result);

} // cdf

template <class RealType, class Policy>

RealType quantile_imp(

      const cauchy_distribution<RealType, Policy>& dist,

      const RealType& p,

      bool complement)

{

   // This routine implements the quantile for the Cauchy distribution,

   // the value p may be the probability, or its complement if complement=true.

   //

   // The procedure first performs argument reduction on p to avoid error

   // when calculating the tangent, then calulates the distance from the

   // mid-point of the distribution.  This is either added or subtracted

   // from the location parameter depending on whether `complement` is true.

   //

   static const char* function = "boost::math::quantile(cauchy<%1%>&, %1%)";

   BOOST_MATH_STD_USING // for ADL of std functions

   RealType result = 0;

   RealType location = dist.location();

   RealType scale = dist.scale();

   if(false == detail::check_location(function, location, &result, Policy()))

   {

     return result;

   }

   if(false == detail::check_scale(function, scale, &result, Policy()))

   {

      return result;

   }

   if(false == detail::check_probability(function, p, &result, Policy()))

   {

      return result;

   }

   // Special cases:

   if(p == 1)

   {

      return (complement ? -1 : 1) * policies::raise_overflow_error<RealType>(function, 0, Policy());

   }

   if(p == 0)

   {

      return (complement ? 1 : -1) * policies::raise_overflow_error<RealType>(function, 0, Policy());

   }

   RealType P = p - floor(p);   // argument reduction of p:

   if(P > 0.5)

   {

      P = P - 1;

   }

   if(P == 0.5)   // special case:

   {

      return location;

   }

   result = -scale / tan(constants::pi<RealType>() * P);

   return complement ? RealType(location - result) : RealType(location + result);

} // quantile

} // namespace detail

template <class RealType = double, class Policy = policies::policy<> >

class cauchy_distribution

{

public:

   typedef RealType value_type;

   typedef Policy policy_type;

   cauchy_distribution(RealType l_location = 0, RealType l_scale = 1)

      : m_a(l_location), m_hg(l_scale)

   {

    static const char* function = "boost::math::cauchy_distribution<%1%>::cauchy_distribution";

     RealType result;

     detail::check_location(function, l_location, &result, Policy());

     detail::check_scale(function, l_scale, &result, Policy());

   } // cauchy_distribution

   RealType location()const

   {

      return m_a;

   }

   RealType scale()const

   {

      return m_hg;

   }

private:

   RealType m_a;    // The location, this is the median of the distribution.

   RealType m_hg;   // The scale )or shape), this is the half width at half height.

};

typedef cauchy_distribution<double> cauchy;

template <class RealType, class Policy>

inline const std::pair<RealType, RealType> range(const cauchy_distribution<RealType, Policy>&)

{ // Range of permissible values for random variable x.

  if (std::numeric_limits<RealType>::has_infinity)

  { 

     return std::pair<RealType, RealType>(-std::numeric_limits<RealType>::infinity(), std::numeric_limits<RealType>::infinity()); // - to + infinity.

  }

  else

  { // Can only use max_value.

   using boost::math::tools::max_value;

   return std::pair<RealType, RealType>(-max_value<RealType>(), max_value<RealType>()); // - to + max.

  }

}

template <class RealType, class Policy>

inline const std::pair<RealType, RealType> support(const cauchy_distribution<RealType, Policy>& )

{ // Range of supported values for random variable x.

   // This is range where cdf rises from 0 to 1, and outside it, the pdf is zero.

  if (std::numeric_limits<RealType>::has_infinity)

  { 

     return std::pair<RealType, RealType>(-std::numeric_limits<RealType>::infinity(), std::numeric_limits<RealType>::infinity()); // - to + infinity.

  }

  else

  { // Can only use max_value.

     using boost::math::tools::max_value;

     return std::pair<RealType, RealType>(-tools::max_value<RealType>(), max_value<RealType>()); // - to + max.

  }

}

template <class RealType, class Policy>

inline RealType pdf(const cauchy_distribution<RealType, Policy>& dist, const RealType& x)

{  

   BOOST_MATH_STD_USING  // for ADL of std functions

   static const char* function = "boost::math::pdf(cauchy<%1%>&, %1%)";

   RealType result = 0;

   RealType location = dist.location();

   RealType scale = dist.scale();

   if(false == detail::check_scale("boost::math::pdf(cauchy<%1%>&, %1%)", scale, &result, Policy()))

   {

      return result;

   }

   if(false == detail::check_location("boost::math::pdf(cauchy<%1%>&, %1%)", location, &result, Policy()))

   {

      return result;

   }

   if((boost::math::isinf)(x))

   {

     return 0; // pdf + and - infinity is zero.

   }

   // These produce MSVC 4127 warnings, so the above used instead.

   //if(std::numeric_limits<RealType>::has_infinity && abs(x) == std::numeric_limits<RealType>::infinity())

   //{ // pdf + and - infinity is zero.

   //  return 0;

   //}

   if(false == detail::check_x(function, x, &result, Policy()))

   { // Catches x = NaN

      return result;

   }

   RealType xs = (x - location) / scale;

   result = 1 / (constants::pi<RealType>() * scale * (1 + xs * xs));

   return result;

} // pdf

template <class RealType, class Policy>

inline RealType cdf(const cauchy_distribution<RealType, Policy>& dist, const RealType& x)

{

   return detail::cdf_imp(dist, x, false);

} // cdf

template <class RealType, class Policy>

inline RealType quantile(const cauchy_distribution<RealType, Policy>& dist, const RealType& p)

{

   return detail::quantile_imp(dist, p, false);

} // quantile

template <class RealType, class Policy>

inline RealType cdf(const complemented2_type<cauchy_distribution<RealType, Policy>, RealType>& c)

{

   return detail::cdf_imp(c.dist, c.param, true);

} //  cdf complement

template <class RealType, class Policy>

inline RealType quantile(const complemented2_type<cauchy_distribution<RealType, Policy>, RealType>& c)

{

   return detail::quantile_imp(c.dist, c.param, true);

} // quantile complement

template <class RealType, class Policy>

inline RealType mean(const cauchy_distribution<RealType, Policy>&)

{  // There is no mean:

   typedef typename Policy::assert_undefined_type assert_type;

   BOOST_STATIC_ASSERT(assert_type::value == 0);

   return policies::raise_domain_error<RealType>(

      "boost::math::mean(cauchy<%1%>&)",

      "The Cauchy distribution does not have a mean: "

      "the only possible return value is %1%.",

      std::numeric_limits<RealType>::quiet_NaN(), Policy());

}

template <class RealType, class Policy>

inline RealType variance(const cauchy_distribution<RealType, Policy>& /*dist*/)

{

   // There is no variance:

   typedef typename Policy::assert_undefined_type assert_type;

   BOOST_STATIC_ASSERT(assert_type::value == 0);

   return policies::raise_domain_error<RealType>(

      "boost::math::variance(cauchy<%1%>&)",

      "The Cauchy distribution does not have a variance: "

      "the only possible return value is %1%.",

      std::numeric_limits<RealType>::quiet_NaN(), Policy());

}

template <class RealType, class Policy>

inline RealType mode(const cauchy_distribution<RealType, Policy>& dist)

{

   return dist.location();

}

template <class RealType, class Policy>

inline RealType median(const cauchy_distribution<RealType, Policy>& dist)

{

   return dist.location();

}

template <class RealType, class Policy>

inline RealType skewness(const cauchy_distribution<RealType, Policy>& /*dist*/)

{

   // There is no skewness:

   typedef typename Policy::assert_undefined_type assert_type;

   BOOST_STATIC_ASSERT(assert_type::value == 0);

   return policies::raise_domain_error<RealType>(

      "boost::math::skewness(cauchy<%1%>&)",

      "The Cauchy distribution does not have a skewness: "

      "the only possible return value is %1%.",

      std::numeric_limits<RealType>::quiet_NaN(), Policy()); // infinity?

}

template <class RealType, class Policy>

inline RealType kurtosis(const cauchy_distribution<RealType, Policy>& /*dist*/)

{

   // There is no kurtosis:

   typedef typename Policy::assert_undefined_type assert_type;

   BOOST_STATIC_ASSERT(assert_type::value == 0);

   return policies::raise_domain_error<RealType>(

      "boost::math::kurtosis(cauchy<%1%>&)",

      "The Cauchy distribution does not have a kurtosis: "

      "the only possible return value is %1%.",

      std::numeric_limits<RealType>::quiet_NaN(), Policy());

}

template <class RealType, class Policy>

inline RealType kurtosis_excess(const cauchy_distribution<RealType, Policy>& /*dist*/)

{

   // There is no kurtosis excess:

   typedef typename Policy::assert_undefined_type assert_type;

   BOOST_STATIC_ASSERT(assert_type::value == 0);

   return policies::raise_domain_error<RealType>(

      "boost::math::kurtosis_excess(cauchy<%1%>&)",

      "The Cauchy distribution does not have a kurtosis: "

      "the only possible return value is %1%.",

      std::numeric_limits<RealType>::quiet_NaN(), Policy());

}

} // namespace math

} // namespace boost

#ifdef _MSC_VER

#pragma warning(pop)

#endif

// This include must be at the end, *after* the accessors

// for this distribution have been defined, in order to

// keep compilers that support two-phase lookup happy.

#include <boost/math/distributions/detail/derived_accessors.hpp>

#endif // BOOST_STATS_CAUCHY_HPP