Added boost header

test/external/boost/math/distributions/rayleigh.hpp

@@ -0,0 +1,293 @@
+//  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_rayleigh_HPP
+#define BOOST_STATS_rayleigh_HPP
+
+#include <boost/math/distributions/fwd.hpp>
+#include <boost/math/constants/constants.hpp>
+#include <boost/math/special_functions/log1p.hpp>
+#include <boost/math/special_functions/expm1.hpp>
+#include <boost/math/distributions/complement.hpp>
+#include <boost/math/distributions/detail/common_error_handling.hpp>
+#include <boost/config/no_tr1/cmath.hpp>
+
+#ifdef BOOST_MSVC
+# pragma warning(push)
+# pragma warning(disable: 4702) // unreachable code (return after domain_error throw).
+#endif
+
+#include <utility>
+
+namespace boost{ namespace math{
+
+namespace detail
+{ // Error checks:
+  template <class RealType, class Policy>
+  inline bool verify_sigma(const char* function, RealType sigma, RealType* presult, const Policy& pol)
+  {
+     if(sigma <= 0)
+     {
+        *presult = policies::raise_domain_error<RealType>(
+           function,
+           "The scale parameter \"sigma\" must be > 0, but was: %1%.", sigma, pol);
+        return false;
+     }
+     return true;
+  } // bool verify_sigma
+
+  template <class RealType, class Policy>
+  inline bool verify_rayleigh_x(const char* function, RealType x, RealType* presult, const Policy& pol)
+  {
+     if(x < 0)
+     {
+        *presult = policies::raise_domain_error<RealType>(
+           function,
+           "The random variable must be >= 0, but was: %1%.", x, pol);
+        return false;
+     }
+     return true;
+  } // bool verify_rayleigh_x
+} // namespace detail
+
+template <class RealType = double, class Policy = policies::policy<> >
+class rayleigh_distribution
+{
+public:
+   typedef RealType value_type;
+   typedef Policy policy_type;
+
+   rayleigh_distribution(RealType sigma = 1)
+      : m_sigma(sigma)
+   {
+      RealType err;
+      detail::verify_sigma("boost::math::rayleigh_distribution<%1%>::rayleigh_distribution", sigma, &err, Policy());
+   } // rayleigh_distribution
+
+   RealType sigma()const
+   { // Accessor.
+     return m_sigma;
+   }
+
+private:
+   RealType m_sigma;
+}; // class rayleigh_distribution
+
+typedef rayleigh_distribution<double> rayleigh;
+
+template <class RealType, class Policy>
+inline const std::pair<RealType, RealType> range(const rayleigh_distribution<RealType, Policy>& /*dist*/)
+{ // Range of permissible values for random variable x.
+   using boost::math::tools::max_value;
+   return std::pair<RealType, RealType>(static_cast<RealType>(0), max_value<RealType>());
+}
+
+template <class RealType, class Policy>
+inline const std::pair<RealType, RealType> support(const rayleigh_distribution<RealType, Policy>& /*dist*/)
+{ // 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.
+   using boost::math::tools::max_value;
+   return std::pair<RealType, RealType>(static_cast<RealType>(0),  max_value<RealType>());
+}
+
+template <class RealType, class Policy>
+inline RealType pdf(const rayleigh_distribution<RealType, Policy>& dist, const RealType& x)
+{
+   BOOST_MATH_STD_USING // for ADL of std function exp.
+
+   RealType sigma = dist.sigma();
+   RealType result = 0;
+   static const char* function = "boost::math::pdf(const rayleigh_distribution<%1%>&, %1%)";
+   if(false == detail::verify_sigma(function, sigma, &result, Policy()))
+   {
+      return result;
+   }
+   if(false == detail::verify_rayleigh_x(function, x, &result, Policy()))
+   {
+      return result;
+   }
+   RealType sigmasqr = sigma * sigma;
+   result = x * (exp(-(x * x) / ( 2 * sigmasqr))) / sigmasqr;
+   return result;
+} // pdf
+
+template <class RealType, class Policy>
+inline RealType cdf(const rayleigh_distribution<RealType, Policy>& dist, const RealType& x)
+{
+   BOOST_MATH_STD_USING // for ADL of std functions
+
+   RealType result = 0;
+   RealType sigma = dist.sigma();
+   static const char* function = "boost::math::cdf(const rayleigh_distribution<%1%>&, %1%)";
+   if(false == detail::verify_sigma(function, sigma, &result, Policy()))
+   {
+      return result;
+   }
+   if(false == detail::verify_rayleigh_x(function, x, &result, Policy()))
+   {
+      return result;
+   }
+   result = -boost::math::expm1(-x * x / ( 2 * sigma * sigma), Policy());
+   return result;
+} // cdf
+
+template <class RealType, class Policy>
+inline RealType quantile(const rayleigh_distribution<RealType, Policy>& dist, const RealType& p)
+{
+   BOOST_MATH_STD_USING // for ADL of std functions
+
+   RealType result = 0;
+   RealType sigma = dist.sigma();
+   static const char* function = "boost::math::quantile(const rayleigh_distribution<%1%>&, %1%)";
+   if(false == detail::verify_sigma(function, sigma, &result, Policy()))
+      return result;
+   if(false == detail::check_probability(function, p, &result, Policy()))
+      return result;
+
+   if(p == 0)
+   {
+      return 0;
+   }
+   if(p == 1)
+   {
+     return policies::raise_overflow_error<RealType>(function, 0, Policy());
+   }
+   result = sqrt(-2 * sigma * sigma * boost::math::log1p(-p, Policy()));
+   return result;
+} // quantile
+
+template <class RealType, class Policy>
+inline RealType cdf(const complemented2_type<rayleigh_distribution<RealType, Policy>, RealType>& c)
+{
+   BOOST_MATH_STD_USING // for ADL of std functions
+
+   RealType result = 0;
+   RealType sigma = c.dist.sigma();
+   static const char* function = "boost::math::cdf(const rayleigh_distribution<%1%>&, %1%)";
+   if(false == detail::verify_sigma(function, sigma, &result, Policy()))
+   {
+      return result;
+   }
+   RealType x = c.param;
+   if(false == detail::verify_rayleigh_x(function, x, &result, Policy()))
+   {
+      return result;
+   }
+   result =  exp(-x * x / ( 2 * sigma * sigma));
+   return result;
+} // cdf complement
+
+template <class RealType, class Policy>
+inline RealType quantile(const complemented2_type<rayleigh_distribution<RealType, Policy>, RealType>& c)
+{
+   BOOST_MATH_STD_USING // for ADL of std functions, log & sqrt.
+
+   RealType result = 0;
+   RealType sigma = c.dist.sigma();
+   static const char* function = "boost::math::quantile(const rayleigh_distribution<%1%>&, %1%)";
+   if(false == detail::verify_sigma(function, sigma, &result, Policy()))
+   {
+      return result;
+   }
+   RealType q = c.param;
+   if(false == detail::check_probability(function, q, &result, Policy()))
+   {
+      return result;
+   }
+   if(q == 1)
+   {
+      return 0;
+   }
+   if(q == 0)
+   {
+     return policies::raise_overflow_error<RealType>(function, 0, Policy());
+   }
+   result = sqrt(-2 * sigma * sigma * log(q));
+   return result;
+} // quantile complement
+
+template <class RealType, class Policy>
+inline RealType mean(const rayleigh_distribution<RealType, Policy>& dist)
+{
+   RealType result = 0;
+   RealType sigma = dist.sigma();
+   static const char* function = "boost::math::mean(const rayleigh_distribution<%1%>&, %1%)";
+   if(false == detail::verify_sigma(function, sigma, &result, Policy()))
+   {
+      return result;
+   }
+   using boost::math::constants::root_half_pi;
+   return sigma * root_half_pi<RealType>();
+} // mean
+
+template <class RealType, class Policy>
+inline RealType variance(const rayleigh_distribution<RealType, Policy>& dist)
+{
+   RealType result = 0;
+   RealType sigma = dist.sigma();
+   static const char* function = "boost::math::variance(const rayleigh_distribution<%1%>&, %1%)";
+   if(false == detail::verify_sigma(function, sigma, &result, Policy()))
+   {
+      return result;
+   }
+   using boost::math::constants::four_minus_pi;
+   return four_minus_pi<RealType>() * sigma * sigma / 2;
+} // variance
+
+template <class RealType, class Policy>
+inline RealType mode(const rayleigh_distribution<RealType, Policy>& dist)
+{
+   return dist.sigma();
+}
+
+template <class RealType, class Policy>
+inline RealType median(const rayleigh_distribution<RealType, Policy>& dist)
+{
+   using boost::math::constants::root_ln_four;
+   return root_ln_four<RealType>() * dist.sigma();
+}
+
+template <class RealType, class Policy>
+inline RealType skewness(const rayleigh_distribution<RealType, Policy>& /*dist*/)
+{
+  // using namespace boost::math::constants;
+  return static_cast<RealType>(0.63111065781893713819189935154422777984404221106391L);
+  // Computed using NTL at 150 bit, about 50 decimal digits.
+  // return 2 * root_pi<RealType>() * pi_minus_three<RealType>() / pow23_four_minus_pi<RealType>();
+}
+
+template <class RealType, class Policy>
+inline RealType kurtosis(const rayleigh_distribution<RealType, Policy>& /*dist*/)
+{
+  // using namespace boost::math::constants;
+  return static_cast<RealType>(3.2450893006876380628486604106197544154170667057995L);
+  // Computed using NTL at 150 bit, about 50 decimal digits.
+  // return 3 - (6 * pi<RealType>() * pi<RealType>() - 24 * pi<RealType>() + 16) /
+  // (four_minus_pi<RealType>() * four_minus_pi<RealType>());
+}
+
+template <class RealType, class Policy>
+inline RealType kurtosis_excess(const rayleigh_distribution<RealType, Policy>& /*dist*/)
+{
+  //using namespace boost::math::constants;
+  // Computed using NTL at 150 bit, about 50 decimal digits.
+  return static_cast<RealType>(0.2450893006876380628486604106197544154170667057995L);
+  // return -(6 * pi<RealType>() * pi<RealType>() - 24 * pi<RealType>() + 16) /
+  //   (four_minus_pi<RealType>() * four_minus_pi<RealType>());
+} // kurtosis
+
+} // namespace math
+} // namespace boost
+
+#ifdef BOOST_MSVC
+# 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_rayleigh_HPP