comparison DEPENDENCIES/generic/include/boost/math/distributions/cauchy.hpp @ 16:2665513ce2d3

Add boost headers

+// 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