Added boost header

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

@@ -0,0 +1,409 @@
+// boost\math\distributions\non_central_f.hpp
+
+// Copyright John Maddock 2008.
+
+// 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_MATH_SPECIAL_NON_CENTRAL_F_HPP
+#define BOOST_MATH_SPECIAL_NON_CENTRAL_F_HPP
+
+#include <boost/math/distributions/non_central_beta.hpp>
+#include <boost/math/distributions/detail/generic_mode.hpp>
+#include <boost/math/special_functions/pow.hpp>
+
+namespace boost
+{
+   namespace math
+   {
+      template <class RealType = double, class Policy = policies::policy<> >
+      class non_central_f_distribution
+      {
+      public:
+         typedef RealType value_type;
+         typedef Policy policy_type;
+
+         non_central_f_distribution(RealType v1_, RealType v2_, RealType lambda) : v1(v1_), v2(v2_), ncp(lambda)
+         {
+            const char* function = "boost::math::non_central_f_distribution<%1%>::non_central_f_distribution(%1%,%1%)";
+            RealType r;
+            detail::check_df(
+               function,
+               v1, &r, Policy());
+            detail::check_df(
+               function,
+               v2, &r, Policy());
+            detail::check_non_centrality(
+               function,
+               lambda,
+               &r,
+               Policy());
+         } // non_central_f_distribution constructor.
+
+         RealType degrees_of_freedom1()const
+         {
+            return v1;
+         }
+         RealType degrees_of_freedom2()const
+         {
+            return v2;
+         }
+         RealType non_centrality() const
+         { // Private data getter function.
+            return ncp;
+         }
+      private:
+         // Data member, initialized by constructor.
+         RealType v1;   // alpha.
+         RealType v2;   // beta.
+         RealType ncp; // non-centrality parameter
+      }; // template <class RealType, class Policy> class non_central_f_distribution
+
+      typedef non_central_f_distribution<double> non_central_f; // Reserved name of type double.
+
+      // Non-member functions to give properties of the distribution.
+
+      template <class RealType, class Policy>
+      inline const std::pair<RealType, RealType> range(const non_central_f_distribution<RealType, Policy>& /* dist */)
+      { // Range of permissible values for random variable k.
+         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 non_central_f_distribution<RealType, Policy>& /* dist */)
+      { // Range of supported values for random variable k.
+         // 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 mean(const non_central_f_distribution<RealType, Policy>& dist)
+      {
+         const char* function = "mean(non_central_f_distribution<%1%> const&)";
+         RealType v1 = dist.degrees_of_freedom1();
+         RealType v2 = dist.degrees_of_freedom2();
+         RealType l = dist.non_centrality();
+         RealType r;
+         if(!detail::check_df(
+            function,
+            v1, &r, Policy())
+               ||
+            !detail::check_df(
+               function,
+               v2, &r, Policy())
+               ||
+            !detail::check_non_centrality(
+               function,
+               l,
+               &r,
+               Policy()))
+               return r;
+         if(v2 <= 2)
+            return policies::raise_domain_error(
+               function,
+               "Second degrees of freedom parameter was %1%, but must be > 2 !",
+               v2, Policy());
+         return v2 * (v1 + l) / (v1 * (v2 - 2));
+      } // mean
+
+      template <class RealType, class Policy>
+      inline RealType mode(const non_central_f_distribution<RealType, Policy>& dist)
+      { // mode.
+         static const char* function = "mode(non_central_chi_squared_distribution<%1%> const&)";
+
+         RealType n = dist.degrees_of_freedom1();
+         RealType m = dist.degrees_of_freedom2();
+         RealType l = dist.non_centrality();
+         RealType r;
+         if(!detail::check_df(
+            function,
+            n, &r, Policy())
+               ||
+            !detail::check_df(
+               function,
+               m, &r, Policy())
+               ||
+            !detail::check_non_centrality(
+               function,
+               l,
+               &r,
+               Policy()))
+               return r;
+         return detail::generic_find_mode(
+            dist,
+            m * (n + l) / (n * (m - 2)),
+            function);
+      }
+
+      template <class RealType, class Policy>
+      inline RealType variance(const non_central_f_distribution<RealType, Policy>& dist)
+      { // variance.
+         const char* function = "variance(non_central_f_distribution<%1%> const&)";
+         RealType n = dist.degrees_of_freedom1();
+         RealType m = dist.degrees_of_freedom2();
+         RealType l = dist.non_centrality();
+         RealType r;
+         if(!detail::check_df(
+            function,
+            n, &r, Policy())
+               ||
+            !detail::check_df(
+               function,
+               m, &r, Policy())
+               ||
+            !detail::check_non_centrality(
+               function,
+               l,
+               &r,
+               Policy()))
+               return r;
+         if(m <= 4)
+            return policies::raise_domain_error(
+               function,
+               "Second degrees of freedom parameter was %1%, but must be > 4 !",
+               m, Policy());
+         RealType result = 2 * m * m * ((n + l) * (n + l)
+            + (m - 2) * (n + 2 * l));
+         result /= (m - 4) * (m - 2) * (m - 2) * n * n;
+         return result;
+      }
+
+      // RealType standard_deviation(const non_central_f_distribution<RealType, Policy>& dist)
+      // standard_deviation provided by derived accessors.
+
+      template <class RealType, class Policy>
+      inline RealType skewness(const non_central_f_distribution<RealType, Policy>& dist)
+      { // skewness = sqrt(l).
+         const char* function = "skewness(non_central_f_distribution<%1%> const&)";
+         BOOST_MATH_STD_USING
+         RealType n = dist.degrees_of_freedom1();
+         RealType m = dist.degrees_of_freedom2();
+         RealType l = dist.non_centrality();
+         RealType r;
+         if(!detail::check_df(
+            function,
+            n, &r, Policy())
+               ||
+            !detail::check_df(
+               function,
+               m, &r, Policy())
+               ||
+            !detail::check_non_centrality(
+               function,
+               l,
+               &r,
+               Policy()))
+               return r;
+         if(m <= 6)
+            return policies::raise_domain_error(
+               function,
+               "Second degrees of freedom parameter was %1%, but must be > 6 !",
+               m, Policy());
+         RealType result = 2 * constants::root_two<RealType>();
+         result *= sqrt(m - 4);
+         result *= (n * (m + n - 2) *(m + 2 * n - 2)
+            + 3 * (m + n - 2) * (m + 2 * n - 2) * l
+            + 6 * (m + n - 2) * l * l + 2 * l * l * l);
+         result /= (m - 6) * pow(n * (m + n - 2) + 2 * (m + n - 2) * l + l * l, RealType(1.5f));
+         return result;
+      }
+
+      template <class RealType, class Policy>
+      inline RealType kurtosis_excess(const non_central_f_distribution<RealType, Policy>& dist)
+      {
+         const char* function = "kurtosis_excess(non_central_f_distribution<%1%> const&)";
+         BOOST_MATH_STD_USING
+         RealType n = dist.degrees_of_freedom1();
+         RealType m = dist.degrees_of_freedom2();
+         RealType l = dist.non_centrality();
+         RealType r;
+         if(!detail::check_df(
+            function,
+            n, &r, Policy())
+               ||
+            !detail::check_df(
+               function,
+               m, &r, Policy())
+               ||
+            !detail::check_non_centrality(
+               function,
+               l,
+               &r,
+               Policy()))
+               return r;
+         if(m <= 8)
+            return policies::raise_domain_error(
+               function,
+               "Second degrees of freedom parameter was %1%, but must be > 8 !",
+               m, Policy());
+         RealType l2 = l * l;
+         RealType l3 = l2 * l;
+         RealType l4 = l2 * l2;
+         RealType result = (3 * (m - 4) * (n * (m + n - 2)
+            * (4 * (m - 2) * (m - 2)
+            + (m - 2) * (m + 10) * n
+            + (10 + m) * n * n)
+            + 4 * (m + n - 2) * (4 * (m - 2) * (m - 2)
+            + (m - 2) * (10 + m) * n
+            + (10 + m) * n * n) * l + 2 * (10 + m)
+            * (m + n - 2) * (2 * m + 3 * n - 4) * l2
+            + 4 * (10 + m) * (-2 + m + n) * l3
+            + (10 + m) * l4))
+            /
+            ((-8 + m) * (-6 + m) * boost::math::pow<2>(n * (-2 + m + n)
+            + 2 * (-2 + m + n) * l + l2));
+            return result;
+      } // kurtosis_excess
+
+      template <class RealType, class Policy>
+      inline RealType kurtosis(const non_central_f_distribution<RealType, Policy>& dist)
+      {
+         return kurtosis_excess(dist) + 3;
+      }
+
+      template <class RealType, class Policy>
+      inline RealType pdf(const non_central_f_distribution<RealType, Policy>& dist, const RealType& x)
+      { // Probability Density/Mass Function.
+         typedef typename policies::evaluation<RealType, Policy>::type value_type;
+         typedef typename policies::normalise<
+            Policy,
+            policies::promote_float<false>,
+            policies::promote_double<false>,
+            policies::discrete_quantile<>,
+            policies::assert_undefined<> >::type forwarding_policy;
+
+         value_type alpha = dist.degrees_of_freedom1() / 2;
+         value_type beta = dist.degrees_of_freedom2() / 2;
+         value_type y = x * alpha / beta;
+         value_type r = pdf(boost::math::non_central_beta_distribution<value_type, forwarding_policy>(alpha, beta, dist.non_centrality()), y / (1 + y));
+         return policies::checked_narrowing_cast<RealType, forwarding_policy>(
+            r * (dist.degrees_of_freedom1() / dist.degrees_of_freedom2()) / ((1 + y) * (1 + y)),
+            "pdf(non_central_f_distribution<%1%>, %1%)");
+      } // pdf
+
+      template <class RealType, class Policy>
+      RealType cdf(const non_central_f_distribution<RealType, Policy>& dist, const RealType& x)
+      {
+         const char* function = "cdf(const non_central_f_distribution<%1%>&, %1%)";
+         RealType r;
+         if(!detail::check_df(
+            function,
+            dist.degrees_of_freedom1(), &r, Policy())
+               ||
+            !detail::check_df(
+               function,
+               dist.degrees_of_freedom2(), &r, Policy())
+               ||
+            !detail::check_non_centrality(
+               function,
+               dist.non_centrality(),
+               &r,
+               Policy()))
+               return r;
+
+         if((x < 0) || !(boost::math::isfinite)(x))
+         {
+            return policies::raise_domain_error<RealType>(
+               function, "Random Variable parameter was %1%, but must be > 0 !", x, Policy());
+         }
+
+         RealType alpha = dist.degrees_of_freedom1() / 2;
+         RealType beta = dist.degrees_of_freedom2() / 2;
+         RealType y = x * alpha / beta;
+         RealType c = y / (1 + y);
+         RealType cp = 1 / (1 + y);
+         //
+         // To ensure accuracy, we pass both x and 1-x to the
+         // non-central beta cdf routine, this ensures accuracy
+         // even when we compute x to be ~ 1:
+         //
+         r = detail::non_central_beta_cdf(c, cp, alpha, beta,
+            dist.non_centrality(), false, Policy());
+         return r;
+      } // cdf
+
+      template <class RealType, class Policy>
+      RealType cdf(const complemented2_type<non_central_f_distribution<RealType, Policy>, RealType>& c)
+      { // Complemented Cumulative Distribution Function
+         const char* function = "cdf(complement(const non_central_f_distribution<%1%>&, %1%))";
+         RealType r;
+         if(!detail::check_df(
+            function,
+            c.dist.degrees_of_freedom1(), &r, Policy())
+               ||
+            !detail::check_df(
+               function,
+               c.dist.degrees_of_freedom2(), &r, Policy())
+               ||
+            !detail::check_non_centrality(
+               function,
+               c.dist.non_centrality(),
+               &r,
+               Policy()))
+               return r;
+
+         if((c.param < 0) || !(boost::math::isfinite)(c.param))
+         {
+            return policies::raise_domain_error<RealType>(
+               function, "Random Variable parameter was %1%, but must be > 0 !", c.param, Policy());
+         }
+
+         RealType alpha = c.dist.degrees_of_freedom1() / 2;
+         RealType beta = c.dist.degrees_of_freedom2() / 2;
+         RealType y = c.param * alpha / beta;
+         RealType x = y / (1 + y);
+         RealType cx = 1 / (1 + y);
+         //
+         // To ensure accuracy, we pass both x and 1-x to the
+         // non-central beta cdf routine, this ensures accuracy
+         // even when we compute x to be ~ 1:
+         //
+         r = detail::non_central_beta_cdf(x, cx, alpha, beta,
+            c.dist.non_centrality(), true, Policy());
+         return r;
+      } // ccdf
+
+      template <class RealType, class Policy>
+      inline RealType quantile(const non_central_f_distribution<RealType, Policy>& dist, const RealType& p)
+      { // Quantile (or Percent Point) function.
+         RealType alpha = dist.degrees_of_freedom1() / 2;
+         RealType beta = dist.degrees_of_freedom2() / 2;
+         RealType x = quantile(boost::math::non_central_beta_distribution<RealType, Policy>(alpha, beta, dist.non_centrality()), p);
+         if(x == 1)
+            return policies::raise_overflow_error<RealType>(
+               "quantile(const non_central_f_distribution<%1%>&, %1%)",
+               "Result of non central F quantile is too large to represent.",
+               Policy());
+         return (x / (1 - x)) * (dist.degrees_of_freedom2() / dist.degrees_of_freedom1());
+      } // quantile
+
+      template <class RealType, class Policy>
+      inline RealType quantile(const complemented2_type<non_central_f_distribution<RealType, Policy>, RealType>& c)
+      { // Quantile (or Percent Point) function.
+         RealType alpha = c.dist.degrees_of_freedom1() / 2;
+         RealType beta = c.dist.degrees_of_freedom2() / 2;
+         RealType x = quantile(complement(boost::math::non_central_beta_distribution<RealType, Policy>(alpha, beta, c.dist.non_centrality()), c.param));
+         if(x == 1)
+            return policies::raise_overflow_error<RealType>(
+               "quantile(complement(const non_central_f_distribution<%1%>&, %1%))",
+               "Result of non central F quantile is too large to represent.",
+               Policy());
+         return (x / (1 - x)) * (c.dist.degrees_of_freedom2() / c.dist.degrees_of_freedom1());
+      } // quantile complement.
+
+   } // namespace math
+} // namespace boost
+
+// 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_MATH_SPECIAL_NON_CENTRAL_F_HPP
+
+
+