diff DEPENDENCIES/generic/include/boost/math/distributions/fisher_f.hpp @ 16:2665513ce2d3

Add boost headers

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/DEPENDENCIES/generic/include/boost/math/distributions/fisher_f.hpp	Tue Aug 05 11:11:38 2014 +0100
@@ -0,0 +1,387 @@
+// Copyright John Maddock 2006.
+
+// 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_DISTRIBUTIONS_FISHER_F_HPP
+#define BOOST_MATH_DISTRIBUTIONS_FISHER_F_HPP
+
+#include <boost/math/distributions/fwd.hpp>
+#include <boost/math/special_functions/beta.hpp> // for incomplete beta.
+#include <boost/math/distributions/complement.hpp> // complements
+#include <boost/math/distributions/detail/common_error_handling.hpp> // error checks
+#include <boost/math/special_functions/fpclassify.hpp>
+
+#include <utility>
+
+namespace boost{ namespace math{
+
+template <class RealType = double, class Policy = policies::policy<> >
+class fisher_f_distribution
+{
+public:
+   typedef RealType value_type;
+   typedef Policy policy_type;
+
+   fisher_f_distribution(const RealType& i, const RealType& j) : m_df1(i), m_df2(j)
+   {
+      static const char* function = "fisher_f_distribution<%1%>::fisher_f_distribution";
+      RealType result;
+      detail::check_df(
+         function, m_df1, &result, Policy());
+      detail::check_df(
+         function, m_df2, &result, Policy());
+   } // fisher_f_distribution
+
+   RealType degrees_of_freedom1()const
+   {
+      return m_df1;
+   }
+   RealType degrees_of_freedom2()const
+   {
+      return m_df2;
+   }
+
+private:
+   //
+   // Data members:
+   //
+   RealType m_df1;  // degrees of freedom are a real number.
+   RealType m_df2;  // degrees of freedom are a real number.
+};
+
+typedef fisher_f_distribution<double> fisher_f;
+
+template <class RealType, class Policy>
+inline const std::pair<RealType, RealType> range(const fisher_f_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 fisher_f_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>
+RealType pdf(const fisher_f_distribution<RealType, Policy>& dist, const RealType& x)
+{
+   BOOST_MATH_STD_USING  // for ADL of std functions
+   RealType df1 = dist.degrees_of_freedom1();
+   RealType df2 = dist.degrees_of_freedom2();
+   // Error check:
+   RealType error_result = 0;
+   static const char* function = "boost::math::pdf(fisher_f_distribution<%1%> const&, %1%)";
+   if(false == detail::check_df(
+         function, df1, &error_result, Policy())
+         && detail::check_df(
+         function, df2, &error_result, Policy()))
+      return error_result;
+
+   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());
+   }
+
+   if(x == 0)
+   {
+      // special cases:
+      if(df1 < 2)
+         return policies::raise_overflow_error<RealType>(
+            function, 0, Policy());
+      else if(df1 == 2)
+         return 1;
+      else
+         return 0;
+   }
+
+   //
+   // You reach this formula by direct differentiation of the
+   // cdf expressed in terms of the incomplete beta.
+   //
+   // There are two versions so we don't pass a value of z
+   // that is very close to 1 to ibeta_derivative: for some values
+   // of df1 and df2, all the change takes place in this area.
+   //
+   RealType v1x = df1 * x;
+   RealType result;
+   if(v1x > df2)
+   {
+      result = (df2 * df1) / ((df2 + v1x) * (df2 + v1x));
+      result *= ibeta_derivative(df2 / 2, df1 / 2, df2 / (df2 + v1x), Policy());
+   }
+   else
+   {
+      result = df2 + df1 * x;
+      result = (result * df1 - x * df1 * df1) / (result * result);
+      result *= ibeta_derivative(df1 / 2, df2 / 2, v1x / (df2 + v1x), Policy());
+   }
+   return result;
+} // pdf
+
+template <class RealType, class Policy>
+inline RealType cdf(const fisher_f_distribution<RealType, Policy>& dist, const RealType& x)
+{
+   static const char* function = "boost::math::cdf(fisher_f_distribution<%1%> const&, %1%)";
+   RealType df1 = dist.degrees_of_freedom1();
+   RealType df2 = dist.degrees_of_freedom2();
+   // Error check:
+   RealType error_result = 0;
+   if(false == detail::check_df(
+         function, df1, &error_result, Policy())
+         && detail::check_df(
+         function, df2, &error_result, Policy()))
+      return error_result;
+
+   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 v1x = df1 * x;
+   //
+   // There are two equivalent formulas used here, the aim is
+   // to prevent the final argument to the incomplete beta
+   // from being too close to 1: for some values of df1 and df2
+   // the rate of change can be arbitrarily large in this area,
+   // whilst the value we're passing will have lost information
+   // content as a result of being 0.999999something.  Better
+   // to switch things around so we're passing 1-z instead.
+   //
+   return v1x > df2
+      ? boost::math::ibetac(df2 / 2, df1 / 2, df2 / (df2 + v1x), Policy())
+      : boost::math::ibeta(df1 / 2, df2 / 2, v1x / (df2 + v1x), Policy());
+} // cdf
+
+template <class RealType, class Policy>
+inline RealType quantile(const fisher_f_distribution<RealType, Policy>& dist, const RealType& p)
+{
+   static const char* function = "boost::math::quantile(fisher_f_distribution<%1%> const&, %1%)";
+   RealType df1 = dist.degrees_of_freedom1();
+   RealType df2 = dist.degrees_of_freedom2();
+   // Error check:
+   RealType error_result = 0;
+   if(false == (detail::check_df(
+            function, df1, &error_result, Policy())
+         && detail::check_df(
+            function, df2, &error_result, Policy())
+         && detail::check_probability(
+            function, p, &error_result, Policy())))
+      return error_result;
+
+   // With optimizations turned on, gcc wrongly warns about y being used
+   // uninitializated unless we initialize it to something:
+   RealType x, y(0);
+
+   x = boost::math::ibeta_inv(df1 / 2, df2 / 2, p, &y, Policy());
+
+   return df2 * x / (df1 * y);
+} // quantile
+
+template <class RealType, class Policy>
+inline RealType cdf(const complemented2_type<fisher_f_distribution<RealType, Policy>, RealType>& c)
+{
+   static const char* function = "boost::math::cdf(fisher_f_distribution<%1%> const&, %1%)";
+   RealType df1 = c.dist.degrees_of_freedom1();
+   RealType df2 = c.dist.degrees_of_freedom2();
+   RealType x = c.param;
+   // Error check:
+   RealType error_result = 0;
+   if(false == detail::check_df(
+         function, df1, &error_result, Policy())
+         && detail::check_df(
+         function, df2, &error_result, Policy()))
+      return error_result;
+
+   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 v1x = df1 * x;
+   //
+   // There are two equivalent formulas used here, the aim is
+   // to prevent the final argument to the incomplete beta
+   // from being too close to 1: for some values of df1 and df2
+   // the rate of change can be arbitrarily large in this area,
+   // whilst the value we're passing will have lost information
+   // content as a result of being 0.999999something.  Better
+   // to switch things around so we're passing 1-z instead.
+   //
+   return v1x > df2
+      ? boost::math::ibeta(df2 / 2, df1 / 2, df2 / (df2 + v1x), Policy())
+      : boost::math::ibetac(df1 / 2, df2 / 2, v1x / (df2 + v1x), Policy());
+}
+
+template <class RealType, class Policy>
+inline RealType quantile(const complemented2_type<fisher_f_distribution<RealType, Policy>, RealType>& c)
+{
+   static const char* function = "boost::math::quantile(fisher_f_distribution<%1%> const&, %1%)";
+   RealType df1 = c.dist.degrees_of_freedom1();
+   RealType df2 = c.dist.degrees_of_freedom2();
+   RealType p = c.param;
+   // Error check:
+   RealType error_result = 0;
+   if(false == (detail::check_df(
+            function, df1, &error_result, Policy())
+         && detail::check_df(
+            function, df2, &error_result, Policy())
+         && detail::check_probability(
+            function, p, &error_result, Policy())))
+      return error_result;
+
+   RealType x, y;
+
+   x = boost::math::ibetac_inv(df1 / 2, df2 / 2, p, &y, Policy());
+
+   return df2 * x / (df1 * y);
+}
+
+template <class RealType, class Policy>
+inline RealType mean(const fisher_f_distribution<RealType, Policy>& dist)
+{ // Mean of F distribution = v.
+   static const char* function = "boost::math::mean(fisher_f_distribution<%1%> const&)";
+   RealType df1 = dist.degrees_of_freedom1();
+   RealType df2 = dist.degrees_of_freedom2();
+   // Error check:
+   RealType error_result = 0;
+   if(false == detail::check_df(
+            function, df1, &error_result, Policy())
+         && detail::check_df(
+            function, df2, &error_result, Policy()))
+      return error_result;
+   if(df2 <= 2)
+   {
+      return policies::raise_domain_error<RealType>(
+         function, "Second degree of freedom was %1% but must be > 2 in order for the distribution to have a mean.", df2, Policy());
+   }
+   return df2 / (df2 - 2);
+} // mean
+
+template <class RealType, class Policy>
+inline RealType variance(const fisher_f_distribution<RealType, Policy>& dist)
+{ // Variance of F distribution.
+   static const char* function = "boost::math::variance(fisher_f_distribution<%1%> const&)";
+   RealType df1 = dist.degrees_of_freedom1();
+   RealType df2 = dist.degrees_of_freedom2();
+   // Error check:
+   RealType error_result = 0;
+   if(false == detail::check_df(
+            function, df1, &error_result, Policy())
+         && detail::check_df(
+            function, df2, &error_result, Policy()))
+      return error_result;
+   if(df2 <= 4)
+   {
+      return policies::raise_domain_error<RealType>(
+         function, "Second degree of freedom was %1% but must be > 4 in order for the distribution to have a valid variance.", df2, Policy());
+   }
+   return 2 * df2 * df2 * (df1 + df2 - 2) / (df1 * (df2 - 2) * (df2 - 2) * (df2 - 4));
+} // variance
+
+template <class RealType, class Policy>
+inline RealType mode(const fisher_f_distribution<RealType, Policy>& dist)
+{
+   static const char* function = "boost::math::mode(fisher_f_distribution<%1%> const&)";
+   RealType df1 = dist.degrees_of_freedom1();
+   RealType df2 = dist.degrees_of_freedom2();
+   // Error check:
+   RealType error_result = 0;
+   if(false == detail::check_df(
+            function, df1, &error_result, Policy())
+         && detail::check_df(
+            function, df2, &error_result, Policy()))
+      return error_result;
+   if(df2 <= 2)
+   {
+      return policies::raise_domain_error<RealType>(
+         function, "Second degree of freedom was %1% but must be > 2 in order for the distribution to have a mode.", df2, Policy());
+   }
+   return df2 * (df1 - 2) / (df1 * (df2 + 2));
+}
+
+//template <class RealType, class Policy>
+//inline RealType median(const fisher_f_distribution<RealType, Policy>& dist)
+//{ // Median of Fisher F distribution is not defined.
+//  return tools::domain_error<RealType>(BOOST_CURRENT_FUNCTION, "Median is not implemented, result is %1%!", std::numeric_limits<RealType>::quiet_NaN());
+//  } // median
+
+// Now implemented via quantile(half) in derived accessors.
+
+template <class RealType, class Policy>
+inline RealType skewness(const fisher_f_distribution<RealType, Policy>& dist)
+{
+   static const char* function = "boost::math::skewness(fisher_f_distribution<%1%> const&)";
+   BOOST_MATH_STD_USING // ADL of std names
+   // See http://mathworld.wolfram.com/F-Distribution.html
+   RealType df1 = dist.degrees_of_freedom1();
+   RealType df2 = dist.degrees_of_freedom2();
+   // Error check:
+   RealType error_result = 0;
+   if(false == detail::check_df(
+            function, df1, &error_result, Policy())
+         && detail::check_df(
+            function, df2, &error_result, Policy()))
+      return error_result;
+   if(df2 <= 6)
+   {
+      return policies::raise_domain_error<RealType>(
+         function, "Second degree of freedom was %1% but must be > 6 in order for the distribution to have a skewness.", df2, Policy());
+   }
+   return 2 * (df2 + 2 * df1 - 2) * sqrt((2 * df2 - 8) / (df1 * (df2 + df1 - 2))) / (df2 - 6);
+}
+
+template <class RealType, class Policy>
+RealType kurtosis_excess(const fisher_f_distribution<RealType, Policy>& dist);
+
+template <class RealType, class Policy>
+inline RealType kurtosis(const fisher_f_distribution<RealType, Policy>& dist)
+{
+   return 3 + kurtosis_excess(dist);
+}
+
+template <class RealType, class Policy>
+inline RealType kurtosis_excess(const fisher_f_distribution<RealType, Policy>& dist)
+{
+   static const char* function = "boost::math::kurtosis_excess(fisher_f_distribution<%1%> const&)";
+   // See http://mathworld.wolfram.com/F-Distribution.html
+   RealType df1 = dist.degrees_of_freedom1();
+   RealType df2 = dist.degrees_of_freedom2();
+   // Error check:
+   RealType error_result = 0;
+   if(false == detail::check_df(
+            function, df1, &error_result, Policy())
+         && detail::check_df(
+            function, df2, &error_result, Policy()))
+      return error_result;
+   if(df2 <= 8)
+   {
+      return policies::raise_domain_error<RealType>(
+         function, "Second degree of freedom was %1% but must be > 8 in order for the distribution to have a kutosis.", df2, Policy());
+   }
+   RealType df2_2 = df2 * df2;
+   RealType df1_2 = df1 * df1;
+   RealType n = -16 + 20 * df2 - 8 * df2_2 + df2_2 * df2 + 44 * df1 - 32 * df2 * df1 + 5 * df2_2 * df1 - 22 * df1_2 + 5 * df2 * df1_2;
+   n *= 12;
+   RealType d = df1 * (df2 - 6) * (df2 - 8) * (df1 + df2 - 2);
+   return n / d;
+}
+
+} // 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_DISTRIBUTIONS_FISHER_F_HPP