Added boost header

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

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+// Copyright John Maddock 2010.
+// Copyright Paul A. Bristow 2010.
+
+// 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_INVERSE_CHI_SQUARED_HPP
+#define BOOST_MATH_DISTRIBUTIONS_INVERSE_CHI_SQUARED_HPP
+
+#include <boost/math/distributions/fwd.hpp>
+#include <boost/math/special_functions/gamma.hpp> // for incomplete beta.
+#include <boost/math/distributions/complement.hpp> // for complements.
+#include <boost/math/distributions/detail/common_error_handling.hpp> // for error checks.
+#include <boost/math/special_functions/fpclassify.hpp> // for isfinite
+
+// See http://en.wikipedia.org/wiki/Scaled-inverse-chi-square_distribution
+// for definitions of this scaled version.
+// See http://en.wikipedia.org/wiki/Inverse-chi-square_distribution
+// for unscaled version.
+
+// http://reference.wolfram.com/mathematica/ref/InverseChiSquareDistribution.html
+// Weisstein, Eric W. "Inverse Chi-Squared Distribution." From MathWorld--A Wolfram Web Resource.
+// http://mathworld.wolfram.com/InverseChi-SquaredDistribution.html
+
+#include <utility>
+
+namespace boost{ namespace math{
+
+namespace detail
+{
+  template <class RealType, class Policy>
+  inline bool check_inverse_chi_squared( // Check both distribution parameters.
+        const char* function,
+        RealType degrees_of_freedom, // degrees_of_freedom (aka nu).
+        RealType scale,  // scale (aka sigma^2)
+        RealType* result,
+        const Policy& pol)
+  {
+     return check_scale(function, scale, result, pol)
+       && check_df(function, degrees_of_freedom,
+       result, pol);
+  } // bool check_inverse_chi_squared
+} // namespace detail
+
+template <class RealType = double, class Policy = policies::policy<> >
+class inverse_chi_squared_distribution
+{
+public:
+   typedef RealType value_type;
+   typedef Policy policy_type;
+
+   inverse_chi_squared_distribution(RealType df, RealType scale) : m_df(df), m_scale (scale)
+   {
+      RealType result;
+      detail::check_df(
+         "boost::math::inverse_chi_squared_distribution<%1%>::inverse_chi_squared_distribution",
+         m_df, &result, Policy())
+         && detail::check_scale(
+"boost::math::inverse_chi_squared_distribution<%1%>::inverse_chi_squared_distribution",
+         m_scale, &result,  Policy());
+   } // inverse_chi_squared_distribution constructor 
+
+   inverse_chi_squared_distribution(RealType df = 1) : m_df(df)
+   {
+      RealType result;
+      m_scale = 1 / m_df ; // Default scale = 1 / degrees of freedom (Wikipedia definition 1).
+      detail::check_df(
+         "boost::math::inverse_chi_squared_distribution<%1%>::inverse_chi_squared_distribution",
+         m_df, &result, Policy());
+   } // inverse_chi_squared_distribution
+
+   RealType degrees_of_freedom()const
+   {
+      return m_df; // aka nu
+   }
+   RealType scale()const
+   {
+      return m_scale;  // aka xi
+   }
+
+   // Parameter estimation:  NOT implemented yet.
+   //static RealType find_degrees_of_freedom(
+   //   RealType difference_from_variance,
+   //   RealType alpha,
+   //   RealType beta,
+   //   RealType variance,
+   //   RealType hint = 100);
+
+private:
+   // Data members:
+   RealType m_df;  // degrees of freedom are treated as a real number.
+   RealType m_scale;  // distribution scale.
+
+}; // class chi_squared_distribution
+
+typedef inverse_chi_squared_distribution<double> inverse_chi_squared;
+
+template <class RealType, class Policy>
+inline const std::pair<RealType, RealType> range(const inverse_chi_squared_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>()); // 0 to + infinity.
+}
+
+template <class RealType, class Policy>
+inline const std::pair<RealType, RealType> support(const inverse_chi_squared_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.
+   return std::pair<RealType, RealType>(static_cast<RealType>(0), tools::max_value<RealType>()); // 0 to + infinity.
+}
+
+template <class RealType, class Policy>
+RealType pdf(const inverse_chi_squared_distribution<RealType, Policy>& dist, const RealType& x)
+{
+   BOOST_MATH_STD_USING  // for ADL of std functions.
+   RealType df = dist.degrees_of_freedom();
+   RealType scale = dist.scale();
+   RealType error_result;
+
+   static const char* function = "boost::math::pdf(const inverse_chi_squared_distribution<%1%>&, %1%)";
+
+   if(false == detail::check_inverse_chi_squared
+     (function, df, scale, &error_result, Policy())
+     )
+   { // Bad distribution.
+      return error_result;
+   }
+   if((x < 0) || !(boost::math::isfinite)(x))
+   { // Bad x.
+      return policies::raise_domain_error<RealType>(
+         function, "inverse Chi Square parameter was %1%, but must be >= 0 !", x, Policy());
+   }
+
+   if(x == 0)
+   { // Treat as special case.
+     return 0;
+   }
+   // Wikipedia scaled inverse chi sq (df, scale) related to inv gamma (df/2, df * scale /2) 
+   // so use inverse gamma pdf with shape = df/2, scale df * scale /2 
+   // RealType shape = df /2; // inv_gamma shape
+   // RealType scale = df * scale/2; // inv_gamma scale
+   // RealType result = gamma_p_derivative(shape, scale / x, Policy()) * scale / (x * x);
+   RealType result = df * scale/2 / x;
+   if(result < tools::min_value<RealType>())
+      return 0; // Random variable is near enough infinite.
+   result = gamma_p_derivative(df/2, result, Policy()) * df * scale/2;
+   if(result != 0) // prevent 0 / 0,  gamma_p_derivative -> 0 faster than x^2
+      result /= (x * x);
+   return result;
+} // pdf
+
+template <class RealType, class Policy>
+inline RealType cdf(const inverse_chi_squared_distribution<RealType, Policy>& dist, const RealType& x)
+{
+   static const char* function = "boost::math::cdf(const inverse_chi_squared_distribution<%1%>&, %1%)";
+   RealType df = dist.degrees_of_freedom();
+   RealType scale = dist.scale();
+   RealType error_result;
+
+   if(false ==
+       detail::check_inverse_chi_squared(function, df, scale, &error_result, Policy())
+     )
+   { // Bad distribution.
+      return error_result;
+   }
+   if((x < 0) || !(boost::math::isfinite)(x))
+   { // Bad x.
+      return policies::raise_domain_error<RealType>(
+         function, "inverse Chi Square parameter was %1%, but must be >= 0 !", x, Policy());
+   }
+   if (x == 0)
+   { // Treat zero as a special case.
+     return 0;
+   }
+   // RealType shape = df /2; // inv_gamma shape,
+   // RealType scale = df * scale/2; // inv_gamma scale,
+   // result = boost::math::gamma_q(shape, scale / x, Policy()); // inverse_gamma code.
+   return boost::math::gamma_q(df / 2, (df * (scale / 2)) / x, Policy());
+} // cdf
+
+template <class RealType, class Policy>
+inline RealType quantile(const inverse_chi_squared_distribution<RealType, Policy>& dist, const RealType& p)
+{
+   using boost::math::gamma_q_inv;
+   RealType df = dist.degrees_of_freedom();
+   RealType scale = dist.scale();
+
+   static const char* function = "boost::math::quantile(const inverse_chi_squared_distribution<%1%>&, %1%)";
+   // Error check:
+   RealType error_result;
+   if(false == detail::check_df(
+         function, df, &error_result, Policy())
+         && detail::check_probability(
+            function, p, &error_result, Policy()))
+   {
+      return error_result;
+   }
+   if(false == detail::check_probability(
+            function, p, &error_result, Policy()))
+   {
+      return error_result;
+   }
+   // RealType shape = df /2; // inv_gamma shape,
+   // RealType scale = df * scale/2; // inv_gamma scale,
+   // result = scale / gamma_q_inv(shape, p, Policy());
+      RealType result = gamma_q_inv(df /2, p, Policy());
+      if(result == 0)
+         return policies::raise_overflow_error<RealType, Policy>(function, "Random variable is infinite.", Policy());
+      result = df * (scale / 2) / result;
+      return result;
+} // quantile
+
+template <class RealType, class Policy>
+inline RealType cdf(const complemented2_type<inverse_chi_squared_distribution<RealType, Policy>, RealType>& c)
+{
+   using boost::math::gamma_q_inv;
+   RealType const& df = c.dist.degrees_of_freedom();
+   RealType const& scale = c.dist.scale();
+   RealType const& x = c.param;
+   static const char* function = "boost::math::cdf(const inverse_chi_squared_distribution<%1%>&, %1%)";
+   // Error check:
+   RealType error_result;
+   if(false == detail::check_df(
+         function, df, &error_result, Policy()))
+   {
+      return error_result;
+   }
+   if (x == 0)
+   { // Treat zero as a special case.
+     return 1;
+   }
+   if((x < 0) || !(boost::math::isfinite)(x))
+   {
+      return policies::raise_domain_error<RealType>(
+         function, "inverse Chi Square parameter was %1%, but must be > 0 !", x, Policy());
+   }
+   // RealType shape = df /2; // inv_gamma shape,
+   // RealType scale = df * scale/2; // inv_gamma scale,
+   // result = gamma_p(shape, scale/c.param, Policy()); use inv_gamma.
+
+   return gamma_p(df / 2, (df * scale/2) / x, Policy()); // OK
+} // cdf(complemented
+
+template <class RealType, class Policy>
+inline RealType quantile(const complemented2_type<inverse_chi_squared_distribution<RealType, Policy>, RealType>& c)
+{
+   using boost::math::gamma_q_inv;
+
+   RealType const& df = c.dist.degrees_of_freedom();
+   RealType const& scale = c.dist.scale();
+   RealType const& q = c.param;
+   static const char* function = "boost::math::quantile(const inverse_chi_squared_distribution<%1%>&, %1%)";
+   // Error check:
+   RealType error_result;
+   if(false == detail::check_df(function, df, &error_result, Policy()))
+   {
+      return error_result;
+   }
+   if(false == detail::check_probability(function, q, &error_result, Policy()))
+   {
+      return error_result;
+   }
+   // RealType shape = df /2; // inv_gamma shape,
+   // RealType scale = df * scale/2; // inv_gamma scale,
+   // result = scale / gamma_p_inv(shape, q, Policy());  // using inv_gamma.
+   RealType result = gamma_p_inv(df/2, q, Policy());
+   if(result == 0)
+      return policies::raise_overflow_error<RealType, Policy>(function, "Random variable is infinite.", Policy());
+   result = (df * scale / 2) / result;
+   return result;
+} // quantile(const complement
+
+template <class RealType, class Policy>
+inline RealType mean(const inverse_chi_squared_distribution<RealType, Policy>& dist)
+{ // Mean of inverse Chi-Squared distribution.
+   RealType df = dist.degrees_of_freedom();
+   RealType scale = dist.scale();
+
+   static const char* function = "boost::math::mean(const inverse_chi_squared_distribution<%1%>&)";
+   if(df <= 2)
+      return policies::raise_domain_error<RealType>(
+         function,
+         "inverse Chi-Squared distribution only has a mode for degrees of freedom > 2, but got degrees of freedom = %1%.",
+         df, Policy());
+  return (df * scale) / (df - 2);
+} // mean
+
+template <class RealType, class Policy>
+inline RealType variance(const inverse_chi_squared_distribution<RealType, Policy>& dist)
+{ // Variance of inverse Chi-Squared distribution.
+   RealType df = dist.degrees_of_freedom();
+   RealType scale = dist.scale();
+   static const char* function = "boost::math::variance(const inverse_chi_squared_distribution<%1%>&)";
+   if(df <= 4)
+   {
+      return policies::raise_domain_error<RealType>(
+         function,
+         "inverse Chi-Squared distribution only has a variance for degrees of freedom > 4, but got degrees of freedom = %1%.",
+         df, Policy());
+   }
+   return 2 * df * df * scale * scale / ((df - 2)*(df - 2) * (df - 4));
+} // variance
+
+template <class RealType, class Policy>
+inline RealType mode(const inverse_chi_squared_distribution<RealType, Policy>& dist)
+{ // mode is not defined in Mathematica.
+  // See Discussion section http://en.wikipedia.org/wiki/Talk:Scaled-inverse-chi-square_distribution
+  // for origin of the formula used below.
+
+   RealType df = dist.degrees_of_freedom();
+   RealType scale = dist.scale();
+   static const char* function = "boost::math::mode(const inverse_chi_squared_distribution<%1%>&)";
+   if(df < 0)
+      return policies::raise_domain_error<RealType>(
+         function,
+         "inverse Chi-Squared distribution only has a mode for degrees of freedom >= 0, but got degrees of freedom = %1%.",
+         df, Policy());
+   return (df * scale) / (df + 2);
+}
+
+//template <class RealType, class Policy>
+//inline RealType median(const inverse_chi_squared_distribution<RealType, Policy>& dist)
+//{ // Median is given by Quantile[dist, 1/2]
+//   RealType df = dist.degrees_of_freedom();
+//   if(df <= 1)
+//      return tools::domain_error<RealType>(
+//         BOOST_CURRENT_FUNCTION,
+//         "The inverse_Chi-Squared distribution only has a median for degrees of freedom >= 0, but got degrees of freedom = %1%.",
+//         df);
+//   return df;
+//}
+// Now implemented via quantile(half) in derived accessors.
+
+template <class RealType, class Policy>
+inline RealType skewness(const inverse_chi_squared_distribution<RealType, Policy>& dist)
+{
+   BOOST_MATH_STD_USING // For ADL
+   RealType df = dist.degrees_of_freedom();
+   static const char* function = "boost::math::skewness(const inverse_chi_squared_distribution<%1%>&)";
+   if(df <= 6)
+      return policies::raise_domain_error<RealType>(
+         function,
+         "inverse Chi-Squared distribution only has a skewness for degrees of freedom > 6, but got degrees of freedom = %1%.",
+         df, Policy());
+
+   return 4 * sqrt (2 * (df - 4)) / (df - 6);  // Not a function of scale.
+}
+
+template <class RealType, class Policy>
+inline RealType kurtosis(const inverse_chi_squared_distribution<RealType, Policy>& dist)
+{
+   RealType df = dist.degrees_of_freedom();
+   static const char* function = "boost::math::kurtosis(const inverse_chi_squared_distribution<%1%>&)";
+   if(df <= 8)
+      return policies::raise_domain_error<RealType>(
+         function,
+         "inverse Chi-Squared distribution only has a kurtosis for degrees of freedom > 8, but got degrees of freedom = %1%.",
+         df, Policy());
+
+   return kurtosis_excess(dist) + 3;
+}
+
+template <class RealType, class Policy>
+inline RealType kurtosis_excess(const inverse_chi_squared_distribution<RealType, Policy>& dist)
+{
+   RealType df = dist.degrees_of_freedom();
+   static const char* function = "boost::math::kurtosis(const inverse_chi_squared_distribution<%1%>&)";
+   if(df <= 8)
+      return policies::raise_domain_error<RealType>(
+         function,
+         "inverse Chi-Squared distribution only has a kurtosis excess for degrees of freedom > 8, but got degrees of freedom = %1%.",
+         df, Policy());
+
+   return 12 * (5 * df - 22) / ((df - 6 )*(df - 8));  // Not a function of scale.
+}
+
+//
+// Parameter estimation comes last:
+//
+
+} // 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_INVERSE_CHI_SQUARED_HPP