diff any/include/boost/math/distributions/arcsine.hpp @ 160:cff480c41f97

Add some cross-platform Boost headers

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/any/include/boost/math/distributions/arcsine.hpp	Sat Feb 16 16:31:25 2019 +0000
@@ -0,0 +1,535 @@
+// boost/math/distributions/arcsine.hpp
+
+// Copyright John Maddock 2014.
+// Copyright Paul A. Bristow 2014.
+
+// 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)
+
+// http://en.wikipedia.org/wiki/arcsine_distribution
+
+// The arcsine Distribution is a continuous probability distribution.
+// http://en.wikipedia.org/wiki/Arcsine_distribution
+// http://www.wolframalpha.com/input/?i=ArcSinDistribution
+
+// Standard arcsine distribution is a special case of beta distribution with both a & b = one half,
+// and 0 <= x <= 1.
+
+// It is generalized to include any bounded support a <= x <= b from 0 <= x <= 1
+// by Wolfram and Wikipedia,
+// but using location and scale parameters by
+// Virtual Laboratories in Probability and Statistics http://www.math.uah.edu/stat/index.html
+// http://www.math.uah.edu/stat/special/Arcsine.html
+// The end-point version is simpler and more obvious, so we implement that.
+// TODO Perhaps provide location and scale functions?
+
+
+#ifndef BOOST_MATH_DIST_ARCSINE_HPP
+#define BOOST_MATH_DIST_ARCSINE_HPP
+
+#include <boost/math/distributions/fwd.hpp>
+#include <boost/math/distributions/complement.hpp> // complements.
+#include <boost/math/distributions/detail/common_error_handling.hpp> // error checks.
+#include <boost/math/constants/constants.hpp>
+
+#include <boost/math/special_functions/fpclassify.hpp> // isnan.
+
+#if defined (BOOST_MSVC)
+#  pragma warning(push)
+#  pragma warning(disable: 4702) // Unreachable code,
+// in domain_error_imp in error_handling.
+#endif
+
+#include <utility>
+#include <exception>  // For std::domain_error.
+
+namespace boost
+{
+  namespace math
+  {
+    namespace arcsine_detail
+    {
+      // Common error checking routines for arcsine distribution functions:
+      // Duplicating for x_min and x_max provides specific error messages.
+      template <class RealType, class Policy>
+      inline bool check_x_min(const char* function, const RealType& x, RealType* result, const Policy& pol)
+      {
+        if (!(boost::math::isfinite)(x))
+        {
+          *result = policies::raise_domain_error<RealType>(
+            function,
+            "x_min argument is %1%, but must be finite !", x, pol);
+          return false;
+        }
+        return true;
+      } // bool check_x_min
+
+      template <class RealType, class Policy>
+      inline bool check_x_max(const char* function, const RealType& x, RealType* result, const Policy& pol)
+      {
+        if (!(boost::math::isfinite)(x))
+        {
+          *result = policies::raise_domain_error<RealType>(
+            function,
+            "x_max argument is %1%, but must be finite !", x, pol);
+          return false;
+        }
+        return true;
+      } // bool check_x_max
+
+
+      template <class RealType, class Policy>
+      inline bool check_x_minmax(const char* function, const RealType& x_min, const RealType& x_max, RealType* result, const Policy& pol)
+      { // Check x_min < x_max
+        if (x_min >= x_max)
+        {
+          std::string msg = "x_max argument is %1%, but must be > x_min = " + lexical_cast<std::string>(x_min) + "!";
+          *result = policies::raise_domain_error<RealType>(
+            function,
+            msg.c_str(), x_max, pol);
+           // "x_max argument is %1%, but must be > x_min !", x_max, pol);
+            //  "x_max argument is %1%, but must be > x_min %2!", x_max, x_min, pol); would be better. 
+          // But would require replication of all helpers functions in /policies/error_handling.hpp for two values,
+          // as well as two value versions of raise_error, raise_domain_error and do_format ...
+          // so use slightly hacky lexical_cast to string instead.
+          return false;
+        }
+        return true;
+      } // bool check_x_minmax
+
+      template <class RealType, class Policy>
+      inline bool check_prob(const char* function, const RealType& p, RealType* result, const Policy& pol)
+      {
+        if ((p < 0) || (p > 1) || !(boost::math::isfinite)(p))
+        {
+          *result = policies::raise_domain_error<RealType>(
+            function,
+            "Probability argument is %1%, but must be >= 0 and <= 1 !", p, pol);
+          return false;
+        }
+        return true;
+      } // bool check_prob
+
+      template <class RealType, class Policy>
+      inline bool check_x(const char* function, const RealType& x_min, const RealType& x_max, const RealType& x, RealType* result, const Policy& pol)
+      { // Check x finite and x_min < x < x_max.
+        if (!(boost::math::isfinite)(x))
+        {
+          *result = policies::raise_domain_error<RealType>(
+            function,
+            "x argument is %1%, but must be finite !", x, pol);
+          return false;
+        }
+        if ((x < x_min) || (x > x_max))
+        {
+          // std::cout << x_min << ' ' << x << x_max << std::endl;
+          *result = policies::raise_domain_error<RealType>(
+            function,
+            "x argument is %1%, but must be x_min < x < x_max !", x, pol);
+          // For example:
+          // Error in function boost::math::pdf(arcsine_distribution<double> const&, double) : x argument is -1.01, but must be x_min < x < x_max !
+          // TODO Perhaps show values of x_min and x_max?
+          return false;
+        }
+        return true;
+      } // bool check_x
+
+      template <class RealType, class Policy>
+      inline bool check_dist(const char* function, const RealType& x_min, const RealType& x_max, RealType* result, const Policy& pol)
+      { // Check both x_min and x_max finite, and x_min  < x_max.
+        return check_x_min(function, x_min, result, pol)
+            && check_x_max(function, x_max, result, pol)
+            && check_x_minmax(function, x_min, x_max, result, pol);
+      } // bool check_dist
+
+      template <class RealType, class Policy>
+      inline bool check_dist_and_x(const char* function, const RealType& x_min, const RealType& x_max, RealType x, RealType* result, const Policy& pol)
+      {
+        return check_dist(function, x_min, x_max, result, pol)
+          && arcsine_detail::check_x(function, x_min, x_max, x, result, pol);
+      } // bool check_dist_and_x
+
+      template <class RealType, class Policy>
+      inline bool check_dist_and_prob(const char* function, const RealType& x_min, const RealType& x_max, RealType p, RealType* result, const Policy& pol)
+      {
+        return check_dist(function, x_min, x_max, result, pol)
+          && check_prob(function, p, result, pol);
+      } // bool check_dist_and_prob
+
+    } // namespace arcsine_detail
+
+    template <class RealType = double, class Policy = policies::policy<> >
+    class arcsine_distribution
+    {
+    public:
+      typedef RealType value_type;
+      typedef Policy policy_type;
+
+      arcsine_distribution(RealType x_min = 0, RealType x_max = 1) : m_x_min(x_min), m_x_max(x_max)
+      { // Default beta (alpha = beta = 0.5) is standard arcsine with x_min = 0, x_max = 1.
+        // Generalized to allow x_min and x_max to be specified.
+        RealType result;
+        arcsine_detail::check_dist(
+          "boost::math::arcsine_distribution<%1%>::arcsine_distribution",
+          m_x_min,
+          m_x_max,
+          &result, Policy());
+      } // arcsine_distribution constructor.
+      // Accessor functions:
+      RealType x_min() const
+      {
+        return m_x_min;
+      }
+      RealType x_max() const
+      {
+        return m_x_max;
+      }
+
+    private:
+      RealType m_x_min; // Two x min and x max parameters of the arcsine distribution.
+      RealType m_x_max;
+    }; // template <class RealType, class Policy> class arcsine_distribution
+
+    // Convenient typedef to construct double version.
+    typedef arcsine_distribution<double> arcsine;
+
+
+    template <class RealType, class Policy>
+    inline const std::pair<RealType, RealType> range(const arcsine_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>(dist.x_min()), static_cast<RealType>(dist.x_max()));
+    }
+
+    template <class RealType, class Policy>
+    inline const std::pair<RealType, RealType> support(const arcsine_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>(dist.x_min()), static_cast<RealType>(dist.x_max()));
+    }
+
+    template <class RealType, class Policy>
+    inline RealType mean(const arcsine_distribution<RealType, Policy>& dist)
+    { // Mean of arcsine distribution .
+      RealType result;
+      RealType x_min = dist.x_min();
+      RealType x_max = dist.x_max();
+
+      if (false == arcsine_detail::check_dist(
+        "boost::math::mean(arcsine_distribution<%1%> const&, %1% )",
+        x_min,
+        x_max,
+        &result, Policy())
+        )
+      {
+        return result;
+      }
+      return  (x_min + x_max) / 2;
+    } // mean
+
+    template <class RealType, class Policy>
+    inline RealType variance(const arcsine_distribution<RealType, Policy>& dist)
+    { // Variance of standard arcsine distribution = (1-0)/8 = 0.125.
+      RealType result;
+      RealType x_min = dist.x_min();
+      RealType x_max = dist.x_max();
+      if (false == arcsine_detail::check_dist(
+        "boost::math::variance(arcsine_distribution<%1%> const&, %1% )",
+        x_min,
+        x_max,
+        &result, Policy())
+        )
+      {
+        return result;
+      }
+      return  (x_max - x_min) * (x_max - x_min) / 8;
+    } // variance
+
+    template <class RealType, class Policy>
+    inline RealType mode(const arcsine_distribution<RealType, Policy>& /* dist */)
+    { //There are always [*two] values for the mode, at ['x_min] and at ['x_max], default 0 and 1,
+      // so instead we raise the exception domain_error.
+      return policies::raise_domain_error<RealType>(
+        "boost::math::mode(arcsine_distribution<%1%>&)",
+        "The arcsine distribution has two modes at x_min and x_max: "
+        "so the return value is %1%.",
+        std::numeric_limits<RealType>::quiet_NaN(), Policy());
+    } // mode
+
+    template <class RealType, class Policy>
+    inline RealType median(const arcsine_distribution<RealType, Policy>& dist)
+    { // Median of arcsine distribution (a + b) / 2 == mean.
+      RealType x_min = dist.x_min();
+      RealType x_max = dist.x_max();
+      RealType result;
+      if (false == arcsine_detail::check_dist(
+        "boost::math::median(arcsine_distribution<%1%> const&, %1% )",
+        x_min,
+        x_max,
+        &result, Policy())
+        )
+      {
+        return result;
+      }
+      return  (x_min + x_max) / 2;
+    }
+
+    template <class RealType, class Policy>
+    inline RealType skewness(const arcsine_distribution<RealType, Policy>& dist)
+    {
+      RealType result;
+      RealType x_min = dist.x_min();
+      RealType x_max = dist.x_max();
+
+      if (false == arcsine_detail::check_dist(
+        "boost::math::skewness(arcsine_distribution<%1%> const&, %1% )",
+        x_min,
+        x_max,
+        &result, Policy())
+        )
+      {
+        return result;
+      }
+      return 0;
+    } // skewness
+
+    template <class RealType, class Policy>
+    inline RealType kurtosis_excess(const arcsine_distribution<RealType, Policy>& dist)
+    {
+      RealType result;
+      RealType x_min = dist.x_min();
+      RealType x_max = dist.x_max();
+
+      if (false == arcsine_detail::check_dist(
+        "boost::math::kurtosis_excess(arcsine_distribution<%1%> const&, %1% )",
+        x_min,
+        x_max,
+        &result, Policy())
+        )
+      {
+        return result;
+      }
+      result = -3;
+      return  result / 2;
+    } // kurtosis_excess
+
+    template <class RealType, class Policy>
+    inline RealType kurtosis(const arcsine_distribution<RealType, Policy>& dist)
+    {
+      RealType result;
+      RealType x_min = dist.x_min();
+      RealType x_max = dist.x_max();
+
+      if (false == arcsine_detail::check_dist(
+        "boost::math::kurtosis(arcsine_distribution<%1%> const&, %1% )",
+        x_min,
+        x_max,
+        &result, Policy())
+        )
+      {
+        return result;
+      }
+
+      return 3 + kurtosis_excess(dist);
+    } // kurtosis
+
+    template <class RealType, class Policy>
+    inline RealType pdf(const arcsine_distribution<RealType, Policy>& dist, const RealType& xx)
+    { // Probability Density/Mass Function arcsine.
+      BOOST_FPU_EXCEPTION_GUARD
+      BOOST_MATH_STD_USING // For ADL of std functions.
+
+      static const char* function = "boost::math::pdf(arcsine_distribution<%1%> const&, %1%)";
+
+      RealType lo = dist.x_min();
+      RealType hi = dist.x_max();
+      RealType x = xx;
+
+      // Argument checks:
+      RealType result = 0; 
+      if (false == arcsine_detail::check_dist_and_x(
+        function,
+        lo, hi, x,
+        &result, Policy()))
+      {
+        return result;
+      }
+      using boost::math::constants::pi;
+      result = static_cast<RealType>(1) / (pi<RealType>() * sqrt((x - lo) * (hi - x)));
+      return result;
+    } // pdf
+
+    template <class RealType, class Policy>
+    inline RealType cdf(const arcsine_distribution<RealType, Policy>& dist, const RealType& x)
+    { // Cumulative Distribution Function arcsine.
+      BOOST_MATH_STD_USING // For ADL of std functions.
+
+      static const char* function = "boost::math::cdf(arcsine_distribution<%1%> const&, %1%)";
+
+      RealType x_min = dist.x_min();
+      RealType x_max = dist.x_max();
+
+      // Argument checks:
+      RealType result = 0;
+      if (false == arcsine_detail::check_dist_and_x(
+        function,
+        x_min, x_max, x,
+        &result, Policy()))
+      {
+        return result;
+      }
+      // Special cases:
+      if (x == x_min)
+      {
+        return 0;
+      }
+      else if (x == x_max)
+      {
+        return 1;
+      }
+      using boost::math::constants::pi;
+      result = static_cast<RealType>(2) * asin(sqrt((x - x_min) / (x_max - x_min))) / pi<RealType>();
+      return result;
+    } // arcsine cdf
+
+    template <class RealType, class Policy>
+    inline RealType cdf(const complemented2_type<arcsine_distribution<RealType, Policy>, RealType>& c)
+    { // Complemented Cumulative Distribution Function arcsine.
+      BOOST_MATH_STD_USING // For ADL of std functions.
+      static const char* function = "boost::math::cdf(arcsine_distribution<%1%> const&, %1%)";
+
+      RealType x = c.param;
+      arcsine_distribution<RealType, Policy> const& dist = c.dist;
+      RealType x_min = dist.x_min();
+      RealType x_max = dist.x_max();
+
+      // Argument checks:
+      RealType result = 0;
+      if (false == arcsine_detail::check_dist_and_x(
+        function,
+        x_min, x_max, x,
+        &result, Policy()))
+      {
+        return result;
+      }
+      if (x == x_min)
+      {
+        return 0;
+      }
+      else if (x == x_max)
+      {
+        return 1;
+      }
+      using boost::math::constants::pi;
+      // Naive version x = 1 - x;
+      // result = static_cast<RealType>(2) * asin(sqrt((x - x_min) / (x_max - x_min))) / pi<RealType>();
+      // is less accurate, so use acos instead of asin for complement.
+      result = static_cast<RealType>(2) * acos(sqrt((x - x_min) / (x_max - x_min))) / pi<RealType>();
+      return result;
+    } // arcine ccdf
+
+    template <class RealType, class Policy>
+    inline RealType quantile(const arcsine_distribution<RealType, Policy>& dist, const RealType& p)
+    { 
+      // Quantile or Percent Point arcsine function or
+      // Inverse Cumulative probability distribution function CDF.
+      // Return x (0 <= x <= 1),
+      // for a given probability p (0 <= p <= 1).
+      // These functions take a probability as an argument
+      // and return a value such that the probability that a random variable x
+      // will be less than or equal to that value
+      // is whatever probability you supplied as an argument.
+      BOOST_MATH_STD_USING // For ADL of std functions.
+
+      using boost::math::constants::half_pi;
+
+      static const char* function = "boost::math::quantile(arcsine_distribution<%1%> const&, %1%)";
+
+      RealType result = 0; // of argument checks:
+      RealType x_min = dist.x_min();
+      RealType x_max = dist.x_max();
+      if (false == arcsine_detail::check_dist_and_prob(
+        function,
+        x_min, x_max, p,
+        &result, Policy()))
+      {
+        return result;
+      }
+      // Special cases:
+      if (p == 0)
+      {
+        return 0;
+      }
+      if (p == 1)
+      {
+        return 1;
+      }
+
+      RealType sin2hpip = sin(half_pi<RealType>() * p);
+      RealType sin2hpip2 = sin2hpip * sin2hpip;
+      result = -x_min * sin2hpip2 + x_min + x_max * sin2hpip2;
+
+      return result;
+    } // quantile
+
+    template <class RealType, class Policy>
+    inline RealType quantile(const complemented2_type<arcsine_distribution<RealType, Policy>, RealType>& c)
+    { 
+      // Complement Quantile or Percent Point arcsine function.
+      // Return the number of expected x for a given
+      // complement of the probability q.
+      BOOST_MATH_STD_USING // For ADL of std functions.
+
+      using boost::math::constants::half_pi;
+      static const char* function = "boost::math::quantile(arcsine_distribution<%1%> const&, %1%)";
+
+      // Error checks:
+      RealType q = c.param;
+      const arcsine_distribution<RealType, Policy>& dist = c.dist;
+      RealType result = 0;
+      RealType x_min = dist.x_min();
+      RealType x_max = dist.x_max();
+      if (false == arcsine_detail::check_dist_and_prob(
+        function,
+        x_min,
+        x_max,
+        q,
+        &result, Policy()))
+      {
+        return result;
+      }
+      // Special cases:
+      if (q == 1)
+      {
+        return 0;
+      }
+      if (q == 0)
+      {
+        return 1;
+      }
+      // Naive RealType p = 1 - q; result = sin(half_pi<RealType>() * p); loses accuracy, so use a cos alternative instead.
+      //result = cos(half_pi<RealType>() * q); // for arcsine(0,1)
+      //result = result * result;
+      // For generalized arcsine:
+      RealType cos2hpip = cos(half_pi<RealType>() * q);
+      RealType cos2hpip2 = cos2hpip * cos2hpip;
+      result = -x_min * cos2hpip2 + x_min + x_max * cos2hpip2;
+
+      return result;
+    } // 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>
+
+#if defined (BOOST_MSVC)
+# pragma warning(pop)
+#endif
+
+#endif // BOOST_MATH_DIST_ARCSINE_HPP