diff any/include/boost/math/distributions/triangular.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/triangular.hpp	Sat Feb 16 16:31:25 2019 +0000
@@ -0,0 +1,531 @@
+//  Copyright John Maddock 2006, 2007.
+//  Copyright Paul A. Bristow 2006, 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_TRIANGULAR_HPP
+#define BOOST_STATS_TRIANGULAR_HPP
+
+// http://mathworld.wolfram.com/TriangularDistribution.html
+// Note that the 'constructors' defined by Wolfram are difference from those here,
+// for example
+// N[variance[triangulardistribution{1, +2}, 1.5], 50] computes 
+// 0.041666666666666666666666666666666666666666666666667
+// TriangularDistribution{1, +2}, 1.5 is the analog of triangular_distribution(1, 1.5, 2)
+
+// http://en.wikipedia.org/wiki/Triangular_distribution
+
+#include <boost/math/distributions/fwd.hpp>
+#include <boost/math/special_functions/expm1.hpp>
+#include <boost/math/distributions/detail/common_error_handling.hpp>
+#include <boost/math/distributions/complement.hpp>
+#include <boost/math/constants/constants.hpp>
+
+#include <utility>
+
+namespace boost{ namespace math
+{
+  namespace detail
+  {
+    template <class RealType, class Policy>
+    inline bool check_triangular_lower(
+      const char* function,
+      RealType lower,
+      RealType* result, const Policy& pol)
+    {
+      if((boost::math::isfinite)(lower))
+      { // Any finite value is OK.
+        return true;
+      }
+      else
+      { // Not finite: infinity or NaN.
+        *result = policies::raise_domain_error<RealType>(
+          function,
+          "Lower parameter is %1%, but must be finite!", lower, pol);
+        return false;
+      }
+    } // bool check_triangular_lower(
+
+    template <class RealType, class Policy>
+    inline bool check_triangular_mode(
+      const char* function,
+      RealType mode,
+      RealType* result, const Policy& pol)
+    {
+      if((boost::math::isfinite)(mode))
+      { // any finite value is OK.
+        return true;
+      }
+      else
+      { // Not finite: infinity or NaN.
+        *result = policies::raise_domain_error<RealType>(
+          function,
+          "Mode parameter is %1%, but must be finite!", mode, pol);
+        return false;
+      }
+    } // bool check_triangular_mode(
+
+    template <class RealType, class Policy>
+    inline bool check_triangular_upper(
+      const char* function,
+      RealType upper,
+      RealType* result, const Policy& pol)
+    {
+      if((boost::math::isfinite)(upper))
+      { // any finite value is OK.
+        return true;
+      }
+      else
+      { // Not finite: infinity or NaN.
+        *result = policies::raise_domain_error<RealType>(
+          function,
+          "Upper parameter is %1%, but must be finite!", upper, pol);
+        return false;
+      }
+    } // bool check_triangular_upper(
+
+    template <class RealType, class Policy>
+    inline bool check_triangular_x(
+      const char* function,
+      RealType const& x,
+      RealType* result, const Policy& pol)
+    {
+      if((boost::math::isfinite)(x))
+      { // Any finite value is OK
+        return true;
+      }
+      else
+      { // Not finite: infinity or NaN.
+        *result = policies::raise_domain_error<RealType>(
+          function,
+          "x parameter is %1%, but must be finite!", x, pol);
+        return false;
+      }
+    } // bool check_triangular_x
+
+    template <class RealType, class Policy>
+    inline bool check_triangular(
+      const char* function,
+      RealType lower,
+      RealType mode,
+      RealType upper,
+      RealType* result, const Policy& pol)
+    {
+      if ((check_triangular_lower(function, lower, result, pol) == false)
+        || (check_triangular_mode(function, mode, result, pol) == false)
+        || (check_triangular_upper(function, upper, result, pol) == false))
+      { // Some parameter not finite.
+        return false;
+      }
+      else if (lower >= upper) // lower == upper NOT useful.
+      { // lower >= upper.
+        *result = policies::raise_domain_error<RealType>(
+          function,
+          "lower parameter is %1%, but must be less than upper!", lower, pol);
+        return false;
+      }
+      else
+      { // Check lower <= mode <= upper.
+        if (mode < lower)
+        {
+          *result = policies::raise_domain_error<RealType>(
+            function,
+            "mode parameter is %1%, but must be >= than lower!", lower, pol);
+          return false;
+        }
+        if (mode > upper)
+        {
+          *result = policies::raise_domain_error<RealType>(
+            function,
+            "mode parameter is %1%, but must be <= than upper!", upper, pol);
+          return false;
+        }
+        return true; // All OK.
+      }
+    } // bool check_triangular
+  } // namespace detail
+
+  template <class RealType = double, class Policy = policies::policy<> >
+  class triangular_distribution
+  {
+  public:
+    typedef RealType value_type;
+    typedef Policy policy_type;
+
+    triangular_distribution(RealType l_lower = -1, RealType l_mode = 0, RealType l_upper = 1)
+      : m_lower(l_lower), m_mode(l_mode), m_upper(l_upper) // Constructor.
+    { // Evans says 'standard triangular' is lower 0, mode 1/2, upper 1,
+      // has median sqrt(c/2) for c <=1/2 and 1 - sqrt(1-c)/2 for c >= 1/2
+      // But this -1, 0, 1 is more useful in most applications to approximate normal distribution,
+      // where the central value is the most likely and deviations either side equally likely.
+      RealType result;
+      detail::check_triangular("boost::math::triangular_distribution<%1%>::triangular_distribution",l_lower, l_mode, l_upper, &result, Policy());
+    }
+    // Accessor functions.
+    RealType lower()const
+    {
+      return m_lower;
+    }
+    RealType mode()const
+    {
+      return m_mode;
+    }
+    RealType upper()const
+    {
+      return m_upper;
+    }
+  private:
+    // Data members:
+    RealType m_lower;  // distribution lower aka a
+    RealType m_mode;  // distribution mode aka c
+    RealType m_upper;  // distribution upper aka b
+  }; // class triangular_distribution
+
+  typedef triangular_distribution<double> triangular;
+
+  template <class RealType, class Policy>
+  inline const std::pair<RealType, RealType> range(const triangular_distribution<RealType, Policy>& /* dist */)
+  { // Range of permissible values for random variable x.
+    using boost::math::tools::max_value;
+    return std::pair<RealType, RealType>(-max_value<RealType>(), max_value<RealType>());
+  }
+
+  template <class RealType, class Policy>
+  inline const std::pair<RealType, RealType> support(const triangular_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>(dist.lower(), dist.upper());
+  }
+
+  template <class RealType, class Policy>
+  RealType pdf(const triangular_distribution<RealType, Policy>& dist, const RealType& x)
+  {
+    static const char* function = "boost::math::pdf(const triangular_distribution<%1%>&, %1%)";
+    RealType lower = dist.lower();
+    RealType mode = dist.mode();
+    RealType upper = dist.upper();
+    RealType result = 0; // of checks.
+    if(false == detail::check_triangular(function, lower, mode, upper, &result, Policy()))
+    {
+      return result;
+    }
+    if(false == detail::check_triangular_x(function, x, &result, Policy()))
+    {
+      return result;
+    }
+    if((x < lower) || (x > upper))
+    {
+      return 0;
+    }
+    if (x == lower)
+    { // (mode - lower) == 0 which would lead to divide by zero!
+      return (mode == lower) ? 2 / (upper - lower) : RealType(0);
+    }
+    else if (x == upper)
+    {
+      return (mode == upper) ? 2 / (upper - lower) : RealType(0);
+    }
+    else if (x <= mode)
+    {
+      return 2 * (x - lower) / ((upper - lower) * (mode - lower));
+    }
+    else
+    {  // (x > mode)
+      return 2 * (upper - x) / ((upper - lower) * (upper - mode));
+    }
+  } // RealType pdf(const triangular_distribution<RealType, Policy>& dist, const RealType& x)
+
+  template <class RealType, class Policy>
+  inline RealType cdf(const triangular_distribution<RealType, Policy>& dist, const RealType& x)
+  {
+    static const char* function = "boost::math::cdf(const triangular_distribution<%1%>&, %1%)";
+    RealType lower = dist.lower();
+    RealType mode = dist.mode();
+    RealType upper = dist.upper();
+    RealType result = 0; // of checks.
+    if(false == detail::check_triangular(function, lower, mode, upper, &result, Policy()))
+    {
+      return result;
+    }
+    if(false == detail::check_triangular_x(function, x, &result, Policy()))
+    {
+      return result;
+    }
+    if((x <= lower))
+    {
+      return 0;
+    }
+    if (x >= upper)
+    {
+      return 1;
+    }
+    // else lower < x < upper
+    if (x <= mode)
+    {
+      return ((x - lower) * (x - lower)) / ((upper - lower) * (mode - lower));
+    }
+    else
+    {
+      return 1 - (upper - x) *  (upper - x) / ((upper - lower) * (upper - mode));
+    }
+  } // RealType cdf(const triangular_distribution<RealType, Policy>& dist, const RealType& x)
+
+  template <class RealType, class Policy>
+  RealType quantile(const triangular_distribution<RealType, Policy>& dist, const RealType& p)
+  {
+    BOOST_MATH_STD_USING  // for ADL of std functions (sqrt).
+    static const char* function = "boost::math::quantile(const triangular_distribution<%1%>&, %1%)";
+    RealType lower = dist.lower();
+    RealType mode = dist.mode();
+    RealType upper = dist.upper();
+    RealType result = 0; // of checks
+    if(false == detail::check_triangular(function,lower, mode, upper, &result, Policy()))
+    {
+      return result;
+    }
+    if(false == detail::check_probability(function, p, &result, Policy()))
+    {
+      return result;
+    }
+    if(p == 0)
+    {
+      return lower;
+    }
+    if(p == 1)
+    {
+      return upper;
+    }
+    RealType p0 = (mode - lower) / (upper - lower);
+    RealType q = 1 - p;
+    if (p < p0)
+    {
+      result = sqrt((upper - lower) * (mode - lower) * p) + lower;
+    }
+    else if (p == p0)
+    {
+      result = mode;
+    }
+    else // p > p0
+    {
+      result = upper - sqrt((upper - lower) * (upper - mode) * q);
+    }
+    return result;
+
+  } // RealType quantile(const triangular_distribution<RealType, Policy>& dist, const RealType& q)
+
+  template <class RealType, class Policy>
+  RealType cdf(const complemented2_type<triangular_distribution<RealType, Policy>, RealType>& c)
+  {
+    static const char* function = "boost::math::cdf(const triangular_distribution<%1%>&, %1%)";
+    RealType lower = c.dist.lower();
+    RealType mode = c.dist.mode();
+    RealType upper = c.dist.upper();
+    RealType x = c.param;
+    RealType result = 0; // of checks.
+    if(false == detail::check_triangular(function, lower, mode, upper, &result, Policy()))
+    {
+      return result;
+    }
+    if(false == detail::check_triangular_x(function, x, &result, Policy()))
+    {
+      return result;
+    }
+    if (x <= lower)
+    {
+      return 1;
+    }
+    if (x >= upper)
+    {
+      return 0;
+    }
+    if (x <= mode)
+    {
+      return 1 - ((x - lower) * (x - lower)) / ((upper - lower) * (mode - lower));
+    }
+    else
+    {
+      return (upper - x) *  (upper - x) / ((upper - lower) * (upper - mode));
+    }
+  } // RealType cdf(const complemented2_type<triangular_distribution<RealType, Policy>, RealType>& c)
+
+  template <class RealType, class Policy>
+  RealType quantile(const complemented2_type<triangular_distribution<RealType, Policy>, RealType>& c)
+  {
+    BOOST_MATH_STD_USING  // Aid ADL for sqrt.
+    static const char* function = "boost::math::quantile(const triangular_distribution<%1%>&, %1%)";
+    RealType l = c.dist.lower();
+    RealType m = c.dist.mode();
+    RealType u = c.dist.upper();
+    RealType q = c.param; // probability 0 to 1.
+    RealType result = 0; // of checks.
+    if(false == detail::check_triangular(function, l, m, u, &result, Policy()))
+    {
+      return result;
+    }
+    if(false == detail::check_probability(function, q, &result, Policy()))
+    {
+      return result;
+    }
+    if(q == 0)
+    {
+      return u;
+    }
+    if(q == 1)
+    {
+      return l;
+    }
+    RealType lower = c.dist.lower();
+    RealType mode = c.dist.mode();
+    RealType upper = c.dist.upper();
+
+    RealType p = 1 - q;
+    RealType p0 = (mode - lower) / (upper - lower);
+    if(p < p0)
+    {
+      RealType s = (upper - lower) * (mode - lower);
+      s *= p;
+      result = sqrt((upper - lower) * (mode - lower) * p) + lower;
+    }
+    else if (p == p0)
+    {
+      result = mode;
+    }
+    else // p > p0
+    {
+      result = upper - sqrt((upper - lower) * (upper - mode) * q);
+    }
+    return result;
+  } // RealType quantile(const complemented2_type<triangular_distribution<RealType, Policy>, RealType>& c)
+
+  template <class RealType, class Policy>
+  inline RealType mean(const triangular_distribution<RealType, Policy>& dist)
+  {
+    static const char* function = "boost::math::mean(const triangular_distribution<%1%>&)";
+    RealType lower = dist.lower();
+    RealType mode = dist.mode();
+    RealType upper = dist.upper();
+    RealType result = 0;  // of checks.
+    if(false == detail::check_triangular(function, lower, mode, upper, &result, Policy()))
+    {
+      return result;
+    }
+    return (lower + upper + mode) / 3;
+  } // RealType mean(const triangular_distribution<RealType, Policy>& dist)
+
+
+  template <class RealType, class Policy>
+  inline RealType variance(const triangular_distribution<RealType, Policy>& dist)
+  {
+    static const char* function = "boost::math::mean(const triangular_distribution<%1%>&)";
+    RealType lower = dist.lower();
+    RealType mode = dist.mode();
+    RealType upper = dist.upper();
+    RealType result = 0; // of checks.
+    if(false == detail::check_triangular(function, lower, mode, upper, &result, Policy()))
+    {
+      return result;
+    }
+    return (lower * lower + upper * upper + mode * mode - lower * upper - lower * mode - upper * mode) / 18;
+  } // RealType variance(const triangular_distribution<RealType, Policy>& dist)
+
+  template <class RealType, class Policy>
+  inline RealType mode(const triangular_distribution<RealType, Policy>& dist)
+  {
+    static const char* function = "boost::math::mode(const triangular_distribution<%1%>&)";
+    RealType mode = dist.mode();
+    RealType result = 0; // of checks.
+    if(false == detail::check_triangular_mode(function, mode, &result, Policy()))
+    { // This should never happen!
+      return result;
+    }
+    return mode;
+  } // RealType mode
+
+  template <class RealType, class Policy>
+  inline RealType median(const triangular_distribution<RealType, Policy>& dist)
+  {
+    BOOST_MATH_STD_USING // ADL of std functions.
+    static const char* function = "boost::math::median(const triangular_distribution<%1%>&)";
+    RealType mode = dist.mode();
+    RealType result = 0; // of checks.
+    if(false == detail::check_triangular_mode(function, mode, &result, Policy()))
+    { // This should never happen!
+      return result;
+    }
+    RealType lower = dist.lower();
+    RealType upper = dist.upper();
+    if (mode >= (upper + lower) / 2)
+    {
+      return lower + sqrt((upper - lower) * (mode - lower)) / constants::root_two<RealType>();
+    }
+    else
+    {
+      return upper - sqrt((upper - lower) * (upper - mode)) / constants::root_two<RealType>();
+    }
+  } // RealType mode
+
+  template <class RealType, class Policy>
+  inline RealType skewness(const triangular_distribution<RealType, Policy>& dist)
+  {
+    BOOST_MATH_STD_USING  // for ADL of std functions
+    using namespace boost::math::constants; // for root_two
+    static const char* function = "boost::math::skewness(const triangular_distribution<%1%>&)";
+
+    RealType lower = dist.lower();
+    RealType mode = dist.mode();
+    RealType upper = dist.upper();
+    RealType result = 0; // of checks.
+    if(false == boost::math::detail::check_triangular(function,lower, mode, upper, &result, Policy()))
+    {
+      return result;
+    }
+    return root_two<RealType>() * (lower + upper - 2 * mode) * (2 * lower - upper - mode) * (lower - 2 * upper + mode) /
+      (5 * pow((lower * lower + upper * upper + mode * mode 
+        - lower * upper - lower * mode - upper * mode), RealType(3)/RealType(2)));
+    // #11768: Skewness formula for triangular distribution is incorrect -  corrected 29 Oct 2015 for release 1.61.
+  } // RealType skewness(const triangular_distribution<RealType, Policy>& dist)
+
+  template <class RealType, class Policy>
+  inline RealType kurtosis(const triangular_distribution<RealType, Policy>& dist)
+  { // These checks may be belt and braces as should have been checked on construction?
+    static const char* function = "boost::math::kurtosis(const triangular_distribution<%1%>&)";
+    RealType lower = dist.lower();
+    RealType upper = dist.upper();
+    RealType mode = dist.mode();
+    RealType result = 0;  // of checks.
+    if(false == detail::check_triangular(function,lower, mode, upper, &result, Policy()))
+    {
+      return result;
+    }
+    return static_cast<RealType>(12)/5; //  12/5 = 2.4;
+  } // RealType kurtosis_excess(const triangular_distribution<RealType, Policy>& dist)
+
+  template <class RealType, class Policy>
+  inline RealType kurtosis_excess(const triangular_distribution<RealType, Policy>& dist)
+  { // These checks may be belt and braces as should have been checked on construction?
+    static const char* function = "boost::math::kurtosis_excess(const triangular_distribution<%1%>&)";
+    RealType lower = dist.lower();
+    RealType upper = dist.upper();
+    RealType mode = dist.mode();
+    RealType result = 0;  // of checks.
+    if(false == detail::check_triangular(function,lower, mode, upper, &result, Policy()))
+    {
+      return result;
+    }
+    return static_cast<RealType>(-3)/5; // - 3/5 = -0.6
+    // Assuming mathworld really means kurtosis excess?  Wikipedia now corrected to match this.
+  }
+
+} // 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_STATS_TRIANGULAR_HPP
+
+
+