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路径: \\game3dprogramming\materials\GameFactory\GameFactoryDemo\references\boost_1_35_0\boost\math\distributions\normal.hpp
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// 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_NORMAL_HPP #define BOOST_STATS_NORMAL_HPP // http://en.wikipedia.org/wiki/Normal_distribution // http://www.itl.nist.gov/div898/handbook/eda/section3/eda3661.htm // Also: // Weisstein, Eric W. "Normal Distribution." // From MathWorld--A Wolfram Web Resource. // http://mathworld.wolfram.com/NormalDistribution.html #include
#include
// for erf/erfc. #include
#include
#include
namespace boost{ namespace math{ template
> class normal_distribution { public: typedef RealType value_type; typedef Policy policy_type; normal_distribution(RealType mean = 0, RealType sd = 1) : m_mean(mean), m_sd(sd) { // Default is a 'standard' normal distribution N01. static const char* function = "boost::math::normal_distribution<%1%>::normal_distribution"; RealType result; detail::check_scale(function, sd, &result, Policy()); detail::check_location(function, mean, &result, Policy()); } RealType mean()const { // alias for location. return m_mean; } RealType standard_deviation()const { // alias for scale. return m_sd; } // Synonyms, provided to allow generic use of find_location and find_scale. RealType location()const { // location. return m_mean; } RealType scale()const { // scale. return m_sd; } private: // // Data members: // RealType m_mean; // distribution mean or location. RealType m_sd; // distribution standard deviation or scale. }; // class normal_distribution typedef normal_distribution
normal; template
inline const std::pair
range(const normal_distribution
& /*dist*/) { // Range of permissible values for random variable x. using boost::math::tools::max_value; return std::pair
(-max_value
(), max_value
()); // - to + max value. } template
inline const std::pair
support(const normal_distribution
& /*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
(-max_value
(), max_value
()); // - to + max value. } template
inline RealType pdf(const normal_distribution
& dist, const RealType& x) { BOOST_MATH_STD_USING // for ADL of std functions RealType sd = dist.standard_deviation(); RealType mean = dist.mean(); static const char* function = "boost::math::pdf(const normal_distribution<%1%>&, %1%)"; if((boost::math::isinf)(x)) { return 0; // pdf + and - infinity is zero. } // Theis produces MSVC 4127 warnings, so the above used instead. //if(std::numeric_limits
::has_infinity && abs(x) == std::numeric_limits
::infinity()) //{ // pdf + and - infinity is zero. // return 0; //} RealType result; if(false == detail::check_scale(function, sd, &result, Policy())) { return result; } if(false == detail::check_location(function, mean, &result, Policy())) { return result; } if(false == detail::check_x(function, x, &result, Policy())) { return result; } RealType exponent = x - mean; exponent *= -exponent; exponent /= 2 * sd * sd; result = exp(exponent); result /= sd * sqrt(2 * constants::pi
()); return result; } // pdf template
inline RealType cdf(const normal_distribution
& dist, const RealType& x) { BOOST_MATH_STD_USING // for ADL of std functions RealType sd = dist.standard_deviation(); RealType mean = dist.mean(); static const char* function = "boost::math::cdf(const normal_distribution<%1%>&, %1%)"; RealType result; if(false == detail::check_scale(function, sd, &result, Policy())) { return result; } if(false == detail::check_location(function, mean, &result, Policy())) { return result; } if((boost::math::isinf)(x)) { if(x < 0) return 0; // -infinity return 1; // + infinity } // These produce MSVC 4127 warnings, so the above used instead. //if(std::numeric_limits
::has_infinity && x == std::numeric_limits
::infinity()) //{ // cdf +infinity is unity. // return 1; //} //if(std::numeric_limits
::has_infinity && x == -std::numeric_limits
::infinity()) //{ // cdf -infinity is zero. // return 0; //} if(false == detail::check_x(function, x, &result, Policy())) { return result; } RealType diff = (x - mean) / (sd * constants::root_two
()); result = boost::math::erfc(-diff, Policy()) / 2; return result; } // cdf template
inline RealType quantile(const normal_distribution
& dist, const RealType& p) { BOOST_MATH_STD_USING // for ADL of std functions RealType sd = dist.standard_deviation(); RealType mean = dist.mean(); static const char* function = "boost::math::quantile(const normal_distribution<%1%>&, %1%)"; RealType result; if(false == detail::check_scale(function, sd, &result, Policy())) return result; if(false == detail::check_location(function, mean, &result, Policy())) return result; if(false == detail::check_probability(function, p, &result, Policy())) return result; result= boost::math::erfc_inv(2 * p, Policy()); result = -result; result *= sd * constants::root_two
(); result += mean; return result; } // quantile template
inline RealType cdf(const complemented2_type
, RealType>& c) { BOOST_MATH_STD_USING // for ADL of std functions RealType sd = c.dist.standard_deviation(); RealType mean = c.dist.mean(); RealType x = c.param; static const char* function = "boost::math::cdf(const complement(normal_distribution<%1%>&), %1%)"; if((boost::math::isinf)(x)) { if(x < 0) return 1; // cdf complement -infinity is unity. return 0; // cdf complement +infinity is zero } // These produce MSVC 4127 warnings, so the above used instead. //if(std::numeric_limits
::has_infinity && x == std::numeric_limits
::infinity()) //{ // cdf complement +infinity is zero. // return 0; //} //if(std::numeric_limits
::has_infinity && x == -std::numeric_limits
::infinity()) //{ // cdf complement -infinity is unity. // return 1; //} RealType result; if(false == detail::check_scale(function, sd, &result, Policy())) return result; if(false == detail::check_location(function, mean, &result, Policy())) return result; if(false == detail::check_x(function, x, &result, Policy())) return result; RealType diff = (x - mean) / (sd * constants::root_two
()); result = boost::math::erfc(diff, Policy()) / 2; return result; } // cdf complement template
inline RealType quantile(const complemented2_type
, RealType>& c) { BOOST_MATH_STD_USING // for ADL of std functions RealType sd = c.dist.standard_deviation(); RealType mean = c.dist.mean(); static const char* function = "boost::math::quantile(const complement(normal_distribution<%1%>&), %1%)"; RealType result; if(false == detail::check_scale(function, sd, &result, Policy())) return result; if(false == detail::check_location(function, mean, &result, Policy())) return result; RealType q = c.param; if(false == detail::check_probability(function, q, &result, Policy())) return result; result = boost::math::erfc_inv(2 * q, Policy()); result *= sd * constants::root_two
(); result += mean; return result; } // quantile template
inline RealType mean(const normal_distribution
& dist) { return dist.mean(); } template
inline RealType standard_deviation(const normal_distribution
& dist) { return dist.standard_deviation(); } template
inline RealType mode(const normal_distribution
& dist) { return dist.mean(); } template
inline RealType median(const normal_distribution
& dist) { return dist.mean(); } template
inline RealType skewness(const normal_distribution
& /*dist*/) { return 0; } template
inline RealType kurtosis(const normal_distribution
& /*dist*/) { return 3; } template
inline RealType kurtosis_excess(const normal_distribution
& /*dist*/) { return 0; } } // 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
#endif // BOOST_STATS_NORMAL_HPP
normal.hpp
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