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Ruta de la carpeta: \\game3dprogramming\materials\GameFactory\GameFactoryDemo\references\boost_1_35_0\boost\math\distributions\triangular.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_TRIANGULAR_HPP #define BOOST_STATS_TRIANGULAR_HPP // http://mathworld.wolfram.com/TriangularDistribution.html // http://en.wikipedia.org/wiki/Triangular_distribution #include
#include
#include
#include
#include
#include
namespace boost{ namespace math { namespace detail { template
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
( function, "Lower parameter is %1%, but must be finite!", lower, pol); return false; } } // bool check_triangular_lower( template
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
( function, "Mode parameter is %1%, but must be finite!", mode, pol); return false; } } // bool check_triangular_mode( template
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
( function, "Upper parameter is %1%, but must be finite!", upper, pol); return false; } } // bool check_triangular_upper( template
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
( function, "x parameter is %1%, but must be finite!", x, pol); return false; } } // bool check_triangular_x template
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) && check_triangular_mode(function, mode, result, pol) && check_triangular_upper(function, upper, result, pol) && (lower < upper) // lower == upper NOT useful. ) { if (mode < lower) { *result = policies::raise_domain_error
( function, "mode parameter is %1%, but must be >= than lower!", lower, pol); return false; } if (mode > upper ) { *result = policies::raise_domain_error
( function, "mode parameter is %1%, but must be <= than upper!", upper, pol); return false; } return true; } else { // upper and lower have each been checked before, so must be lower >= upper. *result = policies::raise_domain_error
( function, "lower parameter is %1%, but must be less than upper!", lower, pol); return false; } } // bool check_triangular } // namespace detail template
> class triangular_distribution { public: typedef RealType value_type; typedef Policy policy_type; triangular_distribution(RealType lower = -1, RealType mode = 0, RealType upper = 1) : m_lower(lower), m_mode(mode), m_upper(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",lower, mode, 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
triangular; template
inline const std::pair
range(const triangular_distribution
& /* dist */) { // Range of permissible values for random variable x. using boost::math::tools::max_value; return std::pair
(-max_value
(), max_value
()); } template
inline const std::pair
support(const triangular_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. return std::pair
(dist.lower(), dist.upper()); } template
RealType pdf(const triangular_distribution
& 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; // 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) : 0; } else if (x == upper) { return (mode == upper) ? 2 / (upper - lower) : 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
& dist, const RealType& x) template
inline RealType cdf(const triangular_distribution
& 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; // 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
& dist, const RealType& x) template
RealType quantile(const triangular_distribution
& 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; // 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
& dist, const RealType& q) template
RealType cdf(const complemented2_type
, 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; // 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
, RealType>& c) template
RealType quantile(const complemented2_type
, 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; // 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
, RealType>& c) template
inline RealType mean(const triangular_distribution
& 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; // 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
& dist) template
inline RealType variance(const triangular_distribution
& 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; // 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
& dist) template
inline RealType mode(const triangular_distribution
& dist) { static const char* function = "boost::math::mode(const triangular_distribution<%1%>&)"; RealType mode = dist.mode(); RealType result; // of checks. if(false == detail::check_triangular_mode(function, mode, &result, Policy())) { // This should never happen! return result; } return mode; } // RealType mode template
inline RealType median(const triangular_distribution
& 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; // 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
(); } else { return upper - sqrt((upper - lower) * (upper - mode)) / constants::root_two
(); } } // RealType mode template
inline RealType skewness(const triangular_distribution
& 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; // of checks. if(false == detail::check_triangular(function,lower, mode, upper, &result, Policy())) { return result; } return root_two
() * (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))); } // RealType skewness(const triangular_distribution
& dist) template
inline RealType kurtosis(const triangular_distribution
& 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; // of checks. if(false == detail::check_triangular(function,lower, mode, upper, &result, Policy())) { return result; } return static_cast
(12)/5; // 12/5 = 2.4; } // RealType kurtosis_excess(const triangular_distribution
& dist) template
inline RealType kurtosis_excess(const triangular_distribution
& 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; // of checks. if(false == detail::check_triangular(function,lower, mode, upper, &result, Policy())) { return result; } return static_cast
(-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
#endif // BOOST_STATS_TRIANGULAR_HPP
triangular.hpp
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