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1// Copyright John Maddock 2006, 2007.2// Copyright Paul A. Bristow 2007.3// Copyright Matt Borland 2024.4 5// Use, modification and distribution are subject to the6// Boost Software License, Version 1.0. (See accompanying file7// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)8 9#ifndef BOOST_STATS_CAUCHY_HPP10#define BOOST_STATS_CAUCHY_HPP11 12#ifdef _MSC_VER13#pragma warning(push)14#pragma warning(disable : 4127) // conditional expression is constant15#endif16 17#include <boost/math/tools/config.hpp>18#include <boost/math/tools/tuple.hpp>19#include <boost/math/tools/numeric_limits.hpp>20#include <boost/math/tools/precision.hpp>21#include <boost/math/tools/promotion.hpp>22#include <boost/math/constants/constants.hpp>23#include <boost/math/distributions/complement.hpp>24#include <boost/math/distributions/detail/common_error_handling.hpp>25#include <boost/math/policies/policy.hpp>26#include <boost/math/policies/error_handling.hpp>27 28#ifndef BOOST_MATH_HAS_NVRTC29#include <boost/math/distributions/fwd.hpp>30#include <utility>31#include <cmath>32#endif33 34namespace boost{ namespace math35{36 37template <class RealType, class Policy>38class cauchy_distribution;39 40namespace detail41{42 43template <class RealType, class Policy>44BOOST_MATH_GPU_ENABLED RealType cdf_imp(const cauchy_distribution<RealType, Policy>& dist, const RealType& x, bool complement)45{46 //47 // This calculates the cdf of the Cauchy distribution and/or its complement.48 //49 // This implementation uses the formula50 //51 // cdf = atan2(1, -x)/pi52 //53 // where x is the standardized (i.e. shifted and scaled) domain variable.54 //55 BOOST_MATH_STD_USING // for ADL of std functions56 constexpr auto function = "boost::math::cdf(cauchy<%1%>&, %1%)";57 RealType result = 0;58 RealType location = dist.location();59 RealType scale = dist.scale();60 if(false == detail::check_location(function, location, &result, Policy()))61 {62 return result;63 }64 if(false == detail::check_scale(function, scale, &result, Policy()))65 {66 return result;67 }68 #ifdef BOOST_MATH_HAS_GPU_SUPPORT69 if(x > tools::max_value<RealType>())70 {71 return static_cast<RealType>((complement) ? 0 : 1);72 }73 if(x < -tools::max_value<RealType>())74 {75 return static_cast<RealType>((complement) ? 1 : 0);76 }77 #else78 if(boost::math::numeric_limits<RealType>::has_infinity && x == boost::math::numeric_limits<RealType>::infinity())79 { // cdf +infinity is unity.80 return static_cast<RealType>((complement) ? 0 : 1);81 }82 if(boost::math::numeric_limits<RealType>::has_infinity && x == -boost::math::numeric_limits<RealType>::infinity())83 { // cdf -infinity is zero.84 return static_cast<RealType>((complement) ? 1 : 0);85 }86 #endif87 if(false == detail::check_x(function, x, &result, Policy()))88 { // Catches x == NaN89 return result;90 }91 RealType x_std = static_cast<RealType>((complement) ? 1 : -1)*(x - location) / scale;92 return atan2(static_cast<RealType>(1), x_std) / constants::pi<RealType>();93} // cdf94 95template <class RealType, class Policy>96BOOST_MATH_GPU_ENABLED RealType quantile_imp(97 const cauchy_distribution<RealType, Policy>& dist,98 RealType p,99 bool complement)100{101 // This routine implements the quantile for the Cauchy distribution,102 // the value p may be the probability, or its complement if complement=true.103 //104 // The procedure calculates the distance from the105 // mid-point of the distribution. This is either added or subtracted106 // from the location parameter depending on whether `complement` is true.107 //108 constexpr auto function = "boost::math::quantile(cauchy<%1%>&, %1%)";109 BOOST_MATH_STD_USING // for ADL of std functions110 111 RealType result = 0;112 RealType location = dist.location();113 RealType scale = dist.scale();114 if(false == detail::check_location(function, location, &result, Policy()))115 {116 return result;117 }118 if(false == detail::check_scale(function, scale, &result, Policy()))119 {120 return result;121 }122 if(false == detail::check_probability(function, p, &result, Policy()))123 {124 return result;125 }126 // Special cases:127 if(p == 1)128 {129 return (complement ? -1 : 1) * policies::raise_overflow_error<RealType>(function, 0, Policy());130 }131 if(p == 0)132 {133 return (complement ? 1 : -1) * policies::raise_overflow_error<RealType>(function, 0, Policy());134 }135 136 if(p > 0.5)137 {138 p = p - 1;139 }140 if(p == 0.5) // special case:141 {142 return location;143 }144 result = -scale / tan(constants::pi<RealType>() * p);145 return complement ? RealType(location - result) : RealType(location + result);146} // quantile147 148} // namespace detail149 150template <class RealType = double, class Policy = policies::policy<> >151class cauchy_distribution152{153public:154 typedef RealType value_type;155 typedef Policy policy_type;156 157 BOOST_MATH_GPU_ENABLED cauchy_distribution(RealType l_location = 0, RealType l_scale = 1)158 : m_a(l_location), m_hg(l_scale)159 {160 constexpr auto function = "boost::math::cauchy_distribution<%1%>::cauchy_distribution";161 RealType result;162 detail::check_location(function, l_location, &result, Policy());163 detail::check_scale(function, l_scale, &result, Policy());164 } // cauchy_distribution165 166 BOOST_MATH_GPU_ENABLED RealType location()const167 {168 return m_a;169 }170 BOOST_MATH_GPU_ENABLED RealType scale()const171 {172 return m_hg;173 }174 175private:176 RealType m_a; // The location, this is the median of the distribution.177 RealType m_hg; // The scale )or shape), this is the half width at half height.178};179 180typedef cauchy_distribution<double> cauchy;181 182#ifdef __cpp_deduction_guides183template <class RealType>184cauchy_distribution(RealType)->cauchy_distribution<typename boost::math::tools::promote_args<RealType>::type>;185template <class RealType>186cauchy_distribution(RealType,RealType)->cauchy_distribution<typename boost::math::tools::promote_args<RealType>::type>;187#endif188 189template <class RealType, class Policy>190BOOST_MATH_GPU_ENABLED inline const boost::math::pair<RealType, RealType> range(const cauchy_distribution<RealType, Policy>&)191{ // Range of permissible values for random variable x.192 BOOST_MATH_IF_CONSTEXPR (boost::math::numeric_limits<RealType>::has_infinity)193 { 194 return boost::math::pair<RealType, RealType>(-boost::math::numeric_limits<RealType>::infinity(), boost::math::numeric_limits<RealType>::infinity()); // - to + infinity.195 }196 else197 { // Can only use max_value.198 using boost::math::tools::max_value;199 return boost::math::pair<RealType, RealType>(-max_value<RealType>(), max_value<RealType>()); // - to + max.200 }201}202 203template <class RealType, class Policy>204BOOST_MATH_GPU_ENABLED inline const boost::math::pair<RealType, RealType> support(const cauchy_distribution<RealType, Policy>& )205{ // Range of supported values for random variable x.206 // This is range where cdf rises from 0 to 1, and outside it, the pdf is zero.207 BOOST_MATH_IF_CONSTEXPR (boost::math::numeric_limits<RealType>::has_infinity)208 { 209 return boost::math::pair<RealType, RealType>(-boost::math::numeric_limits<RealType>::infinity(), boost::math::numeric_limits<RealType>::infinity()); // - to + infinity.210 }211 else212 { // Can only use max_value.213 using boost::math::tools::max_value;214 return boost::math::pair<RealType, RealType>(-tools::max_value<RealType>(), max_value<RealType>()); // - to + max.215 }216}217 218template <class RealType, class Policy>219BOOST_MATH_GPU_ENABLED inline RealType pdf(const cauchy_distribution<RealType, Policy>& dist, const RealType& x)220{ 221 BOOST_MATH_STD_USING // for ADL of std functions222 223 constexpr auto function = "boost::math::pdf(cauchy<%1%>&, %1%)";224 RealType result = 0;225 RealType location = dist.location();226 RealType scale = dist.scale();227 if(false == detail::check_scale(function, scale, &result, Policy()))228 {229 return result;230 }231 if(false == detail::check_location(function, location, &result, Policy()))232 {233 return result;234 }235 if((boost::math::isinf)(x))236 {237 return 0; // pdf + and - infinity is zero.238 }239 // These produce MSVC 4127 warnings, so the above used instead.240 //if(boost::math::numeric_limits<RealType>::has_infinity && abs(x) == boost::math::numeric_limits<RealType>::infinity())241 //{ // pdf + and - infinity is zero.242 // return 0;243 //}244 245 if(false == detail::check_x(function, x, &result, Policy()))246 { // Catches x = NaN247 return result;248 }249 250 RealType xs = (x - location) / scale;251 result = 1 / (constants::pi<RealType>() * scale * (1 + xs * xs));252 return result;253} // pdf254 255template <class RealType, class Policy>256BOOST_MATH_GPU_ENABLED inline RealType cdf(const cauchy_distribution<RealType, Policy>& dist, const RealType& x)257{258 return detail::cdf_imp(dist, x, false);259} // cdf260 261template <class RealType, class Policy>262BOOST_MATH_GPU_ENABLED inline RealType quantile(const cauchy_distribution<RealType, Policy>& dist, const RealType& p)263{264 return detail::quantile_imp(dist, p, false);265} // quantile266 267template <class RealType, class Policy>268BOOST_MATH_GPU_ENABLED inline RealType cdf(const complemented2_type<cauchy_distribution<RealType, Policy>, RealType>& c)269{270 return detail::cdf_imp(c.dist, c.param, true);271} // cdf complement272 273template <class RealType, class Policy>274BOOST_MATH_GPU_ENABLED inline RealType quantile(const complemented2_type<cauchy_distribution<RealType, Policy>, RealType>& c)275{276 return detail::quantile_imp(c.dist, c.param, true);277} // quantile complement278 279template <class RealType, class Policy>280BOOST_MATH_GPU_ENABLED inline RealType mean(const cauchy_distribution<RealType, Policy>&)281{ // There is no mean:282 typedef typename Policy::assert_undefined_type assert_type;283 static_assert(assert_type::value == 0, "The Cauchy Distribution has no mean");284 285 return policies::raise_domain_error<RealType>(286 "boost::math::mean(cauchy<%1%>&)",287 "The Cauchy distribution does not have a mean: "288 "the only possible return value is %1%.",289 boost::math::numeric_limits<RealType>::quiet_NaN(), Policy());290}291 292template <class RealType, class Policy>293BOOST_MATH_GPU_ENABLED inline RealType variance(const cauchy_distribution<RealType, Policy>& /*dist*/)294{295 // There is no variance:296 typedef typename Policy::assert_undefined_type assert_type;297 static_assert(assert_type::value == 0, "The Cauchy Distribution has no variance");298 299 return policies::raise_domain_error<RealType>(300 "boost::math::variance(cauchy<%1%>&)",301 "The Cauchy distribution does not have a variance: "302 "the only possible return value is %1%.",303 boost::math::numeric_limits<RealType>::quiet_NaN(), Policy());304}305 306template <class RealType, class Policy>307BOOST_MATH_GPU_ENABLED inline RealType mode(const cauchy_distribution<RealType, Policy>& dist)308{309 return dist.location();310}311 312template <class RealType, class Policy>313BOOST_MATH_GPU_ENABLED inline RealType median(const cauchy_distribution<RealType, Policy>& dist)314{315 return dist.location();316}317 318template <class RealType, class Policy>319BOOST_MATH_GPU_ENABLED inline RealType skewness(const cauchy_distribution<RealType, Policy>& /*dist*/)320{321 // There is no skewness:322 typedef typename Policy::assert_undefined_type assert_type;323 static_assert(assert_type::value == 0, "The Cauchy Distribution has no skewness");324 325 return policies::raise_domain_error<RealType>(326 "boost::math::skewness(cauchy<%1%>&)",327 "The Cauchy distribution does not have a skewness: "328 "the only possible return value is %1%.",329 boost::math::numeric_limits<RealType>::quiet_NaN(), Policy()); // infinity?330}331 332template <class RealType, class Policy>333BOOST_MATH_GPU_ENABLED inline RealType kurtosis(const cauchy_distribution<RealType, Policy>& /*dist*/)334{335 // There is no kurtosis:336 typedef typename Policy::assert_undefined_type assert_type;337 static_assert(assert_type::value == 0, "The Cauchy Distribution has no kurtosis");338 339 return policies::raise_domain_error<RealType>(340 "boost::math::kurtosis(cauchy<%1%>&)",341 "The Cauchy distribution does not have a kurtosis: "342 "the only possible return value is %1%.",343 boost::math::numeric_limits<RealType>::quiet_NaN(), Policy());344}345 346template <class RealType, class Policy>347BOOST_MATH_GPU_ENABLED inline RealType kurtosis_excess(const cauchy_distribution<RealType, Policy>& /*dist*/)348{349 // There is no kurtosis excess:350 typedef typename Policy::assert_undefined_type assert_type;351 static_assert(assert_type::value == 0, "The Cauchy Distribution has no kurtosis excess");352 353 return policies::raise_domain_error<RealType>(354 "boost::math::kurtosis_excess(cauchy<%1%>&)",355 "The Cauchy distribution does not have a kurtosis: "356 "the only possible return value is %1%.",357 boost::math::numeric_limits<RealType>::quiet_NaN(), Policy());358}359 360template <class RealType, class Policy>361BOOST_MATH_GPU_ENABLED inline RealType entropy(const cauchy_distribution<RealType, Policy> & dist)362{363 using std::log;364 return log(2*constants::two_pi<RealType>()*dist.scale());365}366 367} // namespace math368} // namespace boost369 370#ifdef _MSC_VER371#pragma warning(pop)372#endif373 374// This include must be at the end, *after* the accessors375// for this distribution have been defined, in order to376// keep compilers that support two-phase lookup happy.377#include <boost/math/distributions/detail/derived_accessors.hpp>378 379#endif // BOOST_STATS_CAUCHY_HPP380