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1 | // Copyright John Maddock 2006, 2007. |
2 | // Copyright Paul A. Bristow 2007. | |
3 | ||
4 | // Use, modification and distribution are subject to the | |
5 | // Boost Software License, Version 1.0. (See accompanying file | |
6 | // LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) | |
7 | ||
8 | #ifndef BOOST_STATS_CAUCHY_HPP | |
9 | #define BOOST_STATS_CAUCHY_HPP | |
10 | ||
11 | #ifdef _MSC_VER | |
12 | #pragma warning(push) | |
13 | #pragma warning(disable : 4127) // conditional expression is constant | |
14 | #endif | |
15 | ||
16 | #include <boost/math/distributions/fwd.hpp> | |
17 | #include <boost/math/constants/constants.hpp> | |
18 | #include <boost/math/distributions/complement.hpp> | |
19 | #include <boost/math/distributions/detail/common_error_handling.hpp> | |
7c673cae | 20 | #include <utility> |
1e59de90 | 21 | #include <cmath> |
7c673cae FG |
22 | |
23 | namespace boost{ namespace math | |
24 | { | |
25 | ||
26 | template <class RealType, class Policy> | |
27 | class cauchy_distribution; | |
28 | ||
29 | namespace detail | |
30 | { | |
31 | ||
32 | template <class RealType, class Policy> | |
33 | RealType cdf_imp(const cauchy_distribution<RealType, Policy>& dist, const RealType& x, bool complement) | |
34 | { | |
35 | // | |
36 | // This calculates the cdf of the Cauchy distribution and/or its complement. | |
37 | // | |
38 | // The usual formula for the Cauchy cdf is: | |
39 | // | |
40 | // cdf = 0.5 + atan(x)/pi | |
41 | // | |
42 | // But that suffers from cancellation error as x -> -INF. | |
43 | // | |
44 | // Recall that for x < 0: | |
45 | // | |
46 | // atan(x) = -pi/2 - atan(1/x) | |
47 | // | |
48 | // Substituting into the above we get: | |
49 | // | |
50 | // CDF = -atan(1/x) ; x < 0 | |
51 | // | |
f67539c2 | 52 | // So the procedure is to calculate the cdf for -fabs(x) |
7c673cae FG |
53 | // using the above formula, and then subtract from 1 when required |
54 | // to get the result. | |
55 | // | |
56 | BOOST_MATH_STD_USING // for ADL of std functions | |
57 | static const char* function = "boost::math::cdf(cauchy<%1%>&, %1%)"; | |
58 | RealType result = 0; | |
59 | RealType location = dist.location(); | |
60 | RealType scale = dist.scale(); | |
61 | if(false == detail::check_location(function, location, &result, Policy())) | |
62 | { | |
63 | return result; | |
64 | } | |
65 | if(false == detail::check_scale(function, scale, &result, Policy())) | |
66 | { | |
67 | return result; | |
68 | } | |
69 | if(std::numeric_limits<RealType>::has_infinity && x == std::numeric_limits<RealType>::infinity()) | |
70 | { // cdf +infinity is unity. | |
71 | return static_cast<RealType>((complement) ? 0 : 1); | |
72 | } | |
73 | if(std::numeric_limits<RealType>::has_infinity && x == -std::numeric_limits<RealType>::infinity()) | |
74 | { // cdf -infinity is zero. | |
75 | return static_cast<RealType>((complement) ? 1 : 0); | |
76 | } | |
77 | if(false == detail::check_x(function, x, &result, Policy())) | |
78 | { // Catches x == NaN | |
79 | return result; | |
80 | } | |
81 | RealType mx = -fabs((x - location) / scale); // scale is > 0 | |
82 | if(mx > -tools::epsilon<RealType>() / 8) | |
83 | { // special case first: x extremely close to location. | |
84 | return 0.5; | |
85 | } | |
86 | result = -atan(1 / mx) / constants::pi<RealType>(); | |
87 | return (((x > location) != complement) ? 1 - result : result); | |
88 | } // cdf | |
89 | ||
90 | template <class RealType, class Policy> | |
91 | RealType quantile_imp( | |
92 | const cauchy_distribution<RealType, Policy>& dist, | |
93 | const RealType& p, | |
94 | bool complement) | |
95 | { | |
96 | // This routine implements the quantile for the Cauchy distribution, | |
97 | // the value p may be the probability, or its complement if complement=true. | |
98 | // | |
99 | // The procedure first performs argument reduction on p to avoid error | |
f67539c2 | 100 | // when calculating the tangent, then calculates the distance from the |
7c673cae FG |
101 | // mid-point of the distribution. This is either added or subtracted |
102 | // from the location parameter depending on whether `complement` is true. | |
103 | // | |
104 | static const char* function = "boost::math::quantile(cauchy<%1%>&, %1%)"; | |
105 | BOOST_MATH_STD_USING // for ADL of std functions | |
106 | ||
107 | RealType result = 0; | |
108 | RealType location = dist.location(); | |
109 | RealType scale = dist.scale(); | |
110 | if(false == detail::check_location(function, location, &result, Policy())) | |
111 | { | |
112 | return result; | |
113 | } | |
114 | if(false == detail::check_scale(function, scale, &result, Policy())) | |
115 | { | |
116 | return result; | |
117 | } | |
118 | if(false == detail::check_probability(function, p, &result, Policy())) | |
119 | { | |
120 | return result; | |
121 | } | |
122 | // Special cases: | |
123 | if(p == 1) | |
124 | { | |
125 | return (complement ? -1 : 1) * policies::raise_overflow_error<RealType>(function, 0, Policy()); | |
126 | } | |
127 | if(p == 0) | |
128 | { | |
129 | return (complement ? 1 : -1) * policies::raise_overflow_error<RealType>(function, 0, Policy()); | |
130 | } | |
131 | ||
132 | RealType P = p - floor(p); // argument reduction of p: | |
133 | if(P > 0.5) | |
134 | { | |
135 | P = P - 1; | |
136 | } | |
137 | if(P == 0.5) // special case: | |
138 | { | |
139 | return location; | |
140 | } | |
141 | result = -scale / tan(constants::pi<RealType>() * P); | |
142 | return complement ? RealType(location - result) : RealType(location + result); | |
143 | } // quantile | |
144 | ||
145 | } // namespace detail | |
146 | ||
147 | template <class RealType = double, class Policy = policies::policy<> > | |
148 | class cauchy_distribution | |
149 | { | |
150 | public: | |
151 | typedef RealType value_type; | |
152 | typedef Policy policy_type; | |
153 | ||
154 | cauchy_distribution(RealType l_location = 0, RealType l_scale = 1) | |
155 | : m_a(l_location), m_hg(l_scale) | |
156 | { | |
157 | static const char* function = "boost::math::cauchy_distribution<%1%>::cauchy_distribution"; | |
158 | RealType result; | |
159 | detail::check_location(function, l_location, &result, Policy()); | |
160 | detail::check_scale(function, l_scale, &result, Policy()); | |
161 | } // cauchy_distribution | |
162 | ||
163 | RealType location()const | |
164 | { | |
165 | return m_a; | |
166 | } | |
167 | RealType scale()const | |
168 | { | |
169 | return m_hg; | |
170 | } | |
171 | ||
172 | private: | |
173 | RealType m_a; // The location, this is the median of the distribution. | |
174 | RealType m_hg; // The scale )or shape), this is the half width at half height. | |
175 | }; | |
176 | ||
177 | typedef cauchy_distribution<double> cauchy; | |
178 | ||
1e59de90 TL |
179 | #ifdef __cpp_deduction_guides |
180 | template <class RealType> | |
181 | cauchy_distribution(RealType)->cauchy_distribution<typename boost::math::tools::promote_args<RealType>::type>; | |
182 | template <class RealType> | |
183 | cauchy_distribution(RealType,RealType)->cauchy_distribution<typename boost::math::tools::promote_args<RealType>::type>; | |
184 | #endif | |
185 | ||
7c673cae FG |
186 | template <class RealType, class Policy> |
187 | inline const std::pair<RealType, RealType> range(const cauchy_distribution<RealType, Policy>&) | |
188 | { // Range of permissible values for random variable x. | |
189 | if (std::numeric_limits<RealType>::has_infinity) | |
190 | { | |
191 | return std::pair<RealType, RealType>(-std::numeric_limits<RealType>::infinity(), std::numeric_limits<RealType>::infinity()); // - to + infinity. | |
192 | } | |
193 | else | |
194 | { // Can only use max_value. | |
195 | using boost::math::tools::max_value; | |
196 | return std::pair<RealType, RealType>(-max_value<RealType>(), max_value<RealType>()); // - to + max. | |
197 | } | |
198 | } | |
199 | ||
200 | template <class RealType, class Policy> | |
201 | inline const std::pair<RealType, RealType> support(const cauchy_distribution<RealType, Policy>& ) | |
202 | { // Range of supported values for random variable x. | |
203 | // This is range where cdf rises from 0 to 1, and outside it, the pdf is zero. | |
204 | if (std::numeric_limits<RealType>::has_infinity) | |
205 | { | |
206 | return std::pair<RealType, RealType>(-std::numeric_limits<RealType>::infinity(), std::numeric_limits<RealType>::infinity()); // - to + infinity. | |
207 | } | |
208 | else | |
209 | { // Can only use max_value. | |
210 | using boost::math::tools::max_value; | |
211 | return std::pair<RealType, RealType>(-tools::max_value<RealType>(), max_value<RealType>()); // - to + max. | |
212 | } | |
213 | } | |
214 | ||
215 | template <class RealType, class Policy> | |
216 | inline RealType pdf(const cauchy_distribution<RealType, Policy>& dist, const RealType& x) | |
217 | { | |
218 | BOOST_MATH_STD_USING // for ADL of std functions | |
219 | ||
220 | static const char* function = "boost::math::pdf(cauchy<%1%>&, %1%)"; | |
221 | RealType result = 0; | |
222 | RealType location = dist.location(); | |
223 | RealType scale = dist.scale(); | |
224 | if(false == detail::check_scale("boost::math::pdf(cauchy<%1%>&, %1%)", scale, &result, Policy())) | |
225 | { | |
226 | return result; | |
227 | } | |
228 | if(false == detail::check_location("boost::math::pdf(cauchy<%1%>&, %1%)", location, &result, Policy())) | |
229 | { | |
230 | return result; | |
231 | } | |
232 | if((boost::math::isinf)(x)) | |
233 | { | |
234 | return 0; // pdf + and - infinity is zero. | |
235 | } | |
236 | // These produce MSVC 4127 warnings, so the above used instead. | |
237 | //if(std::numeric_limits<RealType>::has_infinity && abs(x) == std::numeric_limits<RealType>::infinity()) | |
238 | //{ // pdf + and - infinity is zero. | |
239 | // return 0; | |
240 | //} | |
241 | ||
242 | if(false == detail::check_x(function, x, &result, Policy())) | |
243 | { // Catches x = NaN | |
244 | return result; | |
245 | } | |
246 | ||
247 | RealType xs = (x - location) / scale; | |
248 | result = 1 / (constants::pi<RealType>() * scale * (1 + xs * xs)); | |
249 | return result; | |
250 | ||
251 | ||
252 | template <class RealType, class Policy> | |
253 | inline RealType cdf(const cauchy_distribution<RealType, Policy>& dist, const RealType& x) | |
254 | { | |
255 | return detail::cdf_imp(dist, x, false); | |
256 | } // cdf | |
257 | ||
258 | template <class RealType, class Policy> | |
259 | inline RealType quantile(const cauchy_distribution<RealType, Policy>& dist, const RealType& p) | |
260 | { | |
261 | return detail::quantile_imp(dist, p, false); | |
262 | } // quantile | |
263 | ||
264 | template <class RealType, class Policy> | |
265 | inline RealType cdf(const complemented2_type<cauchy_distribution<RealType, Policy>, RealType>& c) | |
266 | { | |
267 | return detail::cdf_imp(c.dist, c.param, true); | |
268 | } // cdf complement | |
269 | ||
270 | template <class RealType, class Policy> | |
271 | inline RealType quantile(const complemented2_type<cauchy_distribution<RealType, Policy>, RealType>& c) | |
272 | { | |
273 | return detail::quantile_imp(c.dist, c.param, true); | |
274 | } // quantile complement | |
275 | ||
276 | template <class RealType, class Policy> | |
277 | inline RealType mean(const cauchy_distribution<RealType, Policy>&) | |
278 | { // There is no mean: | |
279 | typedef typename Policy::assert_undefined_type assert_type; | |
1e59de90 | 280 | static_assert(assert_type::value == 0, "assert type is undefined"); |
7c673cae FG |
281 | |
282 | return policies::raise_domain_error<RealType>( | |
283 | "boost::math::mean(cauchy<%1%>&)", | |
284 | "The Cauchy distribution does not have a mean: " | |
285 | "the only possible return value is %1%.", | |
286 | std::numeric_limits<RealType>::quiet_NaN(), Policy()); | |
287 | } | |
288 | ||
289 | template <class RealType, class Policy> | |
290 | inline RealType variance(const cauchy_distribution<RealType, Policy>& /*dist*/) | |
291 | { | |
292 | // There is no variance: | |
293 | typedef typename Policy::assert_undefined_type assert_type; | |
1e59de90 | 294 | static_assert(assert_type::value == 0, "assert type is undefined"); |
7c673cae FG |
295 | |
296 | return policies::raise_domain_error<RealType>( | |
297 | "boost::math::variance(cauchy<%1%>&)", | |
298 | "The Cauchy distribution does not have a variance: " | |
299 | "the only possible return value is %1%.", | |
300 | std::numeric_limits<RealType>::quiet_NaN(), Policy()); | |
301 | } | |
302 | ||
303 | template <class RealType, class Policy> | |
304 | inline RealType mode(const cauchy_distribution<RealType, Policy>& dist) | |
305 | { | |
306 | return dist.location(); | |
307 | } | |
308 | ||
309 | template <class RealType, class Policy> | |
310 | inline RealType median(const cauchy_distribution<RealType, Policy>& dist) | |
311 | { | |
312 | return dist.location(); | |
313 | } | |
314 | template <class RealType, class Policy> | |
315 | inline RealType skewness(const cauchy_distribution<RealType, Policy>& /*dist*/) | |
316 | { | |
317 | // There is no skewness: | |
318 | typedef typename Policy::assert_undefined_type assert_type; | |
1e59de90 | 319 | static_assert(assert_type::value == 0, "assert type is undefined"); |
7c673cae FG |
320 | |
321 | return policies::raise_domain_error<RealType>( | |
322 | "boost::math::skewness(cauchy<%1%>&)", | |
323 | "The Cauchy distribution does not have a skewness: " | |
324 | "the only possible return value is %1%.", | |
325 | std::numeric_limits<RealType>::quiet_NaN(), Policy()); // infinity? | |
326 | } | |
327 | ||
328 | template <class RealType, class Policy> | |
329 | inline RealType kurtosis(const cauchy_distribution<RealType, Policy>& /*dist*/) | |
330 | { | |
331 | // There is no kurtosis: | |
332 | typedef typename Policy::assert_undefined_type assert_type; | |
1e59de90 | 333 | static_assert(assert_type::value == 0, "assert type is undefined"); |
7c673cae FG |
334 | |
335 | return policies::raise_domain_error<RealType>( | |
336 | "boost::math::kurtosis(cauchy<%1%>&)", | |
337 | "The Cauchy distribution does not have a kurtosis: " | |
338 | "the only possible return value is %1%.", | |
339 | std::numeric_limits<RealType>::quiet_NaN(), Policy()); | |
340 | } | |
341 | ||
342 | template <class RealType, class Policy> | |
343 | inline RealType kurtosis_excess(const cauchy_distribution<RealType, Policy>& /*dist*/) | |
344 | { | |
345 | // There is no kurtosis excess: | |
346 | typedef typename Policy::assert_undefined_type assert_type; | |
1e59de90 | 347 | static_assert(assert_type::value == 0, "assert type is undefined"); |
7c673cae FG |
348 | |
349 | return policies::raise_domain_error<RealType>( | |
350 | "boost::math::kurtosis_excess(cauchy<%1%>&)", | |
351 | "The Cauchy distribution does not have a kurtosis: " | |
352 | "the only possible return value is %1%.", | |
353 | std::numeric_limits<RealType>::quiet_NaN(), Policy()); | |
354 | } | |
355 | ||
f67539c2 TL |
356 | template <class RealType, class Policy> |
357 | inline RealType entropy(const cauchy_distribution<RealType, Policy> & dist) | |
358 | { | |
359 | using std::log; | |
360 | return log(2*constants::two_pi<RealType>()*dist.scale()); | |
361 | } | |
362 | ||
7c673cae FG |
363 | } // namespace math |
364 | } // namespace boost | |
365 | ||
366 | #ifdef _MSC_VER | |
367 | #pragma warning(pop) | |
368 | #endif | |
369 | ||
370 | // This include must be at the end, *after* the accessors | |
371 | // for this distribution have been defined, in order to | |
372 | // keep compilers that support two-phase lookup happy. | |
373 | #include <boost/math/distributions/detail/derived_accessors.hpp> | |
374 | ||
375 | #endif // BOOST_STATS_CAUCHY_HPP |