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diff --git a/src/third_party/boost-1.56.0/boost/math/distributions/geometric.hpp b/src/third_party/boost-1.56.0/boost/math/distributions/geometric.hpp deleted file mode 100644 index 88947d6c57a..00000000000 --- a/src/third_party/boost-1.56.0/boost/math/distributions/geometric.hpp +++ /dev/null @@ -1,516 +0,0 @@ -// boost\math\distributions\geometric.hpp - -// Copyright John Maddock 2010. -// Copyright Paul A. Bristow 2010. - -// 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) - -// geometric distribution is a discrete probability distribution. -// It expresses the probability distribution of the number (k) of -// events, occurrences, failures or arrivals before the first success. -// supported on the set {0, 1, 2, 3...} - -// Note that the set includes zero (unlike some definitions that start at one). - -// The random variate k is the number of events, occurrences or arrivals. -// k argument may be integral, signed, or unsigned, or floating point. -// If necessary, it has already been promoted from an integral type. - -// Note that the geometric distribution -// (like others including the binomial, geometric & Bernoulli) -// is strictly defined as a discrete function: -// only integral values of k are envisaged. -// However because the method of calculation uses a continuous gamma function, -// it is convenient to treat it as if a continous function, -// and permit non-integral values of k. -// To enforce the strict mathematical model, users should use floor or ceil functions -// on k outside this function to ensure that k is integral. - -// See http://en.wikipedia.org/wiki/geometric_distribution -// http://documents.wolfram.com/v5/Add-onsLinks/StandardPackages/Statistics/DiscreteDistributions.html -// http://mathworld.wolfram.com/GeometricDistribution.html - -#ifndef BOOST_MATH_SPECIAL_GEOMETRIC_HPP -#define BOOST_MATH_SPECIAL_GEOMETRIC_HPP - -#include <boost/math/distributions/fwd.hpp> -#include <boost/math/special_functions/beta.hpp> // for ibeta(a, b, x) == Ix(a, b). -#include <boost/math/distributions/complement.hpp> // complement. -#include <boost/math/distributions/detail/common_error_handling.hpp> // error checks domain_error & logic_error. -#include <boost/math/special_functions/fpclassify.hpp> // isnan. -#include <boost/math/tools/roots.hpp> // for root finding. -#include <boost/math/distributions/detail/inv_discrete_quantile.hpp> - -#include <boost/type_traits/is_floating_point.hpp> -#include <boost/type_traits/is_integral.hpp> -#include <boost/type_traits/is_same.hpp> -#include <boost/mpl/if.hpp> - -#include <limits> // using std::numeric_limits; -#include <utility> - -#if defined (BOOST_MSVC) -# pragma warning(push) -// This believed not now necessary, so commented out. -//# pragma warning(disable: 4702) // unreachable code. -// in domain_error_imp in error_handling. -#endif - -namespace boost -{ - namespace math - { - namespace geometric_detail - { - // Common error checking routines for geometric distribution function: - template <class RealType, class Policy> - inline bool check_success_fraction(const char* function, const RealType& p, RealType* result, const Policy& pol) - { - if( !(boost::math::isfinite)(p) || (p < 0) || (p > 1) ) - { - *result = policies::raise_domain_error<RealType>( - function, - "Success fraction argument is %1%, but must be >= 0 and <= 1 !", p, pol); - return false; - } - return true; - } - - template <class RealType, class Policy> - inline bool check_dist(const char* function, const RealType& p, RealType* result, const Policy& pol) - { - return check_success_fraction(function, p, result, pol); - } - - template <class RealType, class Policy> - inline bool check_dist_and_k(const char* function, const RealType& p, RealType k, RealType* result, const Policy& pol) - { - if(check_dist(function, p, result, pol) == false) - { - return false; - } - if( !(boost::math::isfinite)(k) || (k < 0) ) - { // Check k failures. - *result = policies::raise_domain_error<RealType>( - function, - "Number of failures argument is %1%, but must be >= 0 !", k, pol); - return false; - } - return true; - } // Check_dist_and_k - - template <class RealType, class Policy> - inline bool check_dist_and_prob(const char* function, RealType p, RealType prob, RealType* result, const Policy& pol) - { - if(check_dist(function, p, result, pol) && detail::check_probability(function, prob, result, pol) == false) - { - return false; - } - return true; - } // check_dist_and_prob - } // namespace geometric_detail - - template <class RealType = double, class Policy = policies::policy<> > - class geometric_distribution - { - public: - typedef RealType value_type; - typedef Policy policy_type; - - geometric_distribution(RealType p) : m_p(p) - { // Constructor stores success_fraction p. - RealType result; - geometric_detail::check_dist( - "geometric_distribution<%1%>::geometric_distribution", - m_p, // Check success_fraction 0 <= p <= 1. - &result, Policy()); - } // geometric_distribution constructor. - - // Private data getter class member functions. - RealType success_fraction() const - { // Probability of success as fraction in range 0 to 1. - return m_p; - } - RealType successes() const - { // Total number of successes r = 1 (for compatibility with negative binomial?). - return 1; - } - - // Parameter estimation. - // (These are copies of negative_binomial distribution with successes = 1). - static RealType find_lower_bound_on_p( - RealType trials, - RealType alpha) // alpha 0.05 equivalent to 95% for one-sided test. - { - static const char* function = "boost::math::geometric<%1%>::find_lower_bound_on_p"; - RealType result = 0; // of error checks. - RealType successes = 1; - RealType failures = trials - successes; - if(false == detail::check_probability(function, alpha, &result, Policy()) - && geometric_detail::check_dist_and_k( - function, RealType(0), failures, &result, Policy())) - { - return result; - } - // Use complement ibeta_inv function for lower bound. - // This is adapted from the corresponding binomial formula - // here: http://www.itl.nist.gov/div898/handbook/prc/section2/prc241.htm - // This is a Clopper-Pearson interval, and may be overly conservative, - // see also "A Simple Improved Inferential Method for Some - // Discrete Distributions" Yong CAI and K. KRISHNAMOORTHY - // http://www.ucs.louisiana.edu/~kxk4695/Discrete_new.pdf - // - return ibeta_inv(successes, failures + 1, alpha, static_cast<RealType*>(0), Policy()); - } // find_lower_bound_on_p - - static RealType find_upper_bound_on_p( - RealType trials, - RealType alpha) // alpha 0.05 equivalent to 95% for one-sided test. - { - static const char* function = "boost::math::geometric<%1%>::find_upper_bound_on_p"; - RealType result = 0; // of error checks. - RealType successes = 1; - RealType failures = trials - successes; - if(false == geometric_detail::check_dist_and_k( - function, RealType(0), failures, &result, Policy()) - && detail::check_probability(function, alpha, &result, Policy())) - { - return result; - } - if(failures == 0) - { - return 1; - }// Use complement ibetac_inv function for upper bound. - // Note adjusted failures value: *not* failures+1 as usual. - // This is adapted from the corresponding binomial formula - // here: http://www.itl.nist.gov/div898/handbook/prc/section2/prc241.htm - // This is a Clopper-Pearson interval, and may be overly conservative, - // see also "A Simple Improved Inferential Method for Some - // Discrete Distributions" Yong CAI and K. Krishnamoorthy - // http://www.ucs.louisiana.edu/~kxk4695/Discrete_new.pdf - // - return ibetac_inv(successes, failures, alpha, static_cast<RealType*>(0), Policy()); - } // find_upper_bound_on_p - - // Estimate number of trials : - // "How many trials do I need to be P% sure of seeing k or fewer failures?" - - static RealType find_minimum_number_of_trials( - RealType k, // number of failures (k >= 0). - RealType p, // success fraction 0 <= p <= 1. - RealType alpha) // risk level threshold 0 <= alpha <= 1. - { - static const char* function = "boost::math::geometric<%1%>::find_minimum_number_of_trials"; - // Error checks: - RealType result = 0; - if(false == geometric_detail::check_dist_and_k( - function, p, k, &result, Policy()) - && detail::check_probability(function, alpha, &result, Policy())) - { - return result; - } - result = ibeta_inva(k + 1, p, alpha, Policy()); // returns n - k - return result + k; - } // RealType find_number_of_failures - - static RealType find_maximum_number_of_trials( - RealType k, // number of failures (k >= 0). - RealType p, // success fraction 0 <= p <= 1. - RealType alpha) // risk level threshold 0 <= alpha <= 1. - { - static const char* function = "boost::math::geometric<%1%>::find_maximum_number_of_trials"; - // Error checks: - RealType result = 0; - if(false == geometric_detail::check_dist_and_k( - function, p, k, &result, Policy()) - && detail::check_probability(function, alpha, &result, Policy())) - { - return result; - } - result = ibetac_inva(k + 1, p, alpha, Policy()); // returns n - k - return result + k; - } // RealType find_number_of_trials complemented - - private: - //RealType m_r; // successes fixed at unity. - RealType m_p; // success_fraction - }; // template <class RealType, class Policy> class geometric_distribution - - typedef geometric_distribution<double> geometric; // Reserved name of type double. - - template <class RealType, class Policy> - inline const std::pair<RealType, RealType> range(const geometric_distribution<RealType, Policy>& /* dist */) - { // Range of permissible values for random variable k. - using boost::math::tools::max_value; - return std::pair<RealType, RealType>(static_cast<RealType>(0), max_value<RealType>()); // max_integer? - } - - template <class RealType, class Policy> - inline const std::pair<RealType, RealType> support(const geometric_distribution<RealType, Policy>& /* dist */) - { // Range of supported values for random variable k. - // 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<RealType, RealType>(static_cast<RealType>(0), max_value<RealType>()); // max_integer? - } - - template <class RealType, class Policy> - inline RealType mean(const geometric_distribution<RealType, Policy>& dist) - { // Mean of geometric distribution = (1-p)/p. - return (1 - dist.success_fraction() ) / dist.success_fraction(); - } // mean - - // median implemented via quantile(half) in derived accessors. - - template <class RealType, class Policy> - inline RealType mode(const geometric_distribution<RealType, Policy>&) - { // Mode of geometric distribution = zero. - BOOST_MATH_STD_USING // ADL of std functions. - return 0; - } // mode - - template <class RealType, class Policy> - inline RealType variance(const geometric_distribution<RealType, Policy>& dist) - { // Variance of Binomial distribution = (1-p) / p^2. - return (1 - dist.success_fraction()) - / (dist.success_fraction() * dist.success_fraction()); - } // variance - - template <class RealType, class Policy> - inline RealType skewness(const geometric_distribution<RealType, Policy>& dist) - { // skewness of geometric distribution = 2-p / (sqrt(r(1-p)) - BOOST_MATH_STD_USING // ADL of std functions. - RealType p = dist.success_fraction(); - return (2 - p) / sqrt(1 - p); - } // skewness - - template <class RealType, class Policy> - inline RealType kurtosis(const geometric_distribution<RealType, Policy>& dist) - { // kurtosis of geometric distribution - // http://en.wikipedia.org/wiki/geometric is kurtosis_excess so add 3 - RealType p = dist.success_fraction(); - return 3 + (p*p - 6*p + 6) / (1 - p); - } // kurtosis - - template <class RealType, class Policy> - inline RealType kurtosis_excess(const geometric_distribution<RealType, Policy>& dist) - { // kurtosis excess of geometric distribution - // http://mathworld.wolfram.com/Kurtosis.html table of kurtosis_excess - RealType p = dist.success_fraction(); - return (p*p - 6*p + 6) / (1 - p); - } // kurtosis_excess - - // RealType standard_deviation(const geometric_distribution<RealType, Policy>& dist) - // standard_deviation provided by derived accessors. - // RealType hazard(const geometric_distribution<RealType, Policy>& dist) - // hazard of geometric distribution provided by derived accessors. - // RealType chf(const geometric_distribution<RealType, Policy>& dist) - // chf of geometric distribution provided by derived accessors. - - template <class RealType, class Policy> - inline RealType pdf(const geometric_distribution<RealType, Policy>& dist, const RealType& k) - { // Probability Density/Mass Function. - BOOST_FPU_EXCEPTION_GUARD - BOOST_MATH_STD_USING // For ADL of math functions. - static const char* function = "boost::math::pdf(const geometric_distribution<%1%>&, %1%)"; - - RealType p = dist.success_fraction(); - RealType result = 0; - if(false == geometric_detail::check_dist_and_k( - function, - p, - k, - &result, Policy())) - { - return result; - } - if (k == 0) - { - return p; // success_fraction - } - RealType q = 1 - p; // Inaccurate for small p? - // So try to avoid inaccuracy for large or small p. - // but has little effect > last significant bit. - //cout << "p * pow(q, k) " << result << endl; // seems best whatever p - //cout << "exp(p * k * log1p(-p)) " << p * exp(k * log1p(-p)) << endl; - //if (p < 0.5) - //{ - // result = p * pow(q, k); - //} - //else - //{ - // result = p * exp(k * log1p(-p)); - //} - result = p * pow(q, k); - return result; - } // geometric_pdf - - template <class RealType, class Policy> - inline RealType cdf(const geometric_distribution<RealType, Policy>& dist, const RealType& k) - { // Cumulative Distribution Function of geometric. - static const char* function = "boost::math::cdf(const geometric_distribution<%1%>&, %1%)"; - - // k argument may be integral, signed, or unsigned, or floating point. - // If necessary, it has already been promoted from an integral type. - RealType p = dist.success_fraction(); - // Error check: - RealType result = 0; - if(false == geometric_detail::check_dist_and_k( - function, - p, - k, - &result, Policy())) - { - return result; - } - if(k == 0) - { - return p; // success_fraction - } - //RealType q = 1 - p; // Bad for small p - //RealType probability = 1 - std::pow(q, k+1); - - RealType z = boost::math::log1p(-p, Policy()) * (k + 1); - RealType probability = -boost::math::expm1(z, Policy()); - - return probability; - } // cdf Cumulative Distribution Function geometric. - - template <class RealType, class Policy> - inline RealType cdf(const complemented2_type<geometric_distribution<RealType, Policy>, RealType>& c) - { // Complemented Cumulative Distribution Function geometric. - BOOST_MATH_STD_USING - static const char* function = "boost::math::cdf(const geometric_distribution<%1%>&, %1%)"; - // k argument may be integral, signed, or unsigned, or floating point. - // If necessary, it has already been promoted from an integral type. - RealType const& k = c.param; - geometric_distribution<RealType, Policy> const& dist = c.dist; - RealType p = dist.success_fraction(); - // Error check: - RealType result = 0; - if(false == geometric_detail::check_dist_and_k( - function, - p, - k, - &result, Policy())) - { - return result; - } - RealType z = boost::math::log1p(-p, Policy()) * (k+1); - RealType probability = exp(z); - return probability; - } // cdf Complemented Cumulative Distribution Function geometric. - - template <class RealType, class Policy> - inline RealType quantile(const geometric_distribution<RealType, Policy>& dist, const RealType& x) - { // Quantile, percentile/100 or Percent Point geometric function. - // Return the number of expected failures k for a given probability p. - - // Inverse cumulative Distribution Function or Quantile (percentile / 100) of geometric Probability. - // k argument may be integral, signed, or unsigned, or floating point. - - static const char* function = "boost::math::quantile(const geometric_distribution<%1%>&, %1%)"; - BOOST_MATH_STD_USING // ADL of std functions. - - RealType success_fraction = dist.success_fraction(); - // Check dist and x. - RealType result = 0; - if(false == geometric_detail::check_dist_and_prob - (function, success_fraction, x, &result, Policy())) - { - return result; - } - - // Special cases. - if (x == 1) - { // Would need +infinity failures for total confidence. - result = policies::raise_overflow_error<RealType>( - function, - "Probability argument is 1, which implies infinite failures !", Policy()); - return result; - // usually means return +std::numeric_limits<RealType>::infinity(); - // unless #define BOOST_MATH_THROW_ON_OVERFLOW_ERROR - } - if (x == 0) - { // No failures are expected if P = 0. - return 0; // Total trials will be just dist.successes. - } - // if (P <= pow(dist.success_fraction(), 1)) - if (x <= success_fraction) - { // p <= pdf(dist, 0) == cdf(dist, 0) - return 0; - } - if (x == 1) - { - return 0; - } - - // log(1-x) /log(1-success_fraction) -1; but use log1p in case success_fraction is small - result = boost::math::log1p(-x, Policy()) / boost::math::log1p(-success_fraction, Policy()) - 1; - // Subtract a few epsilons here too? - // to make sure it doesn't slip over, so ceil would be one too many. - return result; - } // RealType quantile(const geometric_distribution dist, p) - - template <class RealType, class Policy> - inline RealType quantile(const complemented2_type<geometric_distribution<RealType, Policy>, RealType>& c) - { // Quantile or Percent Point Binomial function. - // Return the number of expected failures k for a given - // complement of the probability Q = 1 - P. - static const char* function = "boost::math::quantile(const geometric_distribution<%1%>&, %1%)"; - BOOST_MATH_STD_USING - // Error checks: - RealType x = c.param; - const geometric_distribution<RealType, Policy>& dist = c.dist; - RealType success_fraction = dist.success_fraction(); - RealType result = 0; - if(false == geometric_detail::check_dist_and_prob( - function, - success_fraction, - x, - &result, Policy())) - { - return result; - } - - // Special cases: - if(x == 1) - { // There may actually be no answer to this question, - // since the probability of zero failures may be non-zero, - return 0; // but zero is the best we can do: - } - if (-x <= boost::math::powm1(dist.success_fraction(), dist.successes(), Policy())) - { // q <= cdf(complement(dist, 0)) == pdf(dist, 0) - return 0; // - } - if(x == 0) - { // Probability 1 - Q == 1 so infinite failures to achieve certainty. - // Would need +infinity failures for total confidence. - result = policies::raise_overflow_error<RealType>( - function, - "Probability argument complement is 0, which implies infinite failures !", Policy()); - return result; - // usually means return +std::numeric_limits<RealType>::infinity(); - // unless #define BOOST_MATH_THROW_ON_OVERFLOW_ERROR - } - // log(x) /log(1-success_fraction) -1; but use log1p in case success_fraction is small - result = log(x) / boost::math::log1p(-success_fraction, Policy()) - 1; - return result; - - } // quantile complement - - } // 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> - -#if defined (BOOST_MSVC) -# pragma warning(pop) -#endif - -#endif // BOOST_MATH_SPECIAL_GEOMETRIC_HPP |