mirror of
https://github.com/bolero-MURAKAMI/Sprout.git
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417 lines
18 KiB
C++
417 lines
18 KiB
C++
/*=============================================================================
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Copyright (c) 2011-2015 Bolero MURAKAMI
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https://github.com/bolero-MURAKAMI/Sprout
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Distributed under the Boost Software License, Version 1.0. (See accompanying
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file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
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=============================================================================*/
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#ifndef SPROUT_RANDOM_POISSON_DISTRIBUTION_HPP
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#define SPROUT_RANDOM_POISSON_DISTRIBUTION_HPP
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#include <istream>
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#include <ostream>
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#include <sprout/config.hpp>
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#include <sprout/limits.hpp>
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#include <sprout/cstdlib/abs.hpp>
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#include <sprout/math/abs.hpp>
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#include <sprout/math/log.hpp>
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#include <sprout/math/floor.hpp>
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#include <sprout/random/random_result.hpp>
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#include <sprout/random/uniform_01.hpp>
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#include <sprout/random/results.hpp>
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#include <sprout/assert.hpp>
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#ifdef SPROUT_WORKAROUND_NOT_TERMINATE_RECURSIVE_CONSTEXPR_FUNCTION_TEMPLATE
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# include <sprout/workaround/recursive_function_template.hpp>
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#endif
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namespace sprout {
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namespace random {
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namespace detail {
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# define SPROUT_POISSON_TABLE_DEF \
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{{ \
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0.0, \
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0.0, \
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0.69314718055994529, \
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1.7917594692280550, \
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3.1780538303479458, \
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4.7874917427820458, \
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6.5792512120101012, \
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8.5251613610654147, \
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10.604602902745251, \
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12.801827480081469 \
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}}
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template<typename RealType>
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struct poisson_table {
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public:
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typedef sprout::array<RealType, 10> table_type;
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public:
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SPROUT_STATIC_CONSTEXPR table_type table
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SPROUT_STATIC_CONSTEXPR_DATA_MEMBER_INNER(SPROUT_POISSON_TABLE_DEF)
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;
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};
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template<typename RealType>
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SPROUT_CONSTEXPR_OR_CONST typename sprout::random::detail::poisson_table<RealType>::table_type
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sprout::random::detail::poisson_table<RealType>::table
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SPROUT_STATIC_CONSTEXPR_DATA_MEMBER_OUTER(SPROUT_POISSON_TABLE_DEF)
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;
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# undef SPROUT_POISSON_TABLE_DEF
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} // namespace detail
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//
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// poisson_distribution
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//
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template<typename IntType = int, typename RealType = double>
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class poisson_distribution {
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public:
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typedef RealType input_type;
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typedef IntType result_type;
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public:
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//
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// param_type
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//
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class param_type {
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public:
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typedef poisson_distribution distribution_type;
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private:
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RealType mean_;
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public:
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SPROUT_CONSTEXPR param_type()
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: mean_(RealType(1))
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{}
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param_type(param_type const&) = default;
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explicit SPROUT_CONSTEXPR param_type(RealType mean_arg)
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: mean_((SPROUT_ASSERT(RealType(0) < mean_arg), mean_arg))
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{}
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SPROUT_CONSTEXPR RealType mean() const SPROUT_NOEXCEPT {
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return mean_;
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}
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template<typename Elem, typename Traits>
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friend SPROUT_NON_CONSTEXPR std::basic_istream<Elem, Traits>& operator>>(
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std::basic_istream<Elem, Traits>& lhs,
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param_type& rhs
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)
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{
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RealType mean;
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if (lhs >> mean) {
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if (RealType(0) < mean) {
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rhs.mean_ = mean;
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} else {
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lhs.setstate(std::ios_base::failbit);
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}
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}
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return lhs;
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}
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template<typename Elem, typename Traits>
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friend SPROUT_NON_CONSTEXPR std::basic_ostream<Elem, Traits>& operator<<(
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std::basic_ostream<Elem, Traits>& lhs,
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param_type const& rhs
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)
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{
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return lhs << rhs.mean_;
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}
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friend SPROUT_CONSTEXPR bool operator==(param_type const& lhs, param_type const& rhs) SPROUT_NOEXCEPT {
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return lhs.mean_ == rhs.mean_;
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}
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friend SPROUT_CONSTEXPR bool operator!=(param_type const& lhs, param_type const& rhs) SPROUT_NOEXCEPT {
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return !(lhs == rhs);
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}
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};
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struct ptrd_type {
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public:
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RealType v_r;
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RealType a;
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RealType b;
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RealType smu;
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RealType inv_alpha;
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};
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private:
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static SPROUT_CONSTEXPR bool use_inversion_check(RealType mean) {
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return mean < 10;
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}
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static SPROUT_CONSTEXPR ptrd_type init_ptrd_2(RealType smu, RealType b) {
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return ptrd_type{
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0.9277 - 3.6224 / (b - 2),
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-0.059 + 0.02483 * b,
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b,
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smu,
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1.1239 + 1.1328 / (b - 3.4)
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};
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}
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static SPROUT_CONSTEXPR ptrd_type init_ptrd_1(RealType smu) {
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return init_ptrd_2(smu, 0.931 + 2.53 * smu);
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}
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static SPROUT_CONSTEXPR ptrd_type init_ptrd(RealType mean) {
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return use_inversion_check(mean) ? ptrd_type()
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: init_ptrd_1(sprout::sqrt(mean))
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;
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}
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static SPROUT_CONSTEXPR RealType init_exp_mean(RealType mean) {
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return !use_inversion_check(mean) ? RealType()
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: sprout::exp(-mean)
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;
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}
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static SPROUT_CONSTEXPR RealType log_factorial(IntType k) {
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return sprout::random::detail::poisson_table<RealType>::table[k];
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}
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static SPROUT_CONSTEXPR RealType log_sqrt_2pi() {
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return 0.91893853320467267;
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}
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static SPROUT_CONSTEXPR RealType generate_us(RealType u) {
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return 0.5 - sprout::abs(u);
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}
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private:
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RealType mean_;
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ptrd_type ptrd_;
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RealType exp_mean_;
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private:
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SPROUT_CONSTEXPR bool use_inversion() const {
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return use_inversion_check(mean_);
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}
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template<typename Engine>
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SPROUT_CXX14_CONSTEXPR result_type do_invert(Engine& eng) const {
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RealType u = sprout::random::uniform_01<RealType>()(eng);
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IntType x = 0;
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RealType p = exp_mean_;
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while (u > p) {
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u -= p;
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++x;
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p = p * mean_ / x;
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}
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return x;
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}
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template<typename Engine, typename Random>
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SPROUT_CONSTEXPR sprout::random::random_result<Engine, poisson_distribution> invert_2(Random const& rnd, RealType u, IntType x, RealType p) const {
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return !(u > p) ? sprout::random::random_result<Engine, poisson_distribution>(x, sprout::random::next(rnd).engine(), *this)
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: invert_2<Engine>(rnd, u - p, x + 1, p * mean_ / (x + 1))
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;
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}
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template<typename Engine, typename Random>
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SPROUT_CONSTEXPR sprout::random::random_result<Engine, poisson_distribution> invert_1(Random const& rnd, IntType x, RealType p) const {
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return invert_2<Engine>(rnd, sprout::random::result(rnd), x, p);
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}
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template<typename Engine>
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SPROUT_CONSTEXPR sprout::random::random_result<Engine, poisson_distribution> invert(Engine const& eng) const {
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return invert_1<Engine>(sprout::random::uniform_01<RealType>()(eng), 0, exp_mean_);
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}
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template<typename Engine>
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SPROUT_CXX14_CONSTEXPR result_type do_generate(Engine& eng) const {
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for (; ; ) {
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RealType v = sprout::random::uniform_01<RealType>()(eng);
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if (v <= 0.86 * ptrd_.v_r) {
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RealType u = v / ptrd_.v_r - 0.43;
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return static_cast<IntType>(sprout::floor((2 * ptrd_.a / (0.5 - sprout::abs(u)) + ptrd_.b) * u + mean_ + 0.445));
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}
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RealType u = RealType();
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if (v >= ptrd_.v_r) {
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u = sprout::random::uniform_01<RealType>()(eng) - 0.5;
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} else {
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u = v / ptrd_.v_r - 0.93;
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u = ((u < 0) ? -0.5 : 0.5) - u;
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v = sprout::random::uniform_01<RealType>()(eng) * ptrd_.v_r;
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}
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RealType us = 0.5 - sprout::abs(u);
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if (us < 0.013 && v > us) {
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continue;
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}
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RealType k = sprout::floor((2 * ptrd_.a / us + ptrd_.b) * u + mean_ + 0.445);
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v = v * ptrd_.inv_alpha / (ptrd_.a / (us * us) + ptrd_.b);
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if ((k >= 10 && sprout::log(v * ptrd_.smu) <= (k + 0.5) * sprout::log(mean_ / k) - mean_ - log_sqrt_2pi() + k - (1 / 12. - (1 / 360. - 1 / (1260. * k * k)) / (k * k)) / k)
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|| (k >= 0 && sprout::log(v) <= k * sprout::log(mean_) - mean_ - log_factorial(static_cast<IntType>(k)))
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)
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{
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return static_cast<IntType>(k);
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}
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}
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}
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template<typename Engine, typename Random>
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SPROUT_CONSTEXPR sprout::random::random_result<Engine, poisson_distribution> generate_4(Random const& rnd, RealType u) const {
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return sprout::random::random_result<Engine, poisson_distribution>(
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static_cast<IntType>(sprout::floor((2 * ptrd_.a / (0.5 - sprout::abs(u)) + ptrd_.b) * u + mean_ + 0.445)),
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sprout::random::next(rnd).engine(),
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*this
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);
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}
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#ifdef SPROUT_WORKAROUND_NOT_TERMINATE_RECURSIVE_CONSTEXPR_FUNCTION_TEMPLATE
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template<typename Engine, int D, typename Random, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_CONTINUE(D)>
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SPROUT_CONSTEXPR sprout::random::random_result<Engine, poisson_distribution> generate_3(Random const& rnd, RealType k, RealType v) const {
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return (k >= 10 && sprout::log(v * ptrd_.smu) <= (k + 0.5) * sprout::log(mean_ / k) - mean_ - log_sqrt_2pi() + k - (1 / 12. - (1 / 360. - 1 / (1260. * k * k)) / (k * k)) / k)
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|| (k >= 0 && sprout::log(v) <= k * sprout::log(mean_) - mean_ - log_factorial(static_cast<IntType>(k)))
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? sprout::random::random_result<Engine, poisson_distribution>(static_cast<IntType>(k), sprout::random::next(rnd).engine(), *this)
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: generate_1<Engine, D + 1>(rnd())
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;
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}
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template<typename Engine, int D, typename Random, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_BREAK(D)>
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SPROUT_CONSTEXPR sprout::random::random_result<Engine, poisson_distribution> generate_3(Random const&, RealType, RealType) const {
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return sprout::throw_recursive_function_template_instantiation_exeeded();
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}
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template<typename Engine, int D, typename Random, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_CONTINUE(D)>
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SPROUT_CONSTEXPR sprout::random::random_result<Engine, poisson_distribution> generate_2(Random const& rnd, RealType v, RealType u, RealType us) const {
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return us < 0.013 && v > us ? generate_1<Engine, D + 1>(rnd())
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: generate_3<Engine, D + 1>(
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rnd,
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sprout::floor((2 * ptrd_.a / us + ptrd_.b) * u + mean_ + 0.445),
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v * ptrd_.inv_alpha / (ptrd_.a / (us * us) + ptrd_.b)
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)
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;
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}
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template<typename Engine, int D, typename Random, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_BREAK(D)>
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SPROUT_CONSTEXPR sprout::random::random_result<Engine, poisson_distribution> generate_2(Random const&, RealType, RealType, RealType) const {
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return sprout::throw_recursive_function_template_instantiation_exeeded();
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}
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template<typename Engine, int D, typename Random, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_CONTINUE(D)>
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SPROUT_CONSTEXPR sprout::random::random_result<Engine, poisson_distribution> generate_1_3(Random const& rnd, RealType, RealType u) const {
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return generate_2<Engine, D + 1>(rnd, sprout::random::result(rnd), ((u < 0) ? -0.5 : 0.5) - u, generate_us(((u < 0) ? -0.5 : 0.5) - u));
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}
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template<typename Engine, int D, typename Random, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_BREAK(D)>
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SPROUT_CONSTEXPR sprout::random::random_result<Engine, poisson_distribution> generate_1_3(Random const&, RealType, RealType) const {
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return sprout::throw_recursive_function_template_instantiation_exeeded();
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}
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template<typename Engine, int D, typename Random, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_CONTINUE(D)>
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SPROUT_CONSTEXPR sprout::random::random_result<Engine, poisson_distribution> generate_1_2(Random const& rnd, RealType v) const {
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return generate_2<Engine, D + 1>(rnd, v, sprout::random::result(rnd) - 0.5, generate_us(sprout::random::result(rnd) - 0.5));
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}
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template<typename Engine, int D, typename Random, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_BREAK(D)>
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SPROUT_CONSTEXPR sprout::random::random_result<Engine, poisson_distribution> generate_1_2(Random const&, RealType) const {
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return sprout::throw_recursive_function_template_instantiation_exeeded();
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}
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template<typename Engine, int D = 16, typename Random, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_CONTINUE(D)>
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SPROUT_CONSTEXPR sprout::random::random_result<Engine, poisson_distribution> generate_1(Random const& rnd) const {
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return sprout::random::result(rnd) <= 0.86 * ptrd_.v_r ? generate_4<Engine>(rnd, sprout::random::result(rnd) / ptrd_.v_r - 0.43)
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: sprout::random::result(rnd) >= ptrd_.v_r
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? generate_1_2<Engine, D + 1>(rnd(), sprout::random::result(rnd))
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: generate_1_3<Engine, D + 1>(rnd(), sprout::random::result(rnd), sprout::random::result(rnd) / ptrd_.v_r - 0.93)
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;
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}
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template<typename Engine, int D = 16, typename Random, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_BREAK(D)>
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SPROUT_CONSTEXPR sprout::random::random_result<Engine, poisson_distribution> generate_1(Random const&) const {
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return sprout::throw_recursive_function_template_instantiation_exeeded();
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}
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#else
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template<typename Engine, typename Random>
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SPROUT_CONSTEXPR sprout::random::random_result<Engine, poisson_distribution> generate_3(Random const& rnd, RealType k, RealType v) const {
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return (k >= 10 && sprout::log(v * ptrd_.smu) <= (k + 0.5) * sprout::log(mean_ / k) - mean_ - log_sqrt_2pi() + k - (1 / 12. - (1 / 360. - 1 / (1260. * k * k)) / (k * k)) / k)
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|| (k >= 0 && sprout::log(v) <= k * sprout::log(mean_) - mean_ - log_factorial(static_cast<IntType>(k)))
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? sprout::random::random_result<Engine, poisson_distribution>(static_cast<IntType>(k), sprout::random::next(rnd).engine(), *this)
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: generate_1<Engine>(rnd())
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;
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}
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template<typename Engine, typename Random>
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SPROUT_CONSTEXPR sprout::random::random_result<Engine, poisson_distribution> generate_2(Random const& rnd, RealType v, RealType u, RealType us) const {
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return us < 0.013 && v > us ? generate_1<Engine>(rnd())
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: generate_3<Engine>(
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rnd,
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sprout::floor((2 * ptrd_.a / us + ptrd_.b) * u + mean_ + 0.445),
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v * ptrd_.inv_alpha / (ptrd_.a / (us * us) + ptrd_.b)
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)
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;
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}
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template<typename Engine, typename Random>
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SPROUT_CONSTEXPR sprout::random::random_result<Engine, poisson_distribution> generate_1_3(Random const& rnd, RealType v, RealType u) const {
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return generate_2<Engine>(rnd, sprout::random::result(rnd), ((u < 0) ? -0.5 : 0.5) - u, generate_us(((u < 0) ? -0.5 : 0.5) - u));
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}
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template<typename Engine, typename Random>
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SPROUT_CONSTEXPR sprout::random::random_result<Engine, poisson_distribution> generate_1_2(Random const& rnd, RealType v) const {
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return generate_2<Engine>(rnd, v, sprout::random::result(rnd) - 0.5, generate_us(sprout::random::result(rnd) - 0.5));
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}
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template<typename Engine, typename Random>
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SPROUT_CONSTEXPR sprout::random::random_result<Engine, poisson_distribution> generate_1(Random const& rnd) const {
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return sprout::random::result(rnd) <= 0.86 * ptrd_.v_r ? generate_4<Engine>(rnd, sprout::random::result(rnd) / ptrd_.v_r - 0.43)
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: sprout::random::result(rnd) >= ptrd_.v_r
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? generate_1_2<Engine>(rnd(), sprout::random::result(rnd))
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: generate_1_3<Engine>(rnd(), sprout::random::result(rnd), sprout::random::result(rnd) / ptrd_.v_r - 0.93)
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;
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}
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#endif
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template<typename Engine>
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SPROUT_CONSTEXPR sprout::random::random_result<Engine, poisson_distribution> generate(Engine const& eng) const {
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return generate_1<Engine>(sprout::random::uniform_01<RealType>()(eng));
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}
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public:
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SPROUT_CONSTEXPR poisson_distribution()
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: mean_(RealType(1))
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, ptrd_(init_ptrd(RealType(1)))
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, exp_mean_(init_exp_mean(RealType(1)))
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{}
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poisson_distribution(poisson_distribution const&) = default;
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explicit SPROUT_CONSTEXPR poisson_distribution(RealType mean_arg)
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: mean_((SPROUT_ASSERT(RealType(0) < mean_arg), mean_arg))
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, ptrd_(init_ptrd(mean_arg))
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, exp_mean_(init_exp_mean(mean_arg))
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{}
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explicit SPROUT_CONSTEXPR poisson_distribution(param_type const& parm)
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: mean_(parm.mean())
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, ptrd_(init_ptrd(parm.mean()))
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, exp_mean_(init_exp_mean(parm.mean()))
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{}
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SPROUT_CONSTEXPR result_type mean() const SPROUT_NOEXCEPT {
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return mean_;
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}
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SPROUT_CONSTEXPR result_type min() const SPROUT_NOEXCEPT {
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return 0;
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}
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SPROUT_CONSTEXPR result_type max() const SPROUT_NOEXCEPT {
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return sprout::numeric_limits<result_type>::max();
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}
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SPROUT_CXX14_CONSTEXPR void reset() SPROUT_NOEXCEPT {}
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SPROUT_CONSTEXPR param_type param() const SPROUT_NOEXCEPT {
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return param_type(mean_);
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}
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SPROUT_CXX14_CONSTEXPR void param(param_type const& parm) {
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mean_ = parm.mean();
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ptrd_ = init_ptrd(mean_);
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exp_mean_ = init_exp_mean(mean_);
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}
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template<typename Engine>
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SPROUT_CXX14_CONSTEXPR result_type operator()(Engine& eng) const {
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return use_inversion() ? do_invert(eng)
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: do_generate(eng)
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;
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}
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template<typename Engine>
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SPROUT_CONSTEXPR sprout::random::random_result<Engine, poisson_distribution> const operator()(Engine const& eng) const {
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return use_inversion() ? invert(eng)
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: generate(eng)
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;
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}
|
|
template<typename Engine>
|
|
SPROUT_CXX14_CONSTEXPR result_type operator()(Engine& eng, param_type const& parm) const {
|
|
return poisson_distribution(parm)(eng);
|
|
}
|
|
template<typename Engine>
|
|
SPROUT_CONSTEXPR sprout::random::random_result<Engine, poisson_distribution> const operator()(Engine const& eng, param_type const& parm) const {
|
|
return poisson_distribution(parm)(eng);
|
|
}
|
|
template<typename Elem, typename Traits>
|
|
friend SPROUT_NON_CONSTEXPR std::basic_istream<Elem, Traits>& operator>>(
|
|
std::basic_istream<Elem, Traits>& lhs,
|
|
poisson_distribution& rhs
|
|
)
|
|
{
|
|
param_type parm;
|
|
if (lhs >> parm) {
|
|
rhs.param(parm);
|
|
}
|
|
return lhs;
|
|
}
|
|
template<typename Elem, typename Traits>
|
|
friend SPROUT_NON_CONSTEXPR std::basic_ostream<Elem, Traits>& operator<<(
|
|
std::basic_ostream<Elem, Traits>& lhs,
|
|
poisson_distribution const& rhs
|
|
)
|
|
{
|
|
return lhs << rhs.param();
|
|
}
|
|
friend SPROUT_CONSTEXPR bool operator==(poisson_distribution const& lhs, poisson_distribution const& rhs) SPROUT_NOEXCEPT {
|
|
return lhs.param() == rhs.param();
|
|
}
|
|
friend SPROUT_CONSTEXPR bool operator!=(poisson_distribution const& lhs, poisson_distribution const& rhs) SPROUT_NOEXCEPT {
|
|
return !(lhs == rhs);
|
|
}
|
|
};
|
|
} // namespace random
|
|
|
|
using sprout::random::poisson_distribution;
|
|
} // namespace sprout
|
|
|
|
#endif // #ifndef SPROUT_RANDOM_POISSON_DISTRIBUTION_HPP
|