mirror of
https://github.com/bolero-MURAKAMI/Sprout
synced 2024-11-12 21:09:01 +00:00
417 lines
18 KiB
C++
417 lines
18 KiB
C++
/*=============================================================================
|
|
Copyright (c) 2011-2017 Bolero MURAKAMI
|
|
https://github.com/bolero-MURAKAMI/Sprout
|
|
|
|
Distributed under 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 SPROUT_RANDOM_POISSON_DISTRIBUTION_HPP
|
|
#define SPROUT_RANDOM_POISSON_DISTRIBUTION_HPP
|
|
|
|
#include <istream>
|
|
#include <ostream>
|
|
#include <sprout/config.hpp>
|
|
#include <sprout/limits.hpp>
|
|
#include <sprout/cstdlib/abs.hpp>
|
|
#include <sprout/math/abs.hpp>
|
|
#include <sprout/math/log.hpp>
|
|
#include <sprout/math/floor.hpp>
|
|
#include <sprout/random/random_result.hpp>
|
|
#include <sprout/random/uniform_01.hpp>
|
|
#include <sprout/random/results.hpp>
|
|
#include <sprout/assert.hpp>
|
|
#ifdef SPROUT_WORKAROUND_NOT_TERMINATE_RECURSIVE_CONSTEXPR_FUNCTION_TEMPLATE
|
|
# include <sprout/workaround/recursive_function_template.hpp>
|
|
#endif
|
|
|
|
namespace sprout {
|
|
namespace random {
|
|
namespace detail {
|
|
# define SPROUT_POISSON_TABLE_DEF \
|
|
{{ \
|
|
0.0, \
|
|
0.0, \
|
|
0.69314718055994529, \
|
|
1.7917594692280550, \
|
|
3.1780538303479458, \
|
|
4.7874917427820458, \
|
|
6.5792512120101012, \
|
|
8.5251613610654147, \
|
|
10.604602902745251, \
|
|
12.801827480081469 \
|
|
}}
|
|
|
|
template<typename RealType>
|
|
struct poisson_table {
|
|
public:
|
|
typedef sprout::array<RealType, 10> table_type;
|
|
public:
|
|
SPROUT_STATIC_CONSTEXPR table_type table
|
|
SPROUT_STATIC_CONSTEXPR_DATA_MEMBER_INNER(SPROUT_POISSON_TABLE_DEF)
|
|
;
|
|
};
|
|
template<typename RealType>
|
|
SPROUT_CONSTEXPR_OR_CONST typename sprout::random::detail::poisson_table<RealType>::table_type
|
|
sprout::random::detail::poisson_table<RealType>::table
|
|
SPROUT_STATIC_CONSTEXPR_DATA_MEMBER_OUTER(SPROUT_POISSON_TABLE_DEF)
|
|
;
|
|
|
|
# undef SPROUT_POISSON_TABLE_DEF
|
|
} // namespace detail
|
|
//
|
|
// poisson_distribution
|
|
//
|
|
template<typename IntType = int, typename RealType = double>
|
|
class poisson_distribution {
|
|
public:
|
|
typedef RealType input_type;
|
|
typedef IntType result_type;
|
|
public:
|
|
//
|
|
// param_type
|
|
//
|
|
class param_type {
|
|
public:
|
|
typedef poisson_distribution distribution_type;
|
|
private:
|
|
RealType mean_;
|
|
public:
|
|
SPROUT_CONSTEXPR param_type()
|
|
: mean_(RealType(1))
|
|
{}
|
|
param_type(param_type const&) = default;
|
|
explicit SPROUT_CONSTEXPR param_type(RealType mean_arg)
|
|
: mean_((SPROUT_ASSERT(RealType(0) < mean_arg), mean_arg))
|
|
{}
|
|
SPROUT_CONSTEXPR RealType mean() const SPROUT_NOEXCEPT {
|
|
return mean_;
|
|
}
|
|
template<typename Elem, typename Traits>
|
|
friend SPROUT_NON_CONSTEXPR std::basic_istream<Elem, Traits>& operator>>(
|
|
std::basic_istream<Elem, Traits>& lhs,
|
|
param_type& rhs
|
|
)
|
|
{
|
|
RealType mean;
|
|
if (lhs >> mean) {
|
|
if (RealType(0) < mean) {
|
|
rhs.mean_ = mean;
|
|
} else {
|
|
lhs.setstate(std::ios_base::failbit);
|
|
}
|
|
}
|
|
return lhs;
|
|
}
|
|
template<typename Elem, typename Traits>
|
|
friend SPROUT_NON_CONSTEXPR std::basic_ostream<Elem, Traits>& operator<<(
|
|
std::basic_ostream<Elem, Traits>& lhs,
|
|
param_type const& rhs
|
|
)
|
|
{
|
|
return lhs << rhs.mean_;
|
|
}
|
|
friend SPROUT_CONSTEXPR bool operator==(param_type const& lhs, param_type const& rhs) SPROUT_NOEXCEPT {
|
|
return lhs.mean_ == rhs.mean_;
|
|
}
|
|
friend SPROUT_CONSTEXPR bool operator!=(param_type const& lhs, param_type const& rhs) SPROUT_NOEXCEPT {
|
|
return !(lhs == rhs);
|
|
}
|
|
};
|
|
struct ptrd_type {
|
|
public:
|
|
RealType v_r;
|
|
RealType a;
|
|
RealType b;
|
|
RealType smu;
|
|
RealType inv_alpha;
|
|
};
|
|
private:
|
|
static SPROUT_CONSTEXPR bool use_inversion_check(RealType mean) {
|
|
return mean < 10;
|
|
}
|
|
static SPROUT_CONSTEXPR ptrd_type init_ptrd_2(RealType smu, RealType b) {
|
|
return ptrd_type{
|
|
0.9277 - 3.6224 / (b - 2),
|
|
-0.059 + 0.02483 * b,
|
|
b,
|
|
smu,
|
|
1.1239 + 1.1328 / (b - 3.4)
|
|
};
|
|
}
|
|
static SPROUT_CONSTEXPR ptrd_type init_ptrd_1(RealType smu) {
|
|
return init_ptrd_2(smu, 0.931 + 2.53 * smu);
|
|
}
|
|
static SPROUT_CONSTEXPR ptrd_type init_ptrd(RealType mean) {
|
|
return use_inversion_check(mean) ? ptrd_type()
|
|
: init_ptrd_1(sprout::sqrt(mean))
|
|
;
|
|
}
|
|
static SPROUT_CONSTEXPR RealType init_exp_mean(RealType mean) {
|
|
return !use_inversion_check(mean) ? RealType()
|
|
: sprout::exp(-mean)
|
|
;
|
|
}
|
|
static SPROUT_CONSTEXPR RealType log_factorial(IntType k) {
|
|
return sprout::random::detail::poisson_table<RealType>::table[k];
|
|
}
|
|
static SPROUT_CONSTEXPR RealType log_sqrt_2pi() {
|
|
return 0.91893853320467267;
|
|
}
|
|
static SPROUT_CONSTEXPR RealType generate_us(RealType u) {
|
|
return 0.5 - sprout::abs(u);
|
|
}
|
|
private:
|
|
RealType mean_;
|
|
ptrd_type ptrd_;
|
|
RealType exp_mean_;
|
|
private:
|
|
SPROUT_CONSTEXPR bool use_inversion() const {
|
|
return use_inversion_check(mean_);
|
|
}
|
|
template<typename Engine>
|
|
SPROUT_CXX14_CONSTEXPR result_type do_invert(Engine& eng) const {
|
|
RealType u = sprout::random::uniform_01<RealType>()(eng);
|
|
IntType x = 0;
|
|
RealType p = exp_mean_;
|
|
while (u > p) {
|
|
u -= p;
|
|
++x;
|
|
p = p * mean_ / x;
|
|
}
|
|
return x;
|
|
}
|
|
template<typename Engine, typename Random>
|
|
SPROUT_CONSTEXPR sprout::random::random_result<Engine, poisson_distribution> invert_2(Random const& rnd, RealType u, IntType x, RealType p) const {
|
|
return !(u > p) ? sprout::random::random_result<Engine, poisson_distribution>(x, sprout::random::next(rnd).engine(), *this)
|
|
: invert_2<Engine>(rnd, u - p, x + 1, p * mean_ / (x + 1))
|
|
;
|
|
}
|
|
template<typename Engine, typename Random>
|
|
SPROUT_CONSTEXPR sprout::random::random_result<Engine, poisson_distribution> invert_1(Random const& rnd, IntType x, RealType p) const {
|
|
return invert_2<Engine>(rnd, sprout::random::result(rnd), x, p);
|
|
}
|
|
template<typename Engine>
|
|
SPROUT_CONSTEXPR sprout::random::random_result<Engine, poisson_distribution> invert(Engine const& eng) const {
|
|
return invert_1<Engine>(sprout::random::uniform_01<RealType>()(eng), 0, exp_mean_);
|
|
}
|
|
template<typename Engine>
|
|
SPROUT_CXX14_CONSTEXPR result_type do_generate(Engine& eng) const {
|
|
for (; ; ) {
|
|
RealType v = sprout::random::uniform_01<RealType>()(eng);
|
|
if (v <= 0.86 * ptrd_.v_r) {
|
|
RealType u = v / ptrd_.v_r - 0.43;
|
|
return static_cast<IntType>(sprout::floor((2 * ptrd_.a / (0.5 - sprout::abs(u)) + ptrd_.b) * u + mean_ + 0.445));
|
|
}
|
|
RealType u = RealType();
|
|
if (v >= ptrd_.v_r) {
|
|
u = sprout::random::uniform_01<RealType>()(eng) - 0.5;
|
|
} else {
|
|
u = v / ptrd_.v_r - 0.93;
|
|
u = ((u < 0) ? -0.5 : 0.5) - u;
|
|
v = sprout::random::uniform_01<RealType>()(eng) * ptrd_.v_r;
|
|
}
|
|
RealType us = 0.5 - sprout::abs(u);
|
|
if (us < 0.013 && v > us) {
|
|
continue;
|
|
}
|
|
RealType k = sprout::floor((2 * ptrd_.a / us + ptrd_.b) * u + mean_ + 0.445);
|
|
v = v * ptrd_.inv_alpha / (ptrd_.a / (us * us) + ptrd_.b);
|
|
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)
|
|
|| (k >= 0 && sprout::log(v) <= k * sprout::log(mean_) - mean_ - log_factorial(static_cast<IntType>(k)))
|
|
)
|
|
{
|
|
return static_cast<IntType>(k);
|
|
}
|
|
}
|
|
}
|
|
template<typename Engine, typename Random>
|
|
SPROUT_CONSTEXPR sprout::random::random_result<Engine, poisson_distribution> generate_4(Random const& rnd, RealType u) const {
|
|
return sprout::random::random_result<Engine, poisson_distribution>(
|
|
static_cast<IntType>(sprout::floor((2 * ptrd_.a / (0.5 - sprout::abs(u)) + ptrd_.b) * u + mean_ + 0.445)),
|
|
sprout::random::next(rnd).engine(),
|
|
*this
|
|
);
|
|
}
|
|
#ifdef SPROUT_WORKAROUND_NOT_TERMINATE_RECURSIVE_CONSTEXPR_FUNCTION_TEMPLATE
|
|
template<typename Engine, int D, typename Random, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_CONTINUE(D)>
|
|
SPROUT_CONSTEXPR sprout::random::random_result<Engine, poisson_distribution> generate_3(Random const& rnd, RealType k, RealType v) const {
|
|
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)
|
|
|| (k >= 0 && sprout::log(v) <= k * sprout::log(mean_) - mean_ - log_factorial(static_cast<IntType>(k)))
|
|
? sprout::random::random_result<Engine, poisson_distribution>(static_cast<IntType>(k), sprout::random::next(rnd).engine(), *this)
|
|
: generate_1<Engine, D + 1>(rnd())
|
|
;
|
|
}
|
|
template<typename Engine, int D, typename Random, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_BREAK(D)>
|
|
SPROUT_CONSTEXPR sprout::random::random_result<Engine, poisson_distribution> generate_3(Random const&, RealType, RealType) const {
|
|
return sprout::throw_recursive_function_template_instantiation_exeeded();
|
|
}
|
|
template<typename Engine, int D, typename Random, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_CONTINUE(D)>
|
|
SPROUT_CONSTEXPR sprout::random::random_result<Engine, poisson_distribution> generate_2(Random const& rnd, RealType v, RealType u, RealType us) const {
|
|
return us < 0.013 && v > us ? generate_1<Engine, D + 1>(rnd())
|
|
: generate_3<Engine, D + 1>(
|
|
rnd,
|
|
sprout::floor((2 * ptrd_.a / us + ptrd_.b) * u + mean_ + 0.445),
|
|
v * ptrd_.inv_alpha / (ptrd_.a / (us * us) + ptrd_.b)
|
|
)
|
|
;
|
|
}
|
|
template<typename Engine, int D, typename Random, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_BREAK(D)>
|
|
SPROUT_CONSTEXPR sprout::random::random_result<Engine, poisson_distribution> generate_2(Random const&, RealType, RealType, RealType) const {
|
|
return sprout::throw_recursive_function_template_instantiation_exeeded();
|
|
}
|
|
template<typename Engine, int D, typename Random, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_CONTINUE(D)>
|
|
SPROUT_CONSTEXPR sprout::random::random_result<Engine, poisson_distribution> generate_1_3(Random const& rnd, RealType, RealType u) const {
|
|
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));
|
|
}
|
|
template<typename Engine, int D, typename Random, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_BREAK(D)>
|
|
SPROUT_CONSTEXPR sprout::random::random_result<Engine, poisson_distribution> generate_1_3(Random const&, RealType, RealType) const {
|
|
return sprout::throw_recursive_function_template_instantiation_exeeded();
|
|
}
|
|
template<typename Engine, int D, typename Random, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_CONTINUE(D)>
|
|
SPROUT_CONSTEXPR sprout::random::random_result<Engine, poisson_distribution> generate_1_2(Random const& rnd, RealType v) const {
|
|
return generate_2<Engine, D + 1>(rnd, v, sprout::random::result(rnd) - 0.5, generate_us(sprout::random::result(rnd) - 0.5));
|
|
}
|
|
template<typename Engine, int D, typename Random, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_BREAK(D)>
|
|
SPROUT_CONSTEXPR sprout::random::random_result<Engine, poisson_distribution> generate_1_2(Random const&, RealType) const {
|
|
return sprout::throw_recursive_function_template_instantiation_exeeded();
|
|
}
|
|
template<typename Engine, int D = 16, typename Random, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_CONTINUE(D)>
|
|
SPROUT_CONSTEXPR sprout::random::random_result<Engine, poisson_distribution> generate_1(Random const& rnd) const {
|
|
return sprout::random::result(rnd) <= 0.86 * ptrd_.v_r ? generate_4<Engine>(rnd, sprout::random::result(rnd) / ptrd_.v_r - 0.43)
|
|
: sprout::random::result(rnd) >= ptrd_.v_r
|
|
? generate_1_2<Engine, D + 1>(rnd(), sprout::random::result(rnd))
|
|
: generate_1_3<Engine, D + 1>(rnd(), sprout::random::result(rnd), sprout::random::result(rnd) / ptrd_.v_r - 0.93)
|
|
;
|
|
}
|
|
template<typename Engine, int D = 16, typename Random, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_BREAK(D)>
|
|
SPROUT_CONSTEXPR sprout::random::random_result<Engine, poisson_distribution> generate_1(Random const&) const {
|
|
return sprout::throw_recursive_function_template_instantiation_exeeded();
|
|
}
|
|
#else
|
|
template<typename Engine, typename Random>
|
|
SPROUT_CONSTEXPR sprout::random::random_result<Engine, poisson_distribution> generate_3(Random const& rnd, RealType k, RealType v) const {
|
|
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)
|
|
|| (k >= 0 && sprout::log(v) <= k * sprout::log(mean_) - mean_ - log_factorial(static_cast<IntType>(k)))
|
|
? sprout::random::random_result<Engine, poisson_distribution>(static_cast<IntType>(k), sprout::random::next(rnd).engine(), *this)
|
|
: generate_1<Engine>(rnd())
|
|
;
|
|
}
|
|
template<typename Engine, typename Random>
|
|
SPROUT_CONSTEXPR sprout::random::random_result<Engine, poisson_distribution> generate_2(Random const& rnd, RealType v, RealType u, RealType us) const {
|
|
return us < 0.013 && v > us ? generate_1<Engine>(rnd())
|
|
: generate_3<Engine>(
|
|
rnd,
|
|
sprout::floor((2 * ptrd_.a / us + ptrd_.b) * u + mean_ + 0.445),
|
|
v * ptrd_.inv_alpha / (ptrd_.a / (us * us) + ptrd_.b)
|
|
)
|
|
;
|
|
}
|
|
template<typename Engine, typename Random>
|
|
SPROUT_CONSTEXPR sprout::random::random_result<Engine, poisson_distribution> generate_1_3(Random const& rnd, RealType v, RealType u) const {
|
|
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));
|
|
}
|
|
template<typename Engine, typename Random>
|
|
SPROUT_CONSTEXPR sprout::random::random_result<Engine, poisson_distribution> generate_1_2(Random const& rnd, RealType v) const {
|
|
return generate_2<Engine>(rnd, v, sprout::random::result(rnd) - 0.5, generate_us(sprout::random::result(rnd) - 0.5));
|
|
}
|
|
template<typename Engine, typename Random>
|
|
SPROUT_CONSTEXPR sprout::random::random_result<Engine, poisson_distribution> generate_1(Random const& rnd) const {
|
|
return sprout::random::result(rnd) <= 0.86 * ptrd_.v_r ? generate_4<Engine>(rnd, sprout::random::result(rnd) / ptrd_.v_r - 0.43)
|
|
: sprout::random::result(rnd) >= ptrd_.v_r
|
|
? generate_1_2<Engine>(rnd(), sprout::random::result(rnd))
|
|
: generate_1_3<Engine>(rnd(), sprout::random::result(rnd), sprout::random::result(rnd) / ptrd_.v_r - 0.93)
|
|
;
|
|
}
|
|
#endif
|
|
template<typename Engine>
|
|
SPROUT_CONSTEXPR sprout::random::random_result<Engine, poisson_distribution> generate(Engine const& eng) const {
|
|
return generate_1<Engine>(sprout::random::uniform_01<RealType>()(eng));
|
|
}
|
|
public:
|
|
SPROUT_CONSTEXPR poisson_distribution()
|
|
: mean_(RealType(1))
|
|
, ptrd_(init_ptrd(RealType(1)))
|
|
, exp_mean_(init_exp_mean(RealType(1)))
|
|
{}
|
|
poisson_distribution(poisson_distribution const&) = default;
|
|
explicit SPROUT_CONSTEXPR poisson_distribution(RealType mean_arg)
|
|
: mean_((SPROUT_ASSERT(RealType(0) < mean_arg), mean_arg))
|
|
, ptrd_(init_ptrd(mean_arg))
|
|
, exp_mean_(init_exp_mean(mean_arg))
|
|
{}
|
|
explicit SPROUT_CONSTEXPR poisson_distribution(param_type const& parm)
|
|
: mean_(parm.mean())
|
|
, ptrd_(init_ptrd(parm.mean()))
|
|
, exp_mean_(init_exp_mean(parm.mean()))
|
|
{}
|
|
SPROUT_CONSTEXPR result_type mean() const SPROUT_NOEXCEPT {
|
|
return mean_;
|
|
}
|
|
SPROUT_CONSTEXPR result_type min() const SPROUT_NOEXCEPT {
|
|
return 0;
|
|
}
|
|
SPROUT_CONSTEXPR result_type max() const SPROUT_NOEXCEPT {
|
|
return sprout::numeric_limits<result_type>::max();
|
|
}
|
|
SPROUT_CXX14_CONSTEXPR void reset() SPROUT_NOEXCEPT {}
|
|
SPROUT_CONSTEXPR param_type param() const SPROUT_NOEXCEPT {
|
|
return param_type(mean_);
|
|
}
|
|
SPROUT_CXX14_CONSTEXPR void param(param_type const& parm) {
|
|
mean_ = parm.mean();
|
|
ptrd_ = init_ptrd(mean_);
|
|
exp_mean_ = init_exp_mean(mean_);
|
|
}
|
|
template<typename Engine>
|
|
SPROUT_CXX14_CONSTEXPR result_type operator()(Engine& eng) const {
|
|
return use_inversion() ? do_invert(eng)
|
|
: do_generate(eng)
|
|
;
|
|
}
|
|
template<typename Engine>
|
|
SPROUT_CONSTEXPR sprout::random::random_result<Engine, poisson_distribution> const operator()(Engine const& eng) const {
|
|
return use_inversion() ? invert(eng)
|
|
: generate(eng)
|
|
;
|
|
}
|
|
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
|