update boost

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2023-11-24 12:56:13 -06:00
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@@ -0,0 +1,387 @@
// Copyright Matthew Pulver 2018 - 2019.
// Distributed under the Boost Software License, Version 1.0.
// (See accompanying file LICENSE_1_0.txt or copy at
// https://www.boost.org/LICENSE_1_0.txt)
// Contributors:
// * Kedar R. Bhat - C++11 compatibility.
// Notes:
// * Any changes to this file should always be downstream from autodiff.cpp.
// C++17 is a higher-level language and is easier to maintain. For example, a number of functions which are
// lucidly read in autodiff.cpp are forced to be split into multiple structs/functions in this file for
// C++11.
// * Use of typename RootType and SizeType is a hack to prevent Visual Studio 2015 from compiling functions
// that are never called, that would otherwise produce compiler errors. Also forces functions to be inline.
#ifndef BOOST_MATH_DIFFERENTIATION_AUTODIFF_HPP
#error \
"Do not #include this file directly. This should only be #included by autodiff.hpp for C++11 compatibility."
#endif
#include <type_traits>
#include <boost/math/tools/mp.hpp>
namespace boost {
namespace math {
namespace mp = tools::meta_programming;
namespace differentiation {
inline namespace autodiff_v1 {
namespace detail {
template <typename RealType, size_t Order>
fvar<RealType, Order>::fvar(root_type const& ca, bool const is_variable) {
fvar_cpp11(is_fvar<RealType>{}, ca, is_variable);
}
template <typename RealType, size_t Order>
template <typename RootType>
void fvar<RealType, Order>::fvar_cpp11(std::true_type, RootType const& ca, bool const is_variable) {
v.front() = RealType(ca, is_variable);
if (0 < Order)
std::fill(v.begin() + 1, v.end(), static_cast<RealType>(0));
}
template <typename RealType, size_t Order>
template <typename RootType>
void fvar<RealType, Order>::fvar_cpp11(std::false_type, RootType const& ca, bool const is_variable) {
v.front() = ca;
if (0 < Order) {
v[1] = static_cast<root_type>(static_cast<int>(is_variable));
if (1 < Order)
std::fill(v.begin() + 2, v.end(), static_cast<RealType>(0));
}
}
template <typename RealType, size_t Order>
template <typename... Orders>
get_type_at<RealType, sizeof...(Orders)> fvar<RealType, Order>::at_cpp11(std::true_type,
size_t order,
Orders...) const {
return v.at(order);
}
template <typename RealType, size_t Order>
template <typename... Orders>
get_type_at<RealType, sizeof...(Orders)> fvar<RealType, Order>::at_cpp11(std::false_type,
size_t order,
Orders... orders) const {
return v.at(order).at(orders...);
}
// Can throw "std::out_of_range: array::at: __n (which is 7) >= _Nm (which is 7)"
template <typename RealType, size_t Order>
template <typename... Orders>
get_type_at<RealType, sizeof...(Orders)> fvar<RealType, Order>::at(size_t order, Orders... orders) const {
return at_cpp11(std::integral_constant<bool, sizeof...(orders) == 0>{}, order, orders...);
}
template <typename T, typename... Ts>
constexpr T product(Ts...) {
return static_cast<T>(1);
}
template <typename T, typename... Ts>
constexpr T product(T factor, Ts... factors) {
return factor * product<T>(factors...);
}
// Can throw "std::out_of_range: array::at: __n (which is 7) >= _Nm (which is 7)"
template <typename RealType, size_t Order>
template <typename... Orders>
get_type_at<fvar<RealType, Order>, sizeof...(Orders)> fvar<RealType, Order>::derivative(
Orders... orders) const {
static_assert(sizeof...(Orders) <= depth,
"Number of parameters to derivative(...) cannot exceed fvar::depth.");
return at(static_cast<size_t>(orders)...) *
product(boost::math::factorial<root_type>(static_cast<unsigned>(orders))...);
}
template <typename RootType, typename Func>
class Curry {
Func const& f_;
size_t const i_;
public:
template <typename SizeType> // typename SizeType to force inline constructor.
Curry(Func const& f, SizeType i) : f_(f), i_(static_cast<std::size_t>(i)) {}
template <typename... Indices>
RootType operator()(Indices... indices) const {
using unsigned_t = typename std::make_unsigned<typename std::common_type<Indices>::type...>::type;
return f_(i_, static_cast<unsigned_t>(indices)...);
}
};
template <typename RealType, size_t Order>
template <typename Func, typename Fvar, typename... Fvars>
promote<fvar<RealType, Order>, Fvar, Fvars...> fvar<RealType, Order>::apply_coefficients(
size_t const order,
Func const& f,
Fvar const& cr,
Fvars&&... fvars) const {
fvar<RealType, Order> const epsilon = fvar<RealType, Order>(*this).set_root(0);
size_t i = order < order_sum ? order : order_sum;
using return_type = promote<fvar<RealType, Order>, Fvar, Fvars...>;
return_type accumulator = cr.apply_coefficients(
order - i, Curry<typename return_type::root_type, Func>(f, i), std::forward<Fvars>(fvars)...);
while (i--)
(accumulator *= epsilon) += cr.apply_coefficients(
order - i, Curry<typename return_type::root_type, Func>(f, i), std::forward<Fvars>(fvars)...);
return accumulator;
}
template <typename RealType, size_t Order>
template <typename Func, typename Fvar, typename... Fvars>
promote<fvar<RealType, Order>, Fvar, Fvars...> fvar<RealType, Order>::apply_coefficients_nonhorner(
size_t const order,
Func const& f,
Fvar const& cr,
Fvars&&... fvars) const {
fvar<RealType, Order> const epsilon = fvar<RealType, Order>(*this).set_root(0);
fvar<RealType, Order> epsilon_i = fvar<RealType, Order>(1); // epsilon to the power of i
using return_type = promote<fvar<RealType, Order>, Fvar, Fvars...>;
return_type accumulator = cr.apply_coefficients_nonhorner(
order, Curry<typename return_type::root_type, Func>(f, 0), std::forward<Fvars>(fvars)...);
size_t const i_max = order < order_sum ? order : order_sum;
for (size_t i = 1; i <= i_max; ++i) {
epsilon_i = epsilon_i.epsilon_multiply(i - 1, 0, epsilon, 1, 0);
accumulator += epsilon_i.epsilon_multiply(
i,
0,
cr.apply_coefficients_nonhorner(
order - i, Curry<typename return_type::root_type, Func>(f, i), std::forward<Fvars>(fvars)...),
0,
0);
}
return accumulator;
}
template <typename RealType, size_t Order>
template <typename Func, typename Fvar, typename... Fvars>
promote<fvar<RealType, Order>, Fvar, Fvars...> fvar<RealType, Order>::apply_derivatives(
size_t const order,
Func const& f,
Fvar const& cr,
Fvars&&... fvars) const {
fvar<RealType, Order> const epsilon = fvar<RealType, Order>(*this).set_root(0);
size_t i = order < order_sum ? order : order_sum;
using return_type = promote<fvar<RealType, Order>, Fvar, Fvars...>;
return_type accumulator =
cr.apply_derivatives(
order - i, Curry<typename return_type::root_type, Func>(f, i), std::forward<Fvars>(fvars)...) /
factorial<root_type>(static_cast<unsigned>(i));
while (i--)
(accumulator *= epsilon) +=
cr.apply_derivatives(
order - i, Curry<typename return_type::root_type, Func>(f, i), std::forward<Fvars>(fvars)...) /
factorial<root_type>(static_cast<unsigned>(i));
return accumulator;
}
template <typename RealType, size_t Order>
template <typename Func, typename Fvar, typename... Fvars>
promote<fvar<RealType, Order>, Fvar, Fvars...> fvar<RealType, Order>::apply_derivatives_nonhorner(
size_t const order,
Func const& f,
Fvar const& cr,
Fvars&&... fvars) const {
fvar<RealType, Order> const epsilon = fvar<RealType, Order>(*this).set_root(0);
fvar<RealType, Order> epsilon_i = fvar<RealType, Order>(1); // epsilon to the power of i
using return_type = promote<fvar<RealType, Order>, Fvar, Fvars...>;
return_type accumulator = cr.apply_derivatives_nonhorner(
order, Curry<typename return_type::root_type, Func>(f, 0), std::forward<Fvars>(fvars)...);
size_t const i_max = order < order_sum ? order : order_sum;
for (size_t i = 1; i <= i_max; ++i) {
epsilon_i = epsilon_i.epsilon_multiply(i - 1, 0, epsilon, 1, 0);
accumulator += epsilon_i.epsilon_multiply(
i,
0,
cr.apply_derivatives_nonhorner(
order - i, Curry<typename return_type::root_type, Func>(f, i), std::forward<Fvars>(fvars)...) /
factorial<root_type>(static_cast<unsigned>(i)),
0,
0);
}
return accumulator;
}
template <typename RealType, size_t Order>
template <typename SizeType>
fvar<RealType, Order> fvar<RealType, Order>::epsilon_multiply_cpp11(std::true_type,
SizeType z0,
size_t isum0,
fvar<RealType, Order> const& cr,
size_t z1,
size_t isum1) const {
size_t const m0 = order_sum + isum0 < Order + z0 ? Order + z0 - (order_sum + isum0) : 0;
size_t const m1 = order_sum + isum1 < Order + z1 ? Order + z1 - (order_sum + isum1) : 0;
size_t const i_max = m0 + m1 < Order ? Order - (m0 + m1) : 0;
fvar<RealType, Order> retval = fvar<RealType, Order>();
for (size_t i = 0, j = Order; i <= i_max; ++i, --j)
retval.v[j] = epsilon_inner_product(z0, isum0, m0, cr, z1, isum1, m1, j);
return retval;
}
template <typename RealType, size_t Order>
template <typename SizeType>
fvar<RealType, Order> fvar<RealType, Order>::epsilon_multiply_cpp11(std::false_type,
SizeType z0,
size_t isum0,
fvar<RealType, Order> const& cr,
size_t z1,
size_t isum1) const {
using ssize_t = typename std::make_signed<std::size_t>::type;
RealType const zero(0);
size_t const m0 = order_sum + isum0 < Order + z0 ? Order + z0 - (order_sum + isum0) : 0;
size_t const m1 = order_sum + isum1 < Order + z1 ? Order + z1 - (order_sum + isum1) : 0;
size_t const i_max = m0 + m1 < Order ? Order - (m0 + m1) : 0;
fvar<RealType, Order> retval = fvar<RealType, Order>();
for (size_t i = 0, j = Order; i <= i_max; ++i, --j)
retval.v[j] = std::inner_product(
v.cbegin() + ssize_t(m0), v.cend() - ssize_t(i + m1), cr.v.crbegin() + ssize_t(i + m0), zero);
return retval;
}
template <typename RealType, size_t Order>
fvar<RealType, Order> fvar<RealType, Order>::epsilon_multiply(size_t z0,
size_t isum0,
fvar<RealType, Order> const& cr,
size_t z1,
size_t isum1) const {
return epsilon_multiply_cpp11(is_fvar<RealType>{}, z0, isum0, cr, z1, isum1);
}
template <typename RealType, size_t Order>
template <typename SizeType>
fvar<RealType, Order> fvar<RealType, Order>::epsilon_multiply_cpp11(std::true_type,
SizeType z0,
size_t isum0,
root_type const& ca) const {
fvar<RealType, Order> retval(*this);
size_t const m0 = order_sum + isum0 < Order + z0 ? Order + z0 - (order_sum + isum0) : 0;
for (size_t i = m0; i <= Order; ++i)
retval.v[i] = retval.v[i].epsilon_multiply(z0, isum0 + i, ca);
return retval;
}
template <typename RealType, size_t Order>
template <typename SizeType>
fvar<RealType, Order> fvar<RealType, Order>::epsilon_multiply_cpp11(std::false_type,
SizeType z0,
size_t isum0,
root_type const& ca) const {
fvar<RealType, Order> retval(*this);
size_t const m0 = order_sum + isum0 < Order + z0 ? Order + z0 - (order_sum + isum0) : 0;
for (size_t i = m0; i <= Order; ++i)
if (retval.v[i] != static_cast<RealType>(0))
retval.v[i] *= ca;
return retval;
}
template <typename RealType, size_t Order>
fvar<RealType, Order> fvar<RealType, Order>::epsilon_multiply(size_t z0,
size_t isum0,
root_type const& ca) const {
return epsilon_multiply_cpp11(is_fvar<RealType>{}, z0, isum0, ca);
}
template <typename RealType, size_t Order>
template <typename RootType>
fvar<RealType, Order>& fvar<RealType, Order>::multiply_assign_by_root_type_cpp11(std::true_type,
bool is_root,
RootType const& ca) {
auto itr = v.begin();
itr->multiply_assign_by_root_type(is_root, ca);
for (++itr; itr != v.end(); ++itr)
itr->multiply_assign_by_root_type(false, ca);
return *this;
}
template <typename RealType, size_t Order>
template <typename RootType>
fvar<RealType, Order>& fvar<RealType, Order>::multiply_assign_by_root_type_cpp11(std::false_type,
bool is_root,
RootType const& ca) {
auto itr = v.begin();
if (is_root || *itr != 0)
*itr *= ca; // Skip multiplication of 0 by ca=inf to avoid nan, except when is_root.
for (++itr; itr != v.end(); ++itr)
if (*itr != 0)
*itr *= ca;
return *this;
}
template <typename RealType, size_t Order>
fvar<RealType, Order>& fvar<RealType, Order>::multiply_assign_by_root_type(bool is_root,
root_type const& ca) {
return multiply_assign_by_root_type_cpp11(is_fvar<RealType>{}, is_root, ca);
}
template <typename RealType, size_t Order>
template <typename RootType>
fvar<RealType, Order>& fvar<RealType, Order>::negate_cpp11(std::true_type, RootType const&) {
std::for_each(v.begin(), v.end(), [](RealType& r) { r.negate(); });
return *this;
}
template <typename RealType, size_t Order>
template <typename RootType>
fvar<RealType, Order>& fvar<RealType, Order>::negate_cpp11(std::false_type, RootType const&) {
std::for_each(v.begin(), v.end(), [](RealType& a) { a = -a; });
return *this;
}
template <typename RealType, size_t Order>
fvar<RealType, Order>& fvar<RealType, Order>::negate() {
return negate_cpp11(is_fvar<RealType>{}, static_cast<root_type>(*this));
}
template <typename RealType, size_t Order>
template <typename RootType>
fvar<RealType, Order>& fvar<RealType, Order>::set_root_cpp11(std::true_type, RootType const& root) {
v.front().set_root(root);
return *this;
}
template <typename RealType, size_t Order>
template <typename RootType>
fvar<RealType, Order>& fvar<RealType, Order>::set_root_cpp11(std::false_type, RootType const& root) {
v.front() = root;
return *this;
}
template <typename RealType, size_t Order>
fvar<RealType, Order>& fvar<RealType, Order>::set_root(root_type const& root) {
return set_root_cpp11(is_fvar<RealType>{}, root);
}
template <typename RealType, size_t Order, size_t... Is>
auto make_fvar_for_tuple(mp::index_sequence<Is...>, RealType const& ca)
-> decltype(make_fvar<RealType, zero<Is>::value..., Order>(ca)) {
return make_fvar<RealType, zero<Is>::value..., Order>(ca);
}
template <typename RealType, size_t... Orders, size_t... Is, typename... RealTypes>
auto make_ftuple_impl(mp::index_sequence<Is...>, RealTypes const&... ca)
-> decltype(std::make_tuple(make_fvar_for_tuple<RealType, Orders>(mp::make_index_sequence<Is>{},
ca)...)) {
return std::make_tuple(make_fvar_for_tuple<RealType, Orders>(mp::make_index_sequence<Is>{}, ca)...);
}
} // namespace detail
template <typename RealType, size_t... Orders, typename... RealTypes>
auto make_ftuple(RealTypes const&... ca)
-> decltype(detail::make_ftuple_impl<RealType, Orders...>(mp::index_sequence_for<RealTypes...>{},
ca...)) {
static_assert(sizeof...(Orders) == sizeof...(RealTypes),
"Number of Orders must match number of function parameters.");
return detail::make_ftuple_impl<RealType, Orders...>(mp::index_sequence_for<RealTypes...>{}, ca...);
}
} // namespace autodiff_v1
} // namespace differentiation
} // namespace math
} // namespace boost

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@@ -153,7 +153,7 @@ namespace detail {
const Real eps = (numeric_limits<Real>::epsilon)();
// Error bound ~eps^4/5
Real h = pow(11.25*eps, (Real)1 / (Real)5);
Real h = pow(Real(11.25)*eps, static_cast<Real>(1) / static_cast<Real>(5));
h = detail::make_xph_representable(x, h);
Real ymth = f(x - 2 * h);
Real yth = f(x + 2 * h);
@@ -186,7 +186,7 @@ namespace detail {
const Real eps = (numeric_limits<Real>::epsilon)();
// Error bound ~eps^6/7
// Error: h^6f^(7)(x)/140 + 5|f(x)|eps/h
Real h = pow(eps / 168, (Real)1 / (Real)7);
Real h = pow(eps / 168, static_cast<Real>(1) / static_cast<Real>(7));
h = detail::make_xph_representable(x, h);
Real yh = f(x + h);
@@ -222,7 +222,7 @@ namespace detail {
// Mathematica code to get the error:
// Series[(f[x+h]-f[x-h])*(4/5) + (1/5)*(f[x-2*h] - f[x+2*h]) + (4/105)*(f[x+3*h] - f[x-3*h]) + (1/280)*(f[x-4*h] - f[x+4*h]), {h, 0, 9}]
// If we used Kahan summation, we could get the max error down to h^8|f^(9)(x)|/630 + |f(x)|eps/h.
Real h = pow(551.25*eps, (Real)1 / (Real)9);
Real h = pow(Real(551.25)*eps, static_cast<Real>(1) / static_cast<Real>(9));
h = detail::make_xph_representable(x, h);
Real yh = f(x + h);
@@ -251,7 +251,7 @@ namespace detail {
Real finite_difference_derivative(const F, Real, Real*, const tag&)
{
// Always fails, but condition is template-arg-dependent so only evaluated if we get instantiated.
BOOST_STATIC_ASSERT_MSG(sizeof(Real) == 0, "Finite difference not implemented for this order: try 1, 2, 4, 6 or 8");
static_assert(sizeof(Real) == 0, "Finite difference not implemented for this order: try 1, 2, 4, 6 or 8");
}
}

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@@ -6,11 +6,22 @@
#ifndef BOOST_MATH_DIFFERENTIATION_LANCZOS_SMOOTHING_HPP
#define BOOST_MATH_DIFFERENTIATION_LANCZOS_SMOOTHING_HPP
#include <cmath> // for std::abs
#include <cstddef>
#include <limits> // to nan initialize
#include <vector>
#include <string>
#include <cstdint>
#include <stdexcept>
#include <boost/assert.hpp>
#include <type_traits>
#include <boost/math/tools/assert.hpp>
#include <boost/math/tools/is_standalone.hpp>
#ifndef BOOST_MATH_STANDALONE
#include <boost/config.hpp>
#ifdef BOOST_NO_CXX17_IF_CONSTEXPR
#error "The header <boost/math/norms.hpp> can only be used in C++17 and later."
#endif
#endif
namespace boost::math::differentiation {
@@ -24,7 +35,7 @@ class discrete_legendre {
m_qrm2pp{0}, m_qrm1pp{0}
{
using std::abs;
BOOST_ASSERT_MSG(abs(m_x) <= 1, "Three term recurrence is stable only for |x| <=1.");
BOOST_MATH_ASSERT_MSG(abs(m_x) <= 1, "Three term recurrence is stable only for |x| <=1.");
// The integer n indexes a family of discrete Legendre polynomials indexed by k <= 2*n
}
@@ -82,7 +93,7 @@ class discrete_legendre {
Real operator()(Real x, std::size_t k)
{
BOOST_ASSERT_MSG(k <= 2 * m_n, "r <= 2n is required.");
BOOST_MATH_ASSERT_MSG(k <= 2 * m_n, "r <= 2n is required.");
if (k == 0)
{
return 1;
@@ -104,7 +115,7 @@ class discrete_legendre {
}
Real prime(Real x, std::size_t k) {
BOOST_ASSERT_MSG(k <= 2 * m_n, "r <= 2n is required.");
BOOST_MATH_ASSERT_MSG(k <= 2 * m_n, "r <= 2n is required.");
if (k == 0) {
return 0;
}
@@ -210,8 +221,8 @@ std::vector<Real> boundary_velocity_filter(std::size_t n, std::size_t p, int64_t
template <class Real>
std::vector<Real> acceleration_filter(std::size_t n, std::size_t p, int64_t s)
{
BOOST_ASSERT_MSG(p <= 2*n, "Approximation order must be <= 2*n");
BOOST_ASSERT_MSG(p > 2, "Approximation order must be > 2");
BOOST_MATH_ASSERT_MSG(p <= 2*n, "Approximation order must be <= 2*n");
BOOST_MATH_ASSERT_MSG(p > 2, "Approximation order must be > 2");
std::vector<Real> coeffs(p+1, std::numeric_limits<Real>::quiet_NaN());
Real sn = Real(s) / Real(n);
@@ -251,14 +262,14 @@ public:
{
static_assert(!std::is_integral_v<Real>,
"Spacing must be a floating point type.");
BOOST_ASSERT_MSG(spacing > 0,
BOOST_MATH_ASSERT_MSG(spacing > 0,
"Spacing between samples must be > 0.");
if constexpr (order == 1)
{
BOOST_ASSERT_MSG(approximation_order <= 2 * n,
BOOST_MATH_ASSERT_MSG(approximation_order <= 2 * n,
"The approximation order must be <= 2n");
BOOST_ASSERT_MSG(approximation_order >= 2,
BOOST_MATH_ASSERT_MSG(approximation_order >= 2,
"The approximation order must be >= 2");
if constexpr (std::is_same_v<Real, float> || std::is_same_v<Real, double>)
@@ -356,7 +367,7 @@ public:
}
else
{
BOOST_ASSERT_MSG(false, "Derivatives of order 3 and higher are not implemented.");
BOOST_MATH_ASSERT_MSG(false, "Derivatives of order 3 and higher are not implemented.");
}
}
@@ -371,7 +382,7 @@ public:
static_assert(std::is_same_v<typename RandomAccessContainer::value_type, Real>,
"The type of the values in the vector provided does not match the type in the filters.");
BOOST_ASSERT_MSG(std::size(v) >= m_boundary_filters[0].size(),
BOOST_MATH_ASSERT_MSG(std::size(v) >= m_boundary_filters[0].size(),
"Vector must be at least as long as the filter length");
if constexpr (order==1)
@@ -567,8 +578,8 @@ public:
discrete_lanczos_derivative& operator=(const discrete_lanczos_derivative&) = delete;
// Allow moves:
discrete_lanczos_derivative(discrete_lanczos_derivative&&) = default;
discrete_lanczos_derivative& operator=(discrete_lanczos_derivative&&) = default;
discrete_lanczos_derivative(discrete_lanczos_derivative&&) noexcept = default;
discrete_lanczos_derivative& operator=(discrete_lanczos_derivative&&) noexcept = default;
private:
std::vector<Real> m_f;