diff options
Diffstat (limited to 'boost/math/quadrature/detail/tanh_sinh_constants.hpp')
| -rw-r--r-- | boost/math/quadrature/detail/tanh_sinh_constants.hpp | 228 |
1 files changed, 228 insertions, 0 deletions
diff --git a/boost/math/quadrature/detail/tanh_sinh_constants.hpp b/boost/math/quadrature/detail/tanh_sinh_constants.hpp new file mode 100644 index 0000000000..6aa5844a81 --- /dev/null +++ b/boost/math/quadrature/detail/tanh_sinh_constants.hpp @@ -0,0 +1,228 @@ +// Copyright Nick Thompson, 2017 +// 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) + +#ifndef BOOST_MATH_QUADRATURE_DETAIL_TANH_SINH_CONSTANTS_HPP +#define BOOST_MATH_QUADRATURE_DETAIL_TANH_SINH_CONSTANTS_HPP + +#include <boost/type_traits/is_constructible.hpp> +#include <boost/lexical_cast.hpp> + +namespace boost { + namespace math { + namespace quadrature { + namespace detail { + + template <class Real> + inline Real abscissa_at_t(const Real& t) + { + using std::tanh; + using std::sinh; + return tanh(constants::half_pi<Real>()*sinh(t)); + } + template <class Real> + inline Real weight_at_t(const Real& t) + { + using std::cosh; + using std::sinh; + Real cs = cosh(constants::half_pi<Real>() * sinh(t)); + return constants::half_pi<Real>() * cosh(t) / (cs * cs); + } + template <class Real> + inline Real abscissa_complement_at_t(const Real& t) + { + using std::cosh; + using std::exp; + using std::sinh; + Real u2 = constants::half_pi<Real>() * sinh(t); + return 1 / (exp(u2) *cosh(u2)); + } + template <class Real> + inline Real t_from_abscissa_complement(const Real& x) + { + using std::log; + using std::sqrt; + Real l = log(sqrt((2 - x) / x)); + return log((sqrt(4 * l * l + constants::pi<Real>() * constants::pi<Real>()) + 2 * l) / constants::pi<Real>()); + }; + + template<class Real, int precision> + class tanh_sinh_detail_constants + { + static const int initializer_selector = + !std::numeric_limits<Real>::is_specialized || (std::numeric_limits<Real>::radix != 2) ? + 0 : + (std::numeric_limits<Real>::digits < 30) && (std::numeric_limits<Real>::max_exponent <= 128) ? + 1 : 0; + public: + tanh_sinh_detail_constants(std::size_t max_refinements, std::size_t initial_commit = 4) : m_max_refinements(max_refinements), m_committed_refinements(initial_commit) + { + typedef mpl::int_<initializer_selector> tag_type; + init(tag_type()); + } + + void init(const mpl::int_<0>&) + { + using std::tanh; + using std::sinh; + using std::asinh; + using std::atanh; + using boost::math::constants::half_pi; + using boost::math::constants::pi; + using boost::math::constants::two_div_pi; + + m_inital_row_length = 7; + std::size_t first_complement = 0; + m_t_max = m_inital_row_length; + m_t_crossover = t_from_abscissa_complement(Real(0.5f)); + + m_abscissas.assign(m_max_refinements + 1, std::vector<Real>()); + m_weights.assign(m_max_refinements + 1, std::vector<Real>()); + m_first_complements.assign(m_max_refinements + 1, 0); + // + // First row is special: + // + Real h = m_t_max / m_inital_row_length; + + std::vector<Real> temp(m_inital_row_length + 1, Real(0)); + for (std::size_t i = 0; i < m_inital_row_length; ++i) + { + Real t = h * i; + if ((first_complement < 0) && (t < m_t_crossover)) + first_complement = i; + temp[i] = t < m_t_crossover ? abscissa_at_t(t) : -abscissa_complement_at_t(t); + } + temp[m_inital_row_length] = abscissa_complement_at_t(m_t_max); + m_abscissas[0].swap(temp); + m_first_complements[0] = first_complement; + temp.assign(m_inital_row_length + 1, Real(0)); + for (std::size_t i = 0; i < m_inital_row_length; ++i) + temp[i] = weight_at_t(Real(h * i)); + temp[m_inital_row_length] = weight_at_t(m_t_max); + m_weights[0].swap(temp); + + for (std::size_t row = 1; row <= m_committed_refinements; ++row) + { + h /= 2; + first_complement = 0; + + for (Real pos = h; pos < m_t_max; pos += 2 * h) + { + if (pos < m_t_crossover) + ++first_complement; + temp.push_back(pos < m_t_crossover ? abscissa_at_t(pos) : -abscissa_complement_at_t(pos)); + } + m_abscissas[row].swap(temp); + m_first_complements[row] = first_complement; + for (Real pos = h; pos < m_t_max; pos += 2 * h) + temp.push_back(weight_at_t(pos)); + m_weights[row].swap(temp); + } + } + void init(const mpl::int_<1>&) + { + m_inital_row_length = 4; + m_abscissas.reserve(m_max_refinements + 1); + m_weights.reserve(m_max_refinements + 1); + m_first_complements.reserve(m_max_refinements + 1); + m_abscissas = { + { 0.0f, -0.04863203593f, -2.252280754e-05f, -4.294161056e-14f, -1.167648898e-37f, }, + { -0.3257285078f, -0.002485143543f, -1.112433512e-08f, -5.378491591e-23f, }, + { 0.3772097382f, -0.1404309413f, -0.01295943949f, -0.0003117359716f, -7.952628853e-07f, -4.714355182e-11f, -5.415222824e-18f, -2.040300394e-29f, }, + { 0.1943570033f, -0.4608532946f, -0.219392561f, -0.08512073674f, -0.0260331318f, -0.005944493369f, -0.0009348035442f, -9.061530486e-05f, -4.683958779e-06f, -1.072183876e-07f, -8.572949078e-10f, -1.767834693e-12f, -6.374878495e-16f, -2.442937279e-20f, -5.251546473e-26f, -2.789467162e-33f, }, + { 0.09792388529f, 0.2878799327f, 0.4612535439f, -0.3897263425f, -0.2689819652f, -0.1766829945f, -0.1101085972f, -0.06483914248f, -0.03588783578f, -0.01854517332f, -0.008873007558f, -0.003891334562f, -0.001545791232f, -0.0005485655647f, -0.0001711779271f, -4.612899437e-05f, -1.051798518e-05f, -1.982859405e-06f, -3.011058474e-07f, -3.576091908e-08f, -3.212800902e-09f, -2.102671378e-10f, -9.606066479e-12f, -2.919026641e-13f, -5.586116639e-15f, -6.328207135e-17f, -3.956461339e-19f, -1.260975845e-21f, -1.872492175e-24f, -1.170030294e-27f, -2.740986178e-31f, -2.112282721e-35f, }, + { 0.04905596731f, 0.1464179843f, 0.2415663195f, 0.3331422646f, 0.4199521113f, -0.4989866106f, -0.4244155094f, -0.356823241f, -0.2964499949f, -0.2433060914f, -0.1972012587f, -0.1577807536f, -0.1245646024f, -0.09698671849f, -0.07443136593f, -0.05626521395f, -0.04186397729f, -0.0306332671f, -0.02202376481f, -0.01554116883f, -0.01075156891f, -0.007283002803f, -0.004823973845f, -0.003119681872f, -0.001966663685f, -0.001206465701f, -0.0007188880782f, 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2.861306549e-28f, 9.896184197e-29f, 3.365200893e-29f, 1.124807055e-29f, 3.694460433e-30f, 1.192093301e-30f, 3.777757876e-31f, 1.175436379e-31f, 3.589879078e-32f, 1.075842686e-32f, 3.162835126e-33f, 9.118674189e-34f, 2.577393168e-34f, 7.139829504e-35f, 1.937828921e-35f, }, + }; + m_first_complements = { + 1, 0, 1, 1, 3, 5, 11, 22, + }; + + while (m_abscissas.size() <= m_committed_refinements) + extend_refinements(); + m_committed_refinements = m_abscissas.size() - 1; + + if (m_max_refinements >= m_abscissas.size()) + { + m_abscissas.resize(m_max_refinements + 1); + m_weights.resize(m_max_refinements + 1); + m_first_complements.resize(m_max_refinements + 1); + } + else + { + m_max_refinements = m_abscissas.size() - 1; + } + m_t_max = m_inital_row_length; + m_t_crossover = t_from_abscissa_complement(Real(0.5f)); + } + + void extend_refinements()const + { + ++m_committed_refinements; + std::size_t row = m_committed_refinements; + Real h = ldexp(Real(1), -static_cast<int>(row)); + std::size_t first_complement = 0; + for (Real pos = h; pos < m_t_max; pos += 2 * h) + { + if (pos < m_t_crossover) + ++first_complement; + m_abscissas[row].push_back(pos < m_t_crossover ? abscissa_at_t(pos) : -abscissa_complement_at_t(pos)); + } + m_first_complements[row] = first_complement; + for (Real pos = h; pos < m_t_max; pos += 2 * h) + m_weights[row].push_back(weight_at_t(pos)); + } + + const std::vector<Real>& get_abscissa_row(std::size_t n)const + { + if (m_committed_refinements < n) + extend_refinements(); + BOOST_ASSERT(m_committed_refinements >= n); + return m_abscissas[n]; + } + const std::vector<Real>& get_weight_row(std::size_t n)const + { + if (m_committed_refinements < n) + extend_refinements(); + BOOST_ASSERT(m_committed_refinements >= n); + return m_weights[n]; + } + std::size_t get_first_complement_index(std::size_t n)const + { + if (m_committed_refinements < n) + extend_refinements(); + BOOST_ASSERT(m_committed_refinements >= n); + return m_first_complements[n]; + } + + protected: + mutable std::vector<std::vector<Real>> m_abscissas; + mutable std::vector<std::vector<Real>> m_weights; + mutable std::vector<std::size_t> m_first_complements; + std::size_t m_max_refinements, m_inital_row_length; + mutable std::size_t m_committed_refinements; + Real m_t_max, m_t_crossover; + }; + + + } + } + } +} + +#endif + + |