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// 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) /* * This class performs exp-sinh quadrature on half infinite intervals. * * References: * * 1) Tanaka, Ken'ichiro, et al. "Function classes for double exponential integration formulas." Numerische Mathematik 111.4 (2009): 631-655. */ #ifndef BOOST_MATH_QUADRATURE_EXP_SINH_HPP #define BOOST_MATH_QUADRATURE_EXP_SINH_HPP #include #include #ifndef BOOST_MATH_HAS_NVRTC #include #include #include #include namespace boost{ namespace math{ namespace quadrature { template > class exp_sinh { public: exp_sinh(size_t max_refinements = 9) : m_imp(std::make_shared>(max_refinements)) {} template auto integrate(const F& f, Real a, Real b, Real tol = boost::math::tools::root_epsilon(), Real* error = nullptr, Real* L1 = nullptr, std::size_t* levels = nullptr) const ->decltype(std::declval()(std::declval())); template auto integrate(const F& f, Real tol = boost::math::tools::root_epsilon(), Real* error = nullptr, Real* L1 = nullptr, std::size_t* levels = nullptr) const ->decltype(std::declval()(std::declval())); private: std::shared_ptr> m_imp; }; template template auto exp_sinh::integrate(const F& f, Real a, Real b, Real tolerance, Real* error, Real* L1, std::size_t* levels) const ->decltype(std::declval()(std::declval())) { typedef decltype(f(a)) K; static_assert(!std::is_integral::value, "The return type cannot be integral, it must be either a real or complex floating point type."); using std::abs; using boost::math::constants::half; using boost::math::quadrature::detail::exp_sinh_detail; static const char* function = "boost::math::quadrature::exp_sinh<%1%>::integrate"; // Neither limit may be a NaN: if((boost::math::isnan)(a) || (boost::math::isnan)(b)) { return static_cast(policies::raise_domain_error(function, "NaN supplied as one limit of integration - sorry I don't know what to do", a, Policy())); } // Right limit is infinite: if ((boost::math::isfinite)(a) && (b >= boost::math::tools::max_value())) { // If a = 0, don't use an additional level of indirection: if (a == static_cast(0)) { return m_imp->integrate(f, error, L1, function, tolerance, levels); } const auto u = [&](Real t)->K { return f(t + a); }; return m_imp->integrate(u, error, L1, function, tolerance, levels); } if ((boost::math::isfinite)(b) && a <= -boost::math::tools::max_value()) { const auto u = [&](Real t)->K { return f(b-t);}; return m_imp->integrate(u, error, L1, function, tolerance, levels); } // Infinite limits: if ((a <= -boost::math::tools::max_value()) && (b >= boost::math::tools::max_value())) { return static_cast(policies::raise_domain_error(function, "Use sinh_sinh quadrature for integration over the whole real line; exp_sinh is for half infinite integrals.", a, Policy())); } // If we get to here then both ends must necessarily be finite: return static_cast(policies::raise_domain_error(function, "Use tanh_sinh quadrature for integration over finite domains; exp_sinh is for half infinite integrals.", a, Policy())); } template template auto exp_sinh::integrate(const F& f, Real tolerance, Real* error, Real* L1, std::size_t* levels) const ->decltype(std::declval()(std::declval())) { static const char* function = "boost::math::quadrature::exp_sinh<%1%>::integrate"; using std::abs; if (abs(tolerance) > 1) { return policies::raise_domain_error(function, "The tolerance provided (%1%) is unusually large; did you confuse it with a domain bound?", tolerance, Policy()); } return m_imp->integrate(f, error, L1, function, tolerance, levels); } }}} #endif // BOOST_MATH_HAS_NVRTC #ifdef BOOST_MATH_ENABLE_CUDA #include #include #include #include #include namespace boost { namespace math { namespace quadrature { template > __device__ auto exp_sinh_integrate(const F& f, Real a, Real b, Real tolerance, Real* error, Real* L1, boost::math::size_t* levels) { BOOST_MATH_STD_USING using K = decltype(f(a)); static_assert(!boost::math::is_integral::value, "The return type cannot be integral, it must be either a real or complex floating point type."); constexpr auto function = "boost::math::quadrature::exp_sinh<%1%>::integrate"; // Neither limit may be a NaN: if((boost::math::isnan)(a) || (boost::math::isnan)(b)) { return static_cast(policies::raise_domain_error(function, "NaN supplied as one limit of integration - sorry I don't know what to do", a, Policy())); } // Right limit is infinite: if ((boost::math::isfinite)(a) && (b >= boost::math::tools::max_value())) { // If a = 0, don't use an additional level of indirection: if (a == static_cast(0)) { return detail::exp_sinh_integrate_impl(f, tolerance, error, L1, levels); } const auto u = [&](Real t)->K { return f(t + a); }; return detail::exp_sinh_integrate_impl(u, tolerance, error, L1, levels); } if ((boost::math::isfinite)(b) && a <= -boost::math::tools::max_value()) { const auto u = [&](Real t)->K { return f(b-t);}; return detail::exp_sinh_integrate_impl(u, tolerance, error, L1, levels); } // Infinite limits: if ((a <= -boost::math::tools::max_value()) && (b >= boost::math::tools::max_value())) { return static_cast(policies::raise_domain_error(function, "Use sinh_sinh quadrature for integration over the whole real line; exp_sinh is for half infinite integrals.", a, Policy())); } // If we get to here then both ends must necessarily be finite: return static_cast(policies::raise_domain_error(function, "Use tanh_sinh quadrature for integration over finite domains; exp_sinh is for half infinite integrals.", a, Policy())); } template > __device__ auto exp_sinh_integrate(const F& f, Real tolerance, Real* error, Real* L1, boost::math::size_t* levels) { BOOST_MATH_STD_USING constexpr auto function = "boost::math::quadrature::exp_sinh<%1%>::integrate"; if (abs(tolerance) > 1) { return policies::raise_domain_error(function, "The tolerance provided (%1%) is unusually large; did you confuse it with a domain bound?", tolerance, Policy()); } return detail::exp_sinh_integrate_impl(f, tolerance, error, L1, levels); } } // namespace quadrature } // namespace math } // namespace boost #endif // BOOST_MATH_ENABLE_CUDA #endif // BOOST_MATH_QUADRATURE_EXP_SINH_HPP