763 lines
28 KiB
C++
763 lines
28 KiB
C++
// Copyright (c) 2007, 2013 John Maddock
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// Copyright Christopher Kormanyos 2013.
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// Use, modification and distribution are subject to the
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// Boost Software License, Version 1.0. (See accompanying file
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// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
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//
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// This header just defines the function entry points, and adds dispatch
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// to the right implementation method. Most of the implementation details
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// are in separate headers and copyright Xiaogang Zhang.
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//
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#ifndef BOOST_MATH_BESSEL_HPP
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#define BOOST_MATH_BESSEL_HPP
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#ifdef _MSC_VER
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# pragma once
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#endif
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#include <limits>
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#include <boost/math/special_functions/math_fwd.hpp>
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#include <boost/math/special_functions/detail/bessel_jy.hpp>
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#include <boost/math/special_functions/detail/bessel_jn.hpp>
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#include <boost/math/special_functions/detail/bessel_yn.hpp>
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#include <boost/math/special_functions/detail/bessel_jy_zero.hpp>
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#include <boost/math/special_functions/detail/bessel_ik.hpp>
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#include <boost/math/special_functions/detail/bessel_i0.hpp>
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#include <boost/math/special_functions/detail/bessel_i1.hpp>
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#include <boost/math/special_functions/detail/bessel_kn.hpp>
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#include <boost/math/special_functions/detail/iconv.hpp>
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#include <boost/math/special_functions/sin_pi.hpp>
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#include <boost/math/special_functions/cos_pi.hpp>
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#include <boost/math/special_functions/sinc.hpp>
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#include <boost/math/special_functions/trunc.hpp>
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#include <boost/math/special_functions/round.hpp>
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#include <boost/math/tools/rational.hpp>
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#include <boost/math/tools/promotion.hpp>
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#include <boost/math/tools/series.hpp>
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#include <boost/math/tools/roots.hpp>
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namespace boost{ namespace math{
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namespace detail{
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template <class T, class Policy>
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struct sph_bessel_j_small_z_series_term
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{
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typedef T result_type;
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sph_bessel_j_small_z_series_term(unsigned v_, T x)
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: N(0), v(v_)
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{
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BOOST_MATH_STD_USING
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mult = x / 2;
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if(v + 3 > max_factorial<T>::value)
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{
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term = v * log(mult) - boost::math::lgamma(v+1+T(0.5f), Policy());
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term = exp(term);
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}
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else
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term = pow(mult, T(v)) / boost::math::tgamma(v+1+T(0.5f), Policy());
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mult *= -mult;
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}
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T operator()()
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{
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T r = term;
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++N;
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term *= mult / (N * T(N + v + 0.5f));
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return r;
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}
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private:
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unsigned N;
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unsigned v;
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T mult;
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T term;
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};
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template <class T, class Policy>
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inline T sph_bessel_j_small_z_series(unsigned v, T x, const Policy& pol)
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{
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BOOST_MATH_STD_USING // ADL of std names
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sph_bessel_j_small_z_series_term<T, Policy> s(v, x);
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boost::uintmax_t max_iter = policies::get_max_series_iterations<Policy>();
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#if BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x582))
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T zero = 0;
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T result = boost::math::tools::sum_series(s, boost::math::policies::get_epsilon<T, Policy>(), max_iter, zero);
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#else
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T result = boost::math::tools::sum_series(s, boost::math::policies::get_epsilon<T, Policy>(), max_iter);
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#endif
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policies::check_series_iterations<T>("boost::math::sph_bessel_j_small_z_series<%1%>(%1%,%1%)", max_iter, pol);
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return result * sqrt(constants::pi<T>() / 4);
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}
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template <class T, class Policy>
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T cyl_bessel_j_imp(T v, T x, const bessel_no_int_tag& t, const Policy& pol)
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{
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BOOST_MATH_STD_USING
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static const char* function = "boost::math::bessel_j<%1%>(%1%,%1%)";
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if(x < 0)
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{
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// better have integer v:
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if(floor(v) == v)
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{
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T r = cyl_bessel_j_imp(v, T(-x), t, pol);
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if(iround(v, pol) & 1)
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r = -r;
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return r;
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}
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else
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return policies::raise_domain_error<T>(
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function,
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"Got x = %1%, but we need x >= 0", x, pol);
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}
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T j, y;
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bessel_jy(v, x, &j, &y, need_j, pol);
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return j;
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}
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template <class T, class Policy>
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inline T cyl_bessel_j_imp(T v, T x, const bessel_maybe_int_tag&, const Policy& pol)
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{
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BOOST_MATH_STD_USING // ADL of std names.
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int ival = detail::iconv(v, pol);
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// If v is an integer, use the integer recursion
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// method, both that and Steeds method are O(v):
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if((0 == v - ival))
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{
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return bessel_jn(ival, x, pol);
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}
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return cyl_bessel_j_imp(v, x, bessel_no_int_tag(), pol);
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}
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template <class T, class Policy>
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inline T cyl_bessel_j_imp(int v, T x, const bessel_int_tag&, const Policy& pol)
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{
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BOOST_MATH_STD_USING
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return bessel_jn(v, x, pol);
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}
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template <class T, class Policy>
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inline T sph_bessel_j_imp(unsigned n, T x, const Policy& pol)
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{
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BOOST_MATH_STD_USING // ADL of std names
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if(x < 0)
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return policies::raise_domain_error<T>(
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"boost::math::sph_bessel_j<%1%>(%1%,%1%)",
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"Got x = %1%, but function requires x > 0.", x, pol);
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//
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// Special case, n == 0 resolves down to the sinus cardinal of x:
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//
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if(n == 0)
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return boost::math::sinc_pi(x, pol);
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//
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// Special case for x == 0:
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//
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if(x == 0)
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return 0;
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//
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// When x is small we may end up with 0/0, use series evaluation
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// instead, especially as it converges rapidly:
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//
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if(x < 1)
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return sph_bessel_j_small_z_series(n, x, pol);
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//
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// Default case is just a naive evaluation of the definition:
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//
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return sqrt(constants::pi<T>() / (2 * x))
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* cyl_bessel_j_imp(T(T(n)+T(0.5f)), x, bessel_no_int_tag(), pol);
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}
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template <class T, class Policy>
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T cyl_bessel_i_imp(T v, T x, const Policy& pol)
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{
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//
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// This handles all the bessel I functions, note that we don't optimise
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// for integer v, other than the v = 0 or 1 special cases, as Millers
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// algorithm is at least as inefficient as the general case (the general
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// case has better error handling too).
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//
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BOOST_MATH_STD_USING
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if(x < 0)
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{
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// better have integer v:
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if(floor(v) == v)
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{
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T r = cyl_bessel_i_imp(v, T(-x), pol);
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if(iround(v, pol) & 1)
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r = -r;
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return r;
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}
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else
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return policies::raise_domain_error<T>(
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"boost::math::cyl_bessel_i<%1%>(%1%,%1%)",
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"Got x = %1%, but we need x >= 0", x, pol);
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}
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if(x == 0)
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{
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return (v == 0) ? static_cast<T>(1) : static_cast<T>(0);
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}
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if(v == 0.5f)
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{
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// common special case, note try and avoid overflow in exp(x):
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if(x >= tools::log_max_value<T>())
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{
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T e = exp(x / 2);
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return e * (e / sqrt(2 * x * constants::pi<T>()));
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}
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return sqrt(2 / (x * constants::pi<T>())) * sinh(x);
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}
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if(policies::digits<T, Policy>() <= 64)
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{
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if(v == 0)
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{
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return bessel_i0(x);
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}
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if(v == 1)
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{
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return bessel_i1(x);
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}
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}
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if((v > 0) && (x / v < 0.25))
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return bessel_i_small_z_series(v, x, pol);
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T I, K;
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bessel_ik(v, x, &I, &K, need_i, pol);
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return I;
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}
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template <class T, class Policy>
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inline T cyl_bessel_k_imp(T v, T x, const bessel_no_int_tag& /* t */, const Policy& pol)
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{
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static const char* function = "boost::math::cyl_bessel_k<%1%>(%1%,%1%)";
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BOOST_MATH_STD_USING
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if(x < 0)
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{
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return policies::raise_domain_error<T>(
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function,
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"Got x = %1%, but we need x > 0", x, pol);
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}
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if(x == 0)
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{
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return (v == 0) ? policies::raise_overflow_error<T>(function, 0, pol)
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: policies::raise_domain_error<T>(
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function,
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"Got x = %1%, but we need x > 0", x, pol);
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}
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T I, K;
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bessel_ik(v, x, &I, &K, need_k, pol);
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return K;
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}
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template <class T, class Policy>
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inline T cyl_bessel_k_imp(T v, T x, const bessel_maybe_int_tag&, const Policy& pol)
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{
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BOOST_MATH_STD_USING
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if((floor(v) == v))
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{
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return bessel_kn(itrunc(v), x, pol);
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}
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return cyl_bessel_k_imp(v, x, bessel_no_int_tag(), pol);
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}
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template <class T, class Policy>
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inline T cyl_bessel_k_imp(int v, T x, const bessel_int_tag&, const Policy& pol)
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{
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return bessel_kn(v, x, pol);
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}
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template <class T, class Policy>
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inline T cyl_neumann_imp(T v, T x, const bessel_no_int_tag&, const Policy& pol)
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{
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static const char* function = "boost::math::cyl_neumann<%1%>(%1%,%1%)";
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BOOST_MATH_INSTRUMENT_VARIABLE(v);
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BOOST_MATH_INSTRUMENT_VARIABLE(x);
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if(x <= 0)
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{
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return (v == 0) && (x == 0) ?
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policies::raise_overflow_error<T>(function, 0, pol)
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: policies::raise_domain_error<T>(
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function,
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"Got x = %1%, but result is complex for x <= 0", x, pol);
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}
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T j, y;
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bessel_jy(v, x, &j, &y, need_y, pol);
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//
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// Post evaluation check for internal overflow during evaluation,
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// can occur when x is small and v is large, in which case the result
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// is -INF:
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//
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if(!(boost::math::isfinite)(y))
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return -policies::raise_overflow_error<T>(function, 0, pol);
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return y;
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}
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template <class T, class Policy>
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inline T cyl_neumann_imp(T v, T x, const bessel_maybe_int_tag&, const Policy& pol)
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{
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BOOST_MATH_STD_USING
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BOOST_MATH_INSTRUMENT_VARIABLE(v);
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BOOST_MATH_INSTRUMENT_VARIABLE(x);
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if(floor(v) == v)
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{
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T r = bessel_yn(itrunc(v, pol), x, pol);
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BOOST_MATH_INSTRUMENT_VARIABLE(r);
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return r;
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}
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T r = cyl_neumann_imp<T>(v, x, bessel_no_int_tag(), pol);
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BOOST_MATH_INSTRUMENT_VARIABLE(r);
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return r;
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}
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template <class T, class Policy>
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inline T cyl_neumann_imp(int v, T x, const bessel_int_tag&, const Policy& pol)
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{
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return bessel_yn(v, x, pol);
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}
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template <class T, class Policy>
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inline T sph_neumann_imp(unsigned v, T x, const Policy& pol)
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{
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BOOST_MATH_STD_USING // ADL of std names
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static const char* function = "boost::math::sph_neumann<%1%>(%1%,%1%)";
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//
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// Nothing much to do here but check for errors, and
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// evaluate the function's definition directly:
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//
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if(x < 0)
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return policies::raise_domain_error<T>(
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function,
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"Got x = %1%, but function requires x > 0.", x, pol);
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if(x < 2 * tools::min_value<T>())
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return -policies::raise_overflow_error<T>(function, 0, pol);
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T result = cyl_neumann_imp(T(T(v)+0.5f), x, bessel_no_int_tag(), pol);
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T tx = sqrt(constants::pi<T>() / (2 * x));
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if((tx > 1) && (tools::max_value<T>() / tx < result))
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return -policies::raise_overflow_error<T>(function, 0, pol);
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return result * tx;
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}
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template <class T, class Policy>
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inline T cyl_bessel_j_zero_imp(T v, int m, const Policy& pol)
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{
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BOOST_MATH_STD_USING // ADL of std names, needed for floor.
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static const char* function = "boost::math::cyl_bessel_j_zero<%1%>(%1%, int)";
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const T half_epsilon(boost::math::tools::epsilon<T>() / 2U);
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// Handle non-finite order.
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if (!(boost::math::isfinite)(v) )
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{
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return policies::raise_domain_error<T>(function, "Order argument is %1%, but must be finite >= 0 !", v, pol);
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}
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// Handle negative rank.
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if(m < 0)
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{
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// Zeros of Jv(x) with negative rank are not defined and requesting one raises a domain error.
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return policies::raise_domain_error<T>(function, "Requested the %1%'th zero, but the rank must be positive !", static_cast<T>(m), pol);
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}
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// Get the absolute value of the order.
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const bool order_is_negative = (v < 0);
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const T vv((!order_is_negative) ? v : T(-v));
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// Check if the order is very close to zero or very close to an integer.
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const bool order_is_zero = (vv < half_epsilon);
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const bool order_is_integer = ((vv - floor(vv)) < half_epsilon);
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if(m == 0)
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{
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if(order_is_zero)
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{
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// The zero'th zero of J0(x) is not defined and requesting it raises a domain error.
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return policies::raise_domain_error<T>(function, "Requested the %1%'th zero of J0, but the rank must be > 0 !", static_cast<T>(m), pol);
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}
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// The zero'th zero of Jv(x) for v < 0 is not defined
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// unless the order is a negative integer.
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if(order_is_negative && (!order_is_integer))
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{
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// For non-integer, negative order, requesting the zero'th zero raises a domain error.
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return policies::raise_domain_error<T>(function, "Requested the %1%'th zero of Jv for negative, non-integer order, but the rank must be > 0 !", static_cast<T>(m), pol);
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}
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// The zero'th zero does exist and its value is zero.
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return T(0);
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}
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// Set up the initial guess for the upcoming root-finding.
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// If the order is a negative integer, then use the corresponding
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// positive integer for the order.
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const T guess_root = boost::math::detail::bessel_zero::cyl_bessel_j_zero_detail::initial_guess<T, Policy>((order_is_integer ? vv : v), m, pol);
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// Select the maximum allowed iterations from the policy.
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boost::uintmax_t number_of_iterations = policies::get_max_root_iterations<Policy>();
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const T delta_lo = ((guess_root > 0.2F) ? T(0.2) : T(guess_root / 2U));
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// Perform the root-finding using Newton-Raphson iteration from Boost.Math.
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const T jvm =
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boost::math::tools::newton_raphson_iterate(
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boost::math::detail::bessel_zero::cyl_bessel_j_zero_detail::function_object_jv_and_jv_prime<T, Policy>((order_is_integer ? vv : v), order_is_zero, pol),
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guess_root,
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T(guess_root - delta_lo),
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T(guess_root + 0.2F),
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policies::digits<T, Policy>(),
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number_of_iterations);
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if(number_of_iterations >= policies::get_max_root_iterations<Policy>())
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{
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return policies::raise_evaluation_error<T>(function, "Unable to locate root in a reasonable time:"
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" Current best guess is %1%", jvm, Policy());
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}
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return jvm;
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}
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template <class T, class Policy>
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inline T cyl_neumann_zero_imp(T v, int m, const Policy& pol)
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{
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BOOST_MATH_STD_USING // ADL of std names, needed for floor.
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static const char* function = "boost::math::cyl_neumann_zero<%1%>(%1%, int)";
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// Handle non-finite order.
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if (!(boost::math::isfinite)(v) )
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{
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return policies::raise_domain_error<T>(function, "Order argument is %1%, but must be finite >= 0 !", v, pol);
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}
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// Handle negative rank.
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if(m < 0)
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{
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return policies::raise_domain_error<T>(function, "Requested the %1%'th zero, but the rank must be positive !", static_cast<T>(m), pol);
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}
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const T half_epsilon(boost::math::tools::epsilon<T>() / 2U);
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// Get the absolute value of the order.
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const bool order_is_negative = (v < 0);
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const T vv((!order_is_negative) ? v : T(-v));
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const bool order_is_integer = ((vv - floor(vv)) < half_epsilon);
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// For negative integers, use reflection to positive integer order.
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if(order_is_negative && order_is_integer)
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return boost::math::detail::cyl_neumann_zero_imp(vv, m, pol);
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// Check if the order is very close to a negative half-integer.
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const T delta_half_integer(vv - (floor(vv) + 0.5F));
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const bool order_is_negative_half_integer =
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(order_is_negative && ((delta_half_integer > -half_epsilon) && (delta_half_integer < +half_epsilon)));
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// The zero'th zero of Yv(x) for v < 0 is not defined
|
|
// unless the order is a negative integer.
|
|
if((m == 0) && (!order_is_negative_half_integer))
|
|
{
|
|
// For non-integer, negative order, requesting the zero'th zero raises a domain error.
|
|
return policies::raise_domain_error<T>(function, "Requested the %1%'th zero of Yv for negative, non-half-integer order, but the rank must be > 0 !", static_cast<T>(m), pol);
|
|
}
|
|
|
|
// For negative half-integers, use the corresponding
|
|
// spherical Bessel function of positive half-integer order.
|
|
if(order_is_negative_half_integer)
|
|
return boost::math::detail::cyl_bessel_j_zero_imp(vv, m, pol);
|
|
|
|
// Set up the initial guess for the upcoming root-finding.
|
|
// If the order is a negative integer, then use the corresponding
|
|
// positive integer for the order.
|
|
const T guess_root = boost::math::detail::bessel_zero::cyl_neumann_zero_detail::initial_guess<T, Policy>(v, m, pol);
|
|
|
|
// Select the maximum allowed iterations from the policy.
|
|
boost::uintmax_t number_of_iterations = policies::get_max_root_iterations<Policy>();
|
|
|
|
const T delta_lo = ((guess_root > 0.2F) ? T(0.2) : T(guess_root / 2U));
|
|
|
|
// Perform the root-finding using Newton-Raphson iteration from Boost.Math.
|
|
const T yvm =
|
|
boost::math::tools::newton_raphson_iterate(
|
|
boost::math::detail::bessel_zero::cyl_neumann_zero_detail::function_object_yv_and_yv_prime<T, Policy>(v, pol),
|
|
guess_root,
|
|
T(guess_root - delta_lo),
|
|
T(guess_root + 0.2F),
|
|
policies::digits<T, Policy>(),
|
|
number_of_iterations);
|
|
|
|
if(number_of_iterations >= policies::get_max_root_iterations<Policy>())
|
|
{
|
|
return policies::raise_evaluation_error<T>(function, "Unable to locate root in a reasonable time:"
|
|
" Current best guess is %1%", yvm, Policy());
|
|
}
|
|
|
|
return yvm;
|
|
}
|
|
|
|
} // namespace detail
|
|
|
|
template <class T1, class T2, class Policy>
|
|
inline typename detail::bessel_traits<T1, T2, Policy>::result_type cyl_bessel_j(T1 v, T2 x, const Policy& /* pol */)
|
|
{
|
|
BOOST_FPU_EXCEPTION_GUARD
|
|
typedef typename detail::bessel_traits<T1, T2, Policy>::result_type result_type;
|
|
typedef typename detail::bessel_traits<T1, T2, Policy>::optimisation_tag tag_type;
|
|
typedef typename policies::evaluation<result_type, Policy>::type value_type;
|
|
typedef typename policies::normalise<
|
|
Policy,
|
|
policies::promote_float<false>,
|
|
policies::promote_double<false>,
|
|
policies::discrete_quantile<>,
|
|
policies::assert_undefined<> >::type forwarding_policy;
|
|
return policies::checked_narrowing_cast<result_type, Policy>(detail::cyl_bessel_j_imp<value_type>(v, static_cast<value_type>(x), tag_type(), forwarding_policy()), "boost::math::cyl_bessel_j<%1%>(%1%,%1%)");
|
|
}
|
|
|
|
template <class T1, class T2>
|
|
inline typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type cyl_bessel_j(T1 v, T2 x)
|
|
{
|
|
return cyl_bessel_j(v, x, policies::policy<>());
|
|
}
|
|
|
|
template <class T, class Policy>
|
|
inline typename detail::bessel_traits<T, T, Policy>::result_type sph_bessel(unsigned v, T x, const Policy& /* pol */)
|
|
{
|
|
BOOST_FPU_EXCEPTION_GUARD
|
|
typedef typename detail::bessel_traits<T, T, Policy>::result_type result_type;
|
|
typedef typename policies::evaluation<result_type, Policy>::type value_type;
|
|
typedef typename policies::normalise<
|
|
Policy,
|
|
policies::promote_float<false>,
|
|
policies::promote_double<false>,
|
|
policies::discrete_quantile<>,
|
|
policies::assert_undefined<> >::type forwarding_policy;
|
|
return policies::checked_narrowing_cast<result_type, Policy>(detail::sph_bessel_j_imp<value_type>(v, static_cast<value_type>(x), forwarding_policy()), "boost::math::sph_bessel<%1%>(%1%,%1%)");
|
|
}
|
|
|
|
template <class T>
|
|
inline typename detail::bessel_traits<T, T, policies::policy<> >::result_type sph_bessel(unsigned v, T x)
|
|
{
|
|
return sph_bessel(v, x, policies::policy<>());
|
|
}
|
|
|
|
template <class T1, class T2, class Policy>
|
|
inline typename detail::bessel_traits<T1, T2, Policy>::result_type cyl_bessel_i(T1 v, T2 x, const Policy& /* pol */)
|
|
{
|
|
BOOST_FPU_EXCEPTION_GUARD
|
|
typedef typename detail::bessel_traits<T1, T2, Policy>::result_type result_type;
|
|
typedef typename policies::evaluation<result_type, Policy>::type value_type;
|
|
typedef typename policies::normalise<
|
|
Policy,
|
|
policies::promote_float<false>,
|
|
policies::promote_double<false>,
|
|
policies::discrete_quantile<>,
|
|
policies::assert_undefined<> >::type forwarding_policy;
|
|
return policies::checked_narrowing_cast<result_type, Policy>(detail::cyl_bessel_i_imp<value_type>(static_cast<value_type>(v), static_cast<value_type>(x), forwarding_policy()), "boost::math::cyl_bessel_i<%1%>(%1%,%1%)");
|
|
}
|
|
|
|
template <class T1, class T2>
|
|
inline typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type cyl_bessel_i(T1 v, T2 x)
|
|
{
|
|
return cyl_bessel_i(v, x, policies::policy<>());
|
|
}
|
|
|
|
template <class T1, class T2, class Policy>
|
|
inline typename detail::bessel_traits<T1, T2, Policy>::result_type cyl_bessel_k(T1 v, T2 x, const Policy& /* pol */)
|
|
{
|
|
BOOST_FPU_EXCEPTION_GUARD
|
|
typedef typename detail::bessel_traits<T1, T2, Policy>::result_type result_type;
|
|
typedef typename detail::bessel_traits<T1, T2, Policy>::optimisation_tag tag_type;
|
|
typedef typename policies::evaluation<result_type, Policy>::type value_type;
|
|
typedef typename policies::normalise<
|
|
Policy,
|
|
policies::promote_float<false>,
|
|
policies::promote_double<false>,
|
|
policies::discrete_quantile<>,
|
|
policies::assert_undefined<> >::type forwarding_policy;
|
|
return policies::checked_narrowing_cast<result_type, Policy>(detail::cyl_bessel_k_imp<value_type>(v, static_cast<value_type>(x), tag_type(), forwarding_policy()), "boost::math::cyl_bessel_k<%1%>(%1%,%1%)");
|
|
}
|
|
|
|
template <class T1, class T2>
|
|
inline typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type cyl_bessel_k(T1 v, T2 x)
|
|
{
|
|
return cyl_bessel_k(v, x, policies::policy<>());
|
|
}
|
|
|
|
template <class T1, class T2, class Policy>
|
|
inline typename detail::bessel_traits<T1, T2, Policy>::result_type cyl_neumann(T1 v, T2 x, const Policy& /* pol */)
|
|
{
|
|
BOOST_FPU_EXCEPTION_GUARD
|
|
typedef typename detail::bessel_traits<T1, T2, Policy>::result_type result_type;
|
|
typedef typename detail::bessel_traits<T1, T2, Policy>::optimisation_tag tag_type;
|
|
typedef typename policies::evaluation<result_type, Policy>::type value_type;
|
|
typedef typename policies::normalise<
|
|
Policy,
|
|
policies::promote_float<false>,
|
|
policies::promote_double<false>,
|
|
policies::discrete_quantile<>,
|
|
policies::assert_undefined<> >::type forwarding_policy;
|
|
return policies::checked_narrowing_cast<result_type, Policy>(detail::cyl_neumann_imp<value_type>(v, static_cast<value_type>(x), tag_type(), forwarding_policy()), "boost::math::cyl_neumann<%1%>(%1%,%1%)");
|
|
}
|
|
|
|
template <class T1, class T2>
|
|
inline typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type cyl_neumann(T1 v, T2 x)
|
|
{
|
|
return cyl_neumann(v, x, policies::policy<>());
|
|
}
|
|
|
|
template <class T, class Policy>
|
|
inline typename detail::bessel_traits<T, T, Policy>::result_type sph_neumann(unsigned v, T x, const Policy& /* pol */)
|
|
{
|
|
BOOST_FPU_EXCEPTION_GUARD
|
|
typedef typename detail::bessel_traits<T, T, Policy>::result_type result_type;
|
|
typedef typename policies::evaluation<result_type, Policy>::type value_type;
|
|
typedef typename policies::normalise<
|
|
Policy,
|
|
policies::promote_float<false>,
|
|
policies::promote_double<false>,
|
|
policies::discrete_quantile<>,
|
|
policies::assert_undefined<> >::type forwarding_policy;
|
|
return policies::checked_narrowing_cast<result_type, Policy>(detail::sph_neumann_imp<value_type>(v, static_cast<value_type>(x), forwarding_policy()), "boost::math::sph_neumann<%1%>(%1%,%1%)");
|
|
}
|
|
|
|
template <class T>
|
|
inline typename detail::bessel_traits<T, T, policies::policy<> >::result_type sph_neumann(unsigned v, T x)
|
|
{
|
|
return sph_neumann(v, x, policies::policy<>());
|
|
}
|
|
|
|
template <class T, class Policy>
|
|
inline typename detail::bessel_traits<T, T, Policy>::result_type cyl_bessel_j_zero(T v, int m, const Policy& /* pol */)
|
|
{
|
|
BOOST_FPU_EXCEPTION_GUARD
|
|
typedef typename detail::bessel_traits<T, T, Policy>::result_type result_type;
|
|
typedef typename policies::evaluation<result_type, Policy>::type value_type;
|
|
typedef typename policies::normalise<
|
|
Policy,
|
|
policies::promote_float<false>,
|
|
policies::promote_double<false>,
|
|
policies::discrete_quantile<>,
|
|
policies::assert_undefined<> >::type forwarding_policy;
|
|
|
|
BOOST_STATIC_ASSERT_MSG( false == std::numeric_limits<T>::is_specialized
|
|
|| ( true == std::numeric_limits<T>::is_specialized
|
|
&& false == std::numeric_limits<T>::is_integer),
|
|
"Order must be a floating-point type.");
|
|
|
|
return policies::checked_narrowing_cast<result_type, Policy>(detail::cyl_bessel_j_zero_imp<value_type>(v, m, forwarding_policy()), "boost::math::cyl_bessel_j_zero<%1%>(%1%,%1%)");
|
|
}
|
|
|
|
template <class T>
|
|
inline typename detail::bessel_traits<T, T, policies::policy<> >::result_type cyl_bessel_j_zero(T v, int m)
|
|
{
|
|
BOOST_STATIC_ASSERT_MSG( false == std::numeric_limits<T>::is_specialized
|
|
|| ( true == std::numeric_limits<T>::is_specialized
|
|
&& false == std::numeric_limits<T>::is_integer),
|
|
"Order must be a floating-point type.");
|
|
|
|
return cyl_bessel_j_zero<T, policies::policy<> >(v, m, policies::policy<>());
|
|
}
|
|
|
|
template <class T, class OutputIterator, class Policy>
|
|
inline OutputIterator cyl_bessel_j_zero(T v,
|
|
int start_index,
|
|
unsigned number_of_zeros,
|
|
OutputIterator out_it,
|
|
const Policy& pol)
|
|
{
|
|
BOOST_STATIC_ASSERT_MSG( false == std::numeric_limits<T>::is_specialized
|
|
|| ( true == std::numeric_limits<T>::is_specialized
|
|
&& false == std::numeric_limits<T>::is_integer),
|
|
"Order must be a floating-point type.");
|
|
|
|
for(int i = 0; i < static_cast<int>(number_of_zeros); ++i)
|
|
{
|
|
*out_it = boost::math::cyl_bessel_j_zero(v, start_index + i, pol);
|
|
++out_it;
|
|
}
|
|
return out_it;
|
|
}
|
|
|
|
template <class T, class OutputIterator>
|
|
inline OutputIterator cyl_bessel_j_zero(T v,
|
|
int start_index,
|
|
unsigned number_of_zeros,
|
|
OutputIterator out_it)
|
|
{
|
|
return cyl_bessel_j_zero(v, start_index, number_of_zeros, out_it, policies::policy<>());
|
|
}
|
|
|
|
template <class T, class Policy>
|
|
inline typename detail::bessel_traits<T, T, Policy>::result_type cyl_neumann_zero(T v, int m, const Policy& /* pol */)
|
|
{
|
|
BOOST_FPU_EXCEPTION_GUARD
|
|
typedef typename detail::bessel_traits<T, T, Policy>::result_type result_type;
|
|
typedef typename policies::evaluation<result_type, Policy>::type value_type;
|
|
typedef typename policies::normalise<
|
|
Policy,
|
|
policies::promote_float<false>,
|
|
policies::promote_double<false>,
|
|
policies::discrete_quantile<>,
|
|
policies::assert_undefined<> >::type forwarding_policy;
|
|
|
|
BOOST_STATIC_ASSERT_MSG( false == std::numeric_limits<T>::is_specialized
|
|
|| ( true == std::numeric_limits<T>::is_specialized
|
|
&& false == std::numeric_limits<T>::is_integer),
|
|
"Order must be a floating-point type.");
|
|
|
|
return policies::checked_narrowing_cast<result_type, Policy>(detail::cyl_neumann_zero_imp<value_type>(v, m, forwarding_policy()), "boost::math::cyl_neumann_zero<%1%>(%1%,%1%)");
|
|
}
|
|
|
|
template <class T>
|
|
inline typename detail::bessel_traits<T, T, policies::policy<> >::result_type cyl_neumann_zero(T v, int m)
|
|
{
|
|
BOOST_STATIC_ASSERT_MSG( false == std::numeric_limits<T>::is_specialized
|
|
|| ( true == std::numeric_limits<T>::is_specialized
|
|
&& false == std::numeric_limits<T>::is_integer),
|
|
"Order must be a floating-point type.");
|
|
|
|
return cyl_neumann_zero<T, policies::policy<> >(v, m, policies::policy<>());
|
|
}
|
|
|
|
template <class T, class OutputIterator, class Policy>
|
|
inline OutputIterator cyl_neumann_zero(T v,
|
|
int start_index,
|
|
unsigned number_of_zeros,
|
|
OutputIterator out_it,
|
|
const Policy& pol)
|
|
{
|
|
BOOST_STATIC_ASSERT_MSG( false == std::numeric_limits<T>::is_specialized
|
|
|| ( true == std::numeric_limits<T>::is_specialized
|
|
&& false == std::numeric_limits<T>::is_integer),
|
|
"Order must be a floating-point type.");
|
|
|
|
for(int i = 0; i < static_cast<int>(number_of_zeros); ++i)
|
|
{
|
|
*out_it = boost::math::cyl_neumann_zero(v, start_index + i, pol);
|
|
++out_it;
|
|
}
|
|
return out_it;
|
|
}
|
|
|
|
template <class T, class OutputIterator>
|
|
inline OutputIterator cyl_neumann_zero(T v,
|
|
int start_index,
|
|
unsigned number_of_zeros,
|
|
OutputIterator out_it)
|
|
{
|
|
return cyl_neumann_zero(v, start_index, number_of_zeros, out_it, policies::policy<>());
|
|
}
|
|
|
|
} // namespace math
|
|
} // namespace boost
|
|
|
|
#endif // BOOST_MATH_BESSEL_HPP
|
|
|
|
|