206 lines
6.4 KiB
Plaintext
206 lines
6.4 KiB
Plaintext
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// (C) Copyright John Maddock 2006.
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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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#ifndef BOOST_MATH_SPECIAL_SPHERICAL_HARMONIC_HPP
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#define BOOST_MATH_SPECIAL_SPHERICAL_HARMONIC_HPP
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#ifdef _MSC_VER
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#pragma once
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#endif
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#include <boost/math/special_functions/math_fwd.hpp>
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#include <boost/math/special_functions/legendre.hpp>
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#include <boost/math/tools/workaround.hpp>
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#include <complex>
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namespace boost{
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namespace math{
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namespace detail{
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//
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// Calculates the prefix term that's common to the real
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// and imaginary parts. Does *not* fix up the sign of the result
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// though.
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//
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template <class T, class Policy>
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inline T spherical_harmonic_prefix(unsigned n, unsigned m, T theta, const Policy& pol)
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{
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BOOST_MATH_STD_USING
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if(m > n)
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return 0;
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T sin_theta = sin(theta);
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T x = cos(theta);
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T leg = detail::legendre_p_imp(n, m, x, static_cast<T>(pow(fabs(sin_theta), T(m))), pol);
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T prefix = boost::math::tgamma_delta_ratio(static_cast<T>(n - m + 1), static_cast<T>(2 * m), pol);
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prefix *= (2 * n + 1) / (4 * constants::pi<T>());
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prefix = sqrt(prefix);
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return prefix * leg;
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}
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//
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// Real Part:
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//
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template <class T, class Policy>
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T spherical_harmonic_r(unsigned n, int m, T theta, T phi, const Policy& pol)
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{
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BOOST_MATH_STD_USING // ADL of std functions
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bool sign = false;
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if(m < 0)
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{
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// Reflect and adjust sign if m < 0:
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sign = m&1;
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m = abs(m);
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}
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if(m&1)
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{
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// Check phase if theta is outside [0, PI]:
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T mod = boost::math::tools::fmod_workaround(theta, T(2 * constants::pi<T>()));
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if(mod < 0)
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mod += 2 * constants::pi<T>();
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if(mod > constants::pi<T>())
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sign = !sign;
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}
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// Get the value and adjust sign as required:
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T prefix = spherical_harmonic_prefix(n, m, theta, pol);
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prefix *= cos(m * phi);
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return sign ? T(-prefix) : prefix;
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}
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template <class T, class Policy>
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T spherical_harmonic_i(unsigned n, int m, T theta, T phi, const Policy& pol)
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{
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BOOST_MATH_STD_USING // ADL of std functions
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bool sign = false;
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if(m < 0)
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{
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// Reflect and adjust sign if m < 0:
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sign = !(m&1);
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m = abs(m);
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}
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if(m&1)
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{
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// Check phase if theta is outside [0, PI]:
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T mod = boost::math::tools::fmod_workaround(theta, T(2 * constants::pi<T>()));
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if(mod < 0)
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mod += 2 * constants::pi<T>();
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if(mod > constants::pi<T>())
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sign = !sign;
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}
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// Get the value and adjust sign as required:
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T prefix = spherical_harmonic_prefix(n, m, theta, pol);
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prefix *= sin(m * phi);
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return sign ? T(-prefix) : prefix;
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}
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template <class T, class U, class Policy>
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std::complex<T> spherical_harmonic(unsigned n, int m, U theta, U phi, const Policy& pol)
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{
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BOOST_MATH_STD_USING
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//
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// Sort out the signs:
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//
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bool r_sign = false;
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bool i_sign = false;
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if(m < 0)
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{
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// Reflect and adjust sign if m < 0:
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r_sign = m&1;
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i_sign = !(m&1);
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m = abs(m);
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}
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if(m&1)
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{
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// Check phase if theta is outside [0, PI]:
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U mod = boost::math::tools::fmod_workaround(theta, U(2 * constants::pi<U>()));
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if(mod < 0)
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mod += 2 * constants::pi<U>();
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if(mod > constants::pi<U>())
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{
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r_sign = !r_sign;
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i_sign = !i_sign;
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}
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}
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//
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// Calculate the value:
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//
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U prefix = spherical_harmonic_prefix(n, m, theta, pol);
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U r = prefix * cos(m * phi);
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U i = prefix * sin(m * phi);
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//
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// Add in the signs:
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//
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if(r_sign)
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r = -r;
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if(i_sign)
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i = -i;
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static const char* function = "boost::math::spherical_harmonic<%1%>(int, int, %1%, %1%)";
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return std::complex<T>(policies::checked_narrowing_cast<T, Policy>(r, function), policies::checked_narrowing_cast<T, Policy>(i, function));
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}
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} // namespace detail
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template <class T1, class T2, class Policy>
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inline std::complex<typename tools::promote_args<T1, T2>::type>
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spherical_harmonic(unsigned n, int m, T1 theta, T2 phi, const Policy& pol)
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{
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typedef typename tools::promote_args<T1, T2>::type result_type;
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typedef typename policies::evaluation<result_type, Policy>::type value_type;
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return detail::spherical_harmonic<result_type, value_type>(n, m, static_cast<value_type>(theta), static_cast<value_type>(phi), pol);
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}
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template <class T1, class T2>
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inline std::complex<typename tools::promote_args<T1, T2>::type>
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spherical_harmonic(unsigned n, int m, T1 theta, T2 phi)
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{
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return boost::math::spherical_harmonic(n, m, theta, phi, policies::policy<>());
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}
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template <class T1, class T2, class Policy>
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inline typename tools::promote_args<T1, T2>::type
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spherical_harmonic_r(unsigned n, int m, T1 theta, T2 phi, const Policy& pol)
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{
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typedef typename tools::promote_args<T1, T2>::type result_type;
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typedef typename policies::evaluation<result_type, Policy>::type value_type;
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return policies::checked_narrowing_cast<result_type, Policy>(detail::spherical_harmonic_r(n, m, static_cast<value_type>(theta), static_cast<value_type>(phi), pol), "bost::math::spherical_harmonic_r<%1%>(unsigned, int, %1%, %1%)");
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}
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template <class T1, class T2>
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inline typename tools::promote_args<T1, T2>::type
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spherical_harmonic_r(unsigned n, int m, T1 theta, T2 phi)
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{
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return boost::math::spherical_harmonic_r(n, m, theta, phi, policies::policy<>());
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}
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template <class T1, class T2, class Policy>
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inline typename tools::promote_args<T1, T2>::type
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spherical_harmonic_i(unsigned n, int m, T1 theta, T2 phi, const Policy& pol)
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{
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typedef typename tools::promote_args<T1, T2>::type result_type;
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typedef typename policies::evaluation<result_type, Policy>::type value_type;
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return policies::checked_narrowing_cast<result_type, Policy>(detail::spherical_harmonic_i(n, m, static_cast<value_type>(theta), static_cast<value_type>(phi), pol), "boost::math::spherical_harmonic_i<%1%>(unsigned, int, %1%, %1%)");
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}
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template <class T1, class T2>
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inline typename tools::promote_args<T1, T2>::type
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spherical_harmonic_i(unsigned n, int m, T1 theta, T2 phi)
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{
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return boost::math::spherical_harmonic_i(n, m, theta, phi, policies::policy<>());
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}
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} // namespace math
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} // namespace boost
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#endif // BOOST_MATH_SPECIAL_SPHERICAL_HARMONIC_HPP
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