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authorAnas Nashif <anas.nashif@intel.com>2012-10-30 12:57:26 -0700
committerAnas Nashif <anas.nashif@intel.com>2012-10-30 12:57:26 -0700
commit1a78a62555be32868418fe52f8e330c9d0f95d5a (patch)
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+
+// (C) Copyright John Maddock 2006.
+// 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_SPECIAL_SPHERICAL_HARMONIC_HPP
+#define BOOST_MATH_SPECIAL_SPHERICAL_HARMONIC_HPP
+
+#ifdef _MSC_VER
+#pragma once
+#endif
+
+#include <boost/math/special_functions/legendre.hpp>
+#include <boost/math/tools/workaround.hpp>
+#include <complex>
+
+namespace boost{
+namespace math{
+
+namespace detail{
+
+//
+// Calculates the prefix term that's common to the real
+// and imaginary parts. Does *not* fix up the sign of the result
+// though.
+//
+template <class T, class Policy>
+inline T spherical_harmonic_prefix(unsigned n, unsigned m, T theta, const Policy& pol)
+{
+ BOOST_MATH_STD_USING
+
+ if(m > n)
+ return 0;
+
+ T sin_theta = sin(theta);
+ T x = cos(theta);
+
+ T leg = detail::legendre_p_imp(n, m, x, static_cast<T>(pow(fabs(sin_theta), T(m))), pol);
+
+ T prefix = boost::math::tgamma_delta_ratio(static_cast<T>(n - m + 1), static_cast<T>(2 * m), pol);
+ prefix *= (2 * n + 1) / (4 * constants::pi<T>());
+ prefix = sqrt(prefix);
+ return prefix * leg;
+}
+//
+// Real Part:
+//
+template <class T, class Policy>
+T spherical_harmonic_r(unsigned n, int m, T theta, T phi, const Policy& pol)
+{
+ BOOST_MATH_STD_USING // ADL of std functions
+
+ bool sign = false;
+ if(m < 0)
+ {
+ // Reflect and adjust sign if m < 0:
+ sign = m&1;
+ m = abs(m);
+ }
+ if(m&1)
+ {
+ // Check phase if theta is outside [0, PI]:
+ T mod = boost::math::tools::fmod_workaround(theta, T(2 * constants::pi<T>()));
+ if(mod < 0)
+ mod += 2 * constants::pi<T>();
+ if(mod > constants::pi<T>())
+ sign = !sign;
+ }
+ // Get the value and adjust sign as required:
+ T prefix = spherical_harmonic_prefix(n, m, theta, pol);
+ prefix *= cos(m * phi);
+ return sign ? T(-prefix) : prefix;
+}
+
+template <class T, class Policy>
+T spherical_harmonic_i(unsigned n, int m, T theta, T phi, const Policy& pol)
+{
+ BOOST_MATH_STD_USING // ADL of std functions
+
+ bool sign = false;
+ if(m < 0)
+ {
+ // Reflect and adjust sign if m < 0:
+ sign = !(m&1);
+ m = abs(m);
+ }
+ if(m&1)
+ {
+ // Check phase if theta is outside [0, PI]:
+ T mod = boost::math::tools::fmod_workaround(theta, T(2 * constants::pi<T>()));
+ if(mod < 0)
+ mod += 2 * constants::pi<T>();
+ if(mod > constants::pi<T>())
+ sign = !sign;
+ }
+ // Get the value and adjust sign as required:
+ T prefix = spherical_harmonic_prefix(n, m, theta, pol);
+ prefix *= sin(m * phi);
+ return sign ? T(-prefix) : prefix;
+}
+
+template <class T, class U, class Policy>
+std::complex<T> spherical_harmonic(unsigned n, int m, U theta, U phi, const Policy& pol)
+{
+ BOOST_MATH_STD_USING
+ //
+ // Sort out the signs:
+ //
+ bool r_sign = false;
+ bool i_sign = false;
+ if(m < 0)
+ {
+ // Reflect and adjust sign if m < 0:
+ r_sign = m&1;
+ i_sign = !(m&1);
+ m = abs(m);
+ }
+ if(m&1)
+ {
+ // Check phase if theta is outside [0, PI]:
+ U mod = boost::math::tools::fmod_workaround(theta, 2 * constants::pi<U>());
+ if(mod < 0)
+ mod += 2 * constants::pi<U>();
+ if(mod > constants::pi<U>())
+ {
+ r_sign = !r_sign;
+ i_sign = !i_sign;
+ }
+ }
+ //
+ // Calculate the value:
+ //
+ U prefix = spherical_harmonic_prefix(n, m, theta, pol);
+ U r = prefix * cos(m * phi);
+ U i = prefix * sin(m * phi);
+ //
+ // Add in the signs:
+ //
+ if(r_sign)
+ r = -r;
+ if(i_sign)
+ i = -i;
+ static const char* function = "boost::math::spherical_harmonic<%1%>(int, int, %1%, %1%)";
+ return std::complex<T>(policies::checked_narrowing_cast<T, Policy>(r, function), policies::checked_narrowing_cast<T, Policy>(i, function));
+}
+
+} // namespace detail
+
+template <class T1, class T2, class Policy>
+inline std::complex<typename tools::promote_args<T1, T2>::type>
+ spherical_harmonic(unsigned n, int m, T1 theta, T2 phi, const Policy& pol)
+{
+ typedef typename tools::promote_args<T1, T2>::type result_type;
+ typedef typename policies::evaluation<result_type, Policy>::type value_type;
+ return detail::spherical_harmonic<result_type, value_type>(n, m, static_cast<value_type>(theta), static_cast<value_type>(phi), pol);
+}
+
+template <class T1, class T2>
+inline std::complex<typename tools::promote_args<T1, T2>::type>
+ spherical_harmonic(unsigned n, int m, T1 theta, T2 phi)
+{
+ return boost::math::spherical_harmonic(n, m, theta, phi, policies::policy<>());
+}
+
+template <class T1, class T2, class Policy>
+inline typename tools::promote_args<T1, T2>::type
+ spherical_harmonic_r(unsigned n, int m, T1 theta, T2 phi, const Policy& pol)
+{
+ typedef typename tools::promote_args<T1, T2>::type result_type;
+ typedef typename policies::evaluation<result_type, Policy>::type value_type;
+ 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%)");
+}
+
+template <class T1, class T2>
+inline typename tools::promote_args<T1, T2>::type
+ spherical_harmonic_r(unsigned n, int m, T1 theta, T2 phi)
+{
+ return boost::math::spherical_harmonic_r(n, m, theta, phi, policies::policy<>());
+}
+
+template <class T1, class T2, class Policy>
+inline typename tools::promote_args<T1, T2>::type
+ spherical_harmonic_i(unsigned n, int m, T1 theta, T2 phi, const Policy& pol)
+{
+ typedef typename tools::promote_args<T1, T2>::type result_type;
+ typedef typename policies::evaluation<result_type, Policy>::type value_type;
+ 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%)");
+}
+
+template <class T1, class T2>
+inline typename tools::promote_args<T1, T2>::type
+ spherical_harmonic_i(unsigned n, int m, T1 theta, T2 phi)
+{
+ return boost::math::spherical_harmonic_i(n, m, theta, phi, policies::policy<>());
+}
+
+} // namespace math
+} // namespace boost
+
+#endif // BOOST_MATH_SPECIAL_SPHERICAL_HARMONIC_HPP
+
+
+