

//  (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



#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, 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, 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 ? -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, 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 ? -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





