# GL Profile Suite / boost_1_51_0 / boost / math / special_functions / spherical_harmonic.hpp

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204``` ``` // (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 #include #include 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 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(pow(fabs(sin_theta), T(m))), pol); T prefix = boost::math::tgamma_delta_ratio(static_cast(n - m + 1), static_cast(2 * m), pol); prefix *= (2 * n + 1) / (4 * constants::pi()); prefix = sqrt(prefix); return prefix * leg; } // // Real Part: // template 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())); if(mod < 0) mod += 2 * constants::pi(); if(mod > constants::pi()) 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 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())); if(mod < 0) mod += 2 * constants::pi(); if(mod > constants::pi()) 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 std::complex 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()); if(mod < 0) mod += 2 * constants::pi(); if(mod > constants::pi()) { 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(policies::checked_narrowing_cast(r, function), policies::checked_narrowing_cast(i, function)); } } // namespace detail template inline std::complex::type> spherical_harmonic(unsigned n, int m, T1 theta, T2 phi, const Policy& pol) { typedef typename tools::promote_args::type result_type; typedef typename policies::evaluation::type value_type; return detail::spherical_harmonic(n, m, static_cast(theta), static_cast(phi), pol); } template inline std::complex::type> spherical_harmonic(unsigned n, int m, T1 theta, T2 phi) { return boost::math::spherical_harmonic(n, m, theta, phi, policies::policy<>()); } template inline typename tools::promote_args::type spherical_harmonic_r(unsigned n, int m, T1 theta, T2 phi, const Policy& pol) { typedef typename tools::promote_args::type result_type; typedef typename policies::evaluation::type value_type; return policies::checked_narrowing_cast(detail::spherical_harmonic_r(n, m, static_cast(theta), static_cast(phi), pol), "bost::math::spherical_harmonic_r<%1%>(unsigned, int, %1%, %1%)"); } template inline typename tools::promote_args::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 inline typename tools::promote_args::type spherical_harmonic_i(unsigned n, int m, T1 theta, T2 phi, const Policy& pol) { typedef typename tools::promote_args::type result_type; typedef typename policies::evaluation::type value_type; return policies::checked_narrowing_cast(detail::spherical_harmonic_i(n, m, static_cast(theta), static_cast(phi), pol), "boost::math::spherical_harmonic_i<%1%>(unsigned, int, %1%, %1%)"); } template inline typename tools::promote_args::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 ```