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 // This file is part of the ACTS project.
 //
 // Copyright (C) 2016 CERN for the benefit of the ACTS project
 //
 // This Source Code Form is subject to the terms of the Mozilla Public
 // License, v. 2.0. If a copy of the MPL was not distributed with this
 // file, You can obtain one at https://mozilla.org/MPL/2.0/.
 
 #include "Acts/MagneticField/SolenoidBField.hpp"
 
 #include "Acts/Utilities/VectorHelpers.hpp"
 
 #include <cmath>
 #include <numbers>
 
 #define BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
 
 #include <boost/exception/exception.hpp>
 #include <boost/math/special_functions/ellint_1.hpp>
 #include <boost/math/special_functions/ellint_2.hpp>
 
 namespace Acts {
 
 SolenoidBField::SolenoidBField(Config config) : m_cfg(config) {
   m_dz = m_cfg.length / m_cfg.nCoils;
   m_R2 = m_cfg.radius * m_cfg.radius;
   // we need to scale so we reproduce the expected B field strength
   // at the center of the solenoid
   Vector2 field = multiCoilField({0, 0}, 1.);  // scale = 1
   m_scale = m_cfg.bMagCenter / field.norm();
 }
 
 MagneticFieldProvider::Cache SolenoidBField::makeCache(
     const MagneticFieldContext& mctx) const {
   return MagneticFieldProvider::Cache(std::in_place_type<Cache>, mctx);
 }
 
 Vector3 SolenoidBField::getField(const Vector3& position) const {
   using VectorHelpers::perp;
   Vector2 rzPos(perp(position), position.z());
   Vector2 rzField = multiCoilField(rzPos, m_scale);
   Vector3 xyzField(0, 0, rzField[1]);
 
   if (rzPos[0] != 0.) {
     // add xy field component, radially symmetric
     Vector3 rDir = Vector3(position.x(), position.y(), 0).normalized();
     xyzField += rDir * rzField[0];
   }
 
   return xyzField;
 }
 
 Result<Vector3> SolenoidBField::getField(
     const Vector3& position, MagneticFieldProvider::Cache& /*cache*/) const {
   return Result<Vector3>::success(getField(position));
 }
 
 Vector2 SolenoidBField::getField(const Vector2& position) const {
   return multiCoilField(position, m_scale);
 }
 
 Vector2 SolenoidBField::multiCoilField(const Vector2& pos, double scale) const {
   // iterate over all coils
   Vector2 resultField(0, 0);
   for (std::size_t coil = 0; coil < m_cfg.nCoils; coil++) {
     Vector2 shiftedPos =
         Vector2(pos[0], pos[1] + m_cfg.length * 0.5 - m_dz * (coil + 0.5));
     resultField += singleCoilField(shiftedPos, scale);
   }
 
   return resultField;
 }
 
 Vector2 SolenoidBField::singleCoilField(const Vector2& pos,
                                         double scale) const {
   return {B_r(pos, scale), B_z(pos, scale)};
 }
 
 double SolenoidBField::B_r(const Vector2& pos, double scale) const {
   //              _
   //     2       /  pi / 2          2    2          - 1 / 2
   // E (k )  =   |         ( 1  -  k  sin {theta} )         dtheta
   //  1         _/  0
   using boost::math::ellint_1;
   //              _          ____________________
   //     2       /  pi / 2| /       2    2
   // E (k )  =   |        |/ 1  -  k  sin {theta} dtheta
   //  2         _/  0
   using boost::math::ellint_2;
 
   double r = std::abs(pos[0]);
   double z = pos[1];
 
   if (r == 0) {
     return 0.;
   }
 
   //                            _                             _
   //              mu  I        |  /     2 \                    |
   //                0     kz   |  |2 - k  |    2          2    |
   // B (r, z)  =  ----- ------ |  |-------|E (k )  -  E (k )   |
   //  r            4pi     ___ |  |      2| 2          1       |
   //                    | /  3 |_ \2 - 2k /                   _|
   //                    |/ Rr
   double k_2 = k2(r, z);
   double k = std::sqrt(k_2);
   double constant =
       scale * k * z /
       (4 * std::numbers::pi * std::sqrt(m_cfg.radius * r * r * r));
 
   double B = (2. - k_2) / (2. - 2. * k_2) * ellint_2(k_2) - ellint_1(k_2);
 
   // pos[0] is still signed!
   return r / pos[0] * constant * B;
 }
 
 double SolenoidBField::B_z(const Vector2& pos, double scale) const {
   //              _
   //     2       /  pi / 2          2    2          - 1 / 2
   // E (k )  =   |         ( 1  -  k  sin {theta} )         dtheta
   //  1         _/  0
   using boost::math::ellint_1;
   //              _          ____________________
   //     2       /  pi / 2| /       2    2
   // E (k )  =   |        |/ 1  -  k  sin {theta} dtheta
   //  2         _/  0
   using boost::math::ellint_2;
 
   double r = std::abs(pos[0]);
   double z = pos[1];
 
   //                         _                                       _
   //             mu  I      |  /         2      \                     |
   //               0     k  |  | (R + r)k  - 2r |     2          2    |
   // B (r,z)  =  ----- ---- |  | -------------- | E (k )  +  E (k )   |
   //  z           4pi    __ |  |           2    |  2          1       |
   //                   |/Rr |_ \   2r(1 - k )   /                    _|
 
   if (r == 0) {
     double res = scale / 2. * m_R2 / (std::sqrt(m_R2 + z * z) * (m_R2 + z * z));
     return res;
   }
 
   double k_2 = k2(r, z);
   double k = std::sqrt(k_2);
   double constant =
       scale * k / (4 * std::numbers::pi * std::sqrt(m_cfg.radius * r));
   double B = ((m_cfg.radius + r) * k_2 - 2. * r) / (2. * r * (1. - k_2)) *
                  ellint_2(k_2) +
              ellint_1(k_2);
 
   return constant * B;
 }
 
 double SolenoidBField::k2(double r, double z) const {
   //  2           4Rr
   // k   =  ---------------
   //               2      2
   //        (R + r)   +  z
   return 4 * m_cfg.radius * r /
          ((m_cfg.radius + r) * (m_cfg.radius + r) + z * z);
 }
 
 }  // namespace Acts

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