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 // This file is part of the Acts project.
 //
 // Copyright (C) 2016-2022 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 http://mozilla.org/MPL/2.0/.
 
 #pragma once
 
 // Workaround for building on clang+libstdc++
 #include "Acts/Utilities/detail/ReferenceWrapperAnyCompat.hpp"
 
 #include "Acts/Definitions/Algebra.hpp"
 #include "Acts/Definitions/Tolerance.hpp"
 #include "Acts/Definitions/Units.hpp"
 #include "Acts/EventData/TrackParameters.hpp"
 #include "Acts/MagneticField/MagneticFieldProvider.hpp"
 #include "Acts/Propagator/ConstrainedStep.hpp"
 #include "Acts/Propagator/DefaultExtension.hpp"
 #include "Acts/Propagator/DenseEnvironmentExtension.hpp"
 #include "Acts/Propagator/EigenStepperError.hpp"
 #include "Acts/Propagator/PropagatorTraits.hpp"
 #include "Acts/Propagator/StepperExtensionList.hpp"
 #include "Acts/Propagator/detail/Auctioneer.hpp"
 #include "Acts/Propagator/detail/SteppingHelper.hpp"
 #include "Acts/Utilities/Intersection.hpp"
 #include "Acts/Utilities/Result.hpp"
 
 #include <cmath>
 #include <functional>
 #include <limits>
 #include <type_traits>
 
 namespace Acts {
 
 /// @brief Runge-Kutta-Nystroem stepper based on Eigen implementation
 /// for the following ODE:
 ///
 /// r = (x,y,z)    ... global position
 /// T = (Ax,Ay,Az) ... momentum direction (normalized)
 ///
 /// dr/ds = T
 /// dT/ds = q/p * (T x B)
 ///
 /// with s being the arc length of the track, q the charge of the particle,
 /// p the momentum magnitude and B the magnetic field
 ///
 template <typename extensionlist_t = StepperExtensionList<DefaultExtension>,
           typename auctioneer_t = detail::VoidAuctioneer>
 class EigenStepper {
  public:
   /// Jacobian, Covariance and State definitions
   using Jacobian = BoundMatrix;
   using Covariance = BoundSquareMatrix;
   using BoundState = std::tuple<BoundTrackParameters, Jacobian, double>;
   using CurvilinearState =
       std::tuple<CurvilinearTrackParameters, Jacobian, double>;
 
   /// @brief State for track parameter propagation
   ///
   /// It contains the stepping information and is provided thread local
   /// by the propagator
   struct State {
     State() = delete;
 
     /// Constructor from the initial bound track parameters
     ///
     /// @param [in] gctx is the context object for the geometry
     /// @param [in] fieldCacheIn is the cache object for the magnetic field
     /// @param [in] par The track parameters at start
     /// @param [in] ssize is the maximum step size
     ///
     /// @note the covariance matrix is copied when needed
     explicit State(const GeometryContext& gctx,
                    MagneticFieldProvider::Cache fieldCacheIn,
                    const BoundTrackParameters& par,
                    double ssize = std::numeric_limits<double>::max())
         : particleHypothesis(par.particleHypothesis()),
           stepSize(ssize),
           fieldCache(std::move(fieldCacheIn)),
           geoContext(gctx) {
       Vector3 position = par.position(gctx);
       Vector3 direction = par.direction();
       pars.template segment<3>(eFreePos0) = position;
       pars.template segment<3>(eFreeDir0) = direction;
       pars[eFreeTime] = par.time();
       pars[eFreeQOverP] = par.parameters()[eBoundQOverP];
 
       // Init the jacobian matrix if needed
       if (par.covariance()) {
         // Get the reference surface for navigation
         const auto& surface = par.referenceSurface();
         // set the covariance transport flag to true and copy
         covTransport = true;
         cov = BoundSquareMatrix(*par.covariance());
         jacToGlobal = surface.boundToFreeJacobian(gctx, position, direction);
       }
     }
 
     /// Internal free vector parameters
     FreeVector pars = FreeVector::Zero();
 
     /// Particle hypothesis
     ParticleHypothesis particleHypothesis = ParticleHypothesis::pion();
 
     /// Covariance matrix (and indicator)
     /// associated with the initial error on track parameters
     bool covTransport = false;
     Covariance cov = Covariance::Zero();
 
     /// The full jacobian of the transport entire transport
     Jacobian jacobian = Jacobian::Identity();
 
     /// Jacobian from local to the global frame
     BoundToFreeMatrix jacToGlobal = BoundToFreeMatrix::Zero();
 
     /// Pure transport jacobian part from runge kutta integration
     FreeMatrix jacTransport = FreeMatrix::Identity();
 
     /// The propagation derivative
     FreeVector derivative = FreeVector::Zero();
 
     /// Accummulated path length state
     double pathAccumulated = 0.;
 
     /// Adaptive step size of the runge-kutta integration
     ConstrainedStep stepSize;
 
     /// Last performed step (for overstep limit calculation)
     double previousStepSize = 0.;
 
     /// This caches the current magnetic field cell and stays
     /// (and interpolates) within it as long as this is valid.
     /// See step() code for details.
     MagneticFieldProvider::Cache fieldCache;
 
     /// The geometry context
     std::reference_wrapper<const GeometryContext> geoContext;
 
     /// List of algorithmic extensions
     extensionlist_t extension;
 
     /// Auctioneer for choosing the extension
     auctioneer_t auctioneer;
 
     /// @brief Storage of magnetic field and the sub steps during a RKN4 step
     struct {
       /// Magnetic field evaulations
       Vector3 B_first, B_middle, B_last;
       /// k_i of the RKN4 algorithm
       Vector3 k1, k2, k3, k4;
       /// k_i elements of the momenta
       std::array<double, 4> kQoP{};
     } stepData;
   };
 
   /// Constructor requires knowledge of the detector's magnetic field
   EigenStepper(std::shared_ptr<const MagneticFieldProvider> bField,
                double overstepLimit = 100 * UnitConstants::um);
 
   State makeState(std::reference_wrapper<const GeometryContext> gctx,
                   std::reference_wrapper<const MagneticFieldContext> mctx,
                   const BoundTrackParameters& par,
                   double ssize = std::numeric_limits<double>::max()) const;
 
   /// @brief Resets the state
   ///
   /// @param [in, out] state State of the stepper
   /// @param [in] boundParams Parameters in bound parametrisation
   /// @param [in] cov Covariance matrix
   /// @param [in] surface The reference surface of the bound parameters
   /// @param [in] stepSize Step size
   void resetState(
       State& state, const BoundVector& boundParams,
       const BoundSquareMatrix& cov, const Surface& surface,
       const double stepSize = std::numeric_limits<double>::max()) const;
 
   /// Get the field for the stepping, it checks first if the access is still
   /// within the Cell, and updates the cell if necessary.
   ///
   /// @param [in,out] state is the propagation state associated with the track
   ///                 the magnetic field cell is used (and potentially updated)
   /// @param [in] pos is the field position
   Result<Vector3> getField(State& state, const Vector3& pos) const {
     // get the field from the cell
     return m_bField->getField(pos, state.fieldCache);
   }
 
   /// Global particle position accessor
   ///
   /// @param state [in] The stepping state (thread-local cache)
   Vector3 position(const State& state) const {
     return state.pars.template segment<3>(eFreePos0);
   }
 
   /// Momentum direction accessor
   ///
   /// @param state [in] The stepping state (thread-local cache)
   Vector3 direction(const State& state) const {
     return state.pars.template segment<3>(eFreeDir0);
   }
 
   /// QoP direction accessor
   ///
   /// @param state [in] The stepping state (thread-local cache)
   double qOverP(const State& state) const { return state.pars[eFreeQOverP]; }
 
   /// Absolute momentum accessor
   ///
   /// @param state [in] The stepping state (thread-local cache)
   double absoluteMomentum(const State& state) const {
     return particleHypothesis(state).extractMomentum(qOverP(state));
   }
 
   /// Momentum accessor
   ///
   /// @param state [in] The stepping state (thread-local cache)
   Vector3 momentum(const State& state) const {
     return absoluteMomentum(state) * direction(state);
   }
 
   /// Charge access
   ///
   /// @param state [in] The stepping state (thread-local cache)
   double charge(const State& state) const {
     return particleHypothesis(state).extractCharge(qOverP(state));
   }
 
   /// Particle hypothesis
   ///
   /// @param state [in] The stepping state (thread-local cache)
   const ParticleHypothesis& particleHypothesis(const State& state) const {
     return state.particleHypothesis;
   }
 
   /// Time access
   ///
   /// @param state [in] The stepping state (thread-local cache)
   double time(const State& state) const { return state.pars[eFreeTime]; }
 
   /// Update surface status
   ///
   /// It checks the status to the reference surface & updates
   /// the step size accordingly
   ///
   /// @param [in,out] state The stepping state (thread-local cache)
   /// @param [in] surface The surface provided
   /// @param [in] index The surface intersection index
   /// @param [in] navDir The navigation direction
   /// @param [in] bcheck The boundary check for this status update
   /// @param [in] surfaceTolerance Surface tolerance used for intersection
   /// @param [in] logger A @c Logger instance
   Intersection3D::Status updateSurfaceStatus(
       State& state, const Surface& surface, std::uint8_t index,
       Direction navDir, const BoundaryCheck& bcheck,
       ActsScalar surfaceTolerance = s_onSurfaceTolerance,
       const Logger& logger = getDummyLogger()) const {
     return detail::updateSingleSurfaceStatus<EigenStepper>(
         *this, state, surface, index, navDir, bcheck, surfaceTolerance, logger);
   }
 
   /// Update step size
   ///
   /// This method intersects the provided surface and update the navigation
   /// step estimation accordingly (hence it changes the state). It also
   /// returns the status of the intersection to trigger onSurface in case
   /// the surface is reached.
   ///
   /// @param state [in,out] The stepping state (thread-local cache)
   /// @param oIntersection [in] The ObjectIntersection to layer, boundary, etc
   /// @param release [in] boolean to trigger step size release
   template <typename object_intersection_t>
   void updateStepSize(State& state, const object_intersection_t& oIntersection,
                       Direction /*direction*/, bool release = true) const {
     detail::updateSingleStepSize<EigenStepper>(state, oIntersection, release);
   }
 
   /// Update step size - explicitly with a double
   ///
   /// @param state [in,out] The stepping state (thread-local cache)
   /// @param stepSize [in] The step size value
   /// @param stype [in] The step size type to be set
   /// @param release [in] Do we release the step size?
   void updateStepSize(State& state, double stepSize,
                       ConstrainedStep::Type stype, bool release = true) const {
     state.previousStepSize = state.stepSize.value();
     state.stepSize.update(stepSize, stype, release);
   }
 
   /// Get the step size
   ///
   /// @param state [in] The stepping state (thread-local cache)
   /// @param stype [in] The step size type to be returned
   double getStepSize(const State& state, ConstrainedStep::Type stype) const {
     return state.stepSize.value(stype);
   }
 
   /// Release the Step size
   ///
   /// @param state [in,out] The stepping state (thread-local cache)
   /// @param [in] stype The step size type to be released
   void releaseStepSize(State& state, ConstrainedStep::Type stype) const {
     state.stepSize.release(stype);
   }
 
   /// Output the Step Size - single component
   ///
   /// @param state [in,out] The stepping state (thread-local cache)
   std::string outputStepSize(const State& state) const {
     return state.stepSize.toString();
   }
 
   /// Overstep limit
   double overstepLimit(const State& /*state*/) const {
     // A dynamic overstep limit could sit here
     return -m_overstepLimit;
   }
 
   /// Create and return the bound state at the current position
   ///
   /// @brief This transports (if necessary) the covariance
   /// to the surface and creates a bound state. It does not check
   /// if the transported state is at the surface, this needs to
   /// be guaranteed by the propagator
   ///
   /// @param [in] state State that will be presented as @c BoundState
   /// @param [in] surface The surface to which we bind the state
   /// @param [in] transportCov Flag steering covariance transport
   /// @param [in] freeToBoundCorrection Correction for non-linearity effect during transform from free to bound
   ///
   /// @return A bound state:
   ///   - the parameters at the surface
   ///   - the stepwise jacobian towards it (from last bound)
   ///   - and the path length (from start - for ordering)
   Result<BoundState> boundState(
       State& state, const Surface& surface, bool transportCov = true,
       const FreeToBoundCorrection& freeToBoundCorrection =
           FreeToBoundCorrection(false)) const;
 
   /// @brief If necessary fill additional members needed for curvilinearState
   ///
   /// Compute path length derivatives in case they have not been computed
   /// yet, which is the case if no step has been executed yet.
   ///
   /// @param [in, out] prop_state State that will be presented as @c BoundState
   /// @param [in] navigator the navigator of the propagation
   /// @return true if nothing is missing after this call, false otherwise.
   template <typename propagator_state_t, typename navigator_t>
   bool prepareCurvilinearState(propagator_state_t& prop_state,
                                const navigator_t& navigator) const;
 
   /// Create and return a curvilinear state at the current position
   ///
   /// @brief This transports (if necessary) the covariance
   /// to the current position and creates a curvilinear state.
   ///
   /// @param [in] state State that will be presented as @c CurvilinearState
   /// @param [in] transportCov Flag steering covariance transport
   ///
   /// @return A curvilinear state:
   ///   - the curvilinear parameters at given position
   ///   - the stepweise jacobian towards it (from last bound)
   ///   - and the path length (from start - for ordering)
   CurvilinearState curvilinearState(State& state,
                                     bool transportCov = true) const;
 
   /// Method to update a stepper state to the some parameters
   ///
   /// @param [in,out] state State object that will be updated
   /// @param [in] freeParams Free parameters that will be written into @p state
   /// @param [in] boundParams Corresponding bound parameters used to update jacToGlobal in @p state
   /// @param [in] covariance The covariance that will be written into @p state
   /// @param [in] surface The surface used to update the jacToGlobal
   void update(State& state, const FreeVector& freeParams,
               const BoundVector& boundParams, const Covariance& covariance,
               const Surface& surface) const;
 
   /// Method to update the stepper state
   ///
   /// @param [in,out] state State object that will be updated
   /// @param [in] uposition the updated position
   /// @param [in] udirection the updated direction
   /// @param [in] qOverP the updated qOverP value
   /// @param [in] time the updated time value
   void update(State& state, const Vector3& uposition, const Vector3& udirection,
               double qOverP, double time) const;
 
   /// Method for on-demand transport of the covariance
   /// to a new curvilinear frame at current  position,
   /// or direction of the state
   ///
   /// @param [in,out] state State of the stepper
   void transportCovarianceToCurvilinear(State& state) const;
 
   /// Method for on-demand transport of the covariance
   /// to a new curvilinear frame at current position,
   /// or direction of the state
   ///
   /// @tparam surface_t the Surface type
   ///
   /// @param [in,out] state State of the stepper
   /// @param [in] surface is the surface to which the covariance is forwarded to
   /// @param [in] freeToBoundCorrection Correction for non-linearity effect during transform from free to bound
   /// @note no check is done if the position is actually on the surface
   void transportCovarianceToBound(
       State& state, const Surface& surface,
       const FreeToBoundCorrection& freeToBoundCorrection =
           FreeToBoundCorrection(false)) const;
 
   /// Perform a Runge-Kutta track parameter propagation step
   ///
   /// @param [in,out] state the propagation state
   /// @param [in] navigator the navigator of the propagation
   /// @note The state contains the desired step size.  It can be negative during
   ///       backwards track propagation, and since we're using an adaptive
   ///       algorithm, it can be modified by the stepper class during
   ///       propagation.
   template <typename propagator_state_t, typename navigator_t>
   Result<double> step(propagator_state_t& state,
                       const navigator_t& navigator) const;
 
   /// Method that reset the Jacobian to the Identity for when no bound state are
   /// available
   ///
   /// @param [in,out] state State of the stepper
   void setIdentityJacobian(State& state) const;
 
  protected:
   /// Magnetic field inside of the detector
   std::shared_ptr<const MagneticFieldProvider> m_bField;
 
   /// Overstep limit
   double m_overstepLimit;
 };
 
 template <typename navigator_t>
 struct SupportsBoundParameters<EigenStepper<>, navigator_t>
     : public std::true_type {};
 
 }  // namespace Acts
 
 #include "Acts/Propagator/EigenStepper.ipp"

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