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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/Vertexing/NumericalTrackLinearizer.hpp"
 
 #include "Acts/EventData/TrackParameters.hpp"
 #include "Acts/Propagator/PropagatorOptions.hpp"
 #include "Acts/Utilities/Intersection.hpp"
 #include "Acts/Utilities/UnitVectors.hpp"
 #include "Acts/Vertexing/LinearizerTrackParameters.hpp"
 
 #include <numbers>
 
 Acts::Result<Acts::LinearizedTrack>
 Acts::NumericalTrackLinearizer::linearizeTrack(
     const BoundTrackParameters& params, double linPointTime,
     const Surface& perigeeSurface, const Acts::GeometryContext& gctx,
     const Acts::MagneticFieldContext& mctx,
     MagneticFieldProvider::Cache& /*fieldCache*/) const {
   // Create propagator options
   PropagatorPlainOptions pOptions(gctx, mctx);
 
   // Length scale at which we consider to be sufficiently close to the Perigee
   // surface to skip the propagation.
   pOptions.surfaceTolerance = m_cfg.targetTolerance;
 
   // Get intersection of the track with the Perigee if the particle would
   // move on a straight line.
   // This allows us to determine whether we need to propagate the track
   // forward or backward to arrive at the PCA.
   Intersection3D intersection =
       perigeeSurface
           .intersect(gctx, params.position(gctx), params.direction(),
                      BoundaryTolerance::Infinite())
           .closest();
 
   // Setting the propagation direction using the intersection length from
   // above.
   // We handle zero path length as forward propagation, but we could actually
   // skip the whole propagation in this case.
   pOptions.direction =
       Direction::fromScalarZeroAsPositive(intersection.pathLength());
 
   // Propagate to the PCA of the reference point
   auto result =
       m_cfg.propagator->propagateToSurface(params, perigeeSurface, pOptions);
   if (!result.ok()) {
     return result.error();
   }
 
   // Extracting the Perigee representation of the track wrt the reference point
   auto endParams = *result;
   BoundVector perigeeParams = endParams.parameters();
 
   // Covariance and weight matrix at the PCA to the reference point
   BoundSquareMatrix parCovarianceAtPCA = endParams.covariance().value();
   BoundSquareMatrix weightAtPCA = parCovarianceAtPCA.inverse();
 
   // Vector containing the track parameters at the PCA
   // Note that we parametrize the track using the following parameters:
   // (x, y, z, t, phi, theta, q/p),
   // where
   // -) (x, y, z, t) is the global 4D position of the PCA
   // -) phi and theta are the global angles of the momentum at the PCA
   // -) q/p is the charge divided by the total momentum at the PCA
   Acts::ActsVector<eLinSize> paramVec;
 
   // 4D PCA and the momentum of the track at the PCA
   // These quantities will be used in the computation of the constant term in
   // the Taylor expansion
   Vector4 pca;
   Vector3 momentumAtPCA;
 
   // Fill "paramVec", "pca", and "momentumAtPCA"
   {
     Vector3 globalCoords = endParams.position(gctx);
     double globalTime = endParams.time();
     double phi = perigeeParams(BoundIndices::eBoundPhi);
     double theta = perigeeParams(BoundIndices::eBoundTheta);
     double qOvP = perigeeParams(BoundIndices::eBoundQOverP);
 
     paramVec << globalCoords, globalTime, phi, theta, qOvP;
     pca << globalCoords, globalTime;
     momentumAtPCA << phi, theta, qOvP;
   }
 
   // Complete Jacobian (consists of positionJacobian and momentumJacobian)
   ActsMatrix<eBoundSize, eLinSize> completeJacobian =
       ActsMatrix<eBoundSize, eLinSize>::Zero(eBoundSize, eLinSize);
 
   // Perigee parameters wrt the reference point after wiggling
   BoundVector newPerigeeParams;
 
   // Check if wiggled angle theta are within definition range [0, pi]
   if (paramVec(eLinTheta) + m_cfg.delta > std::numbers::pi) {
     ACTS_ERROR(
         "Wiggled theta outside range, choose a smaller wiggle (i.e., delta)! "
         "You might need to decrease targetTolerance as well.");
   }
 
   // Wiggling each of the parameters at the PCA and computing the Perigee
   // parametrization of the resulting new track. This allows us to approximate
   // the numerical derivatives.
   for (unsigned int i = 0; i < eLinSize; i++) {
     Acts::ActsVector<eLinSize> paramVecCopy = paramVec;
     // Wiggle
     paramVecCopy(i) += m_cfg.delta;
 
     // Create curvilinear track object from our parameters. This is needed for
     // the propagation. Note that we work without covariance since we don't need
     // it to compute the derivative.
     Vector3 wiggledDir = makeDirectionFromPhiTheta(paramVecCopy(eLinPhi),
                                                    paramVecCopy(eLinTheta));
     // Since we work in 4D we have eLinPosSize = 4
     BoundTrackParameters wiggledCurvilinearParams =
         BoundTrackParameters::createCurvilinear(
             paramVecCopy.template head<eLinPosSize>(), wiggledDir,
             paramVecCopy(eLinQOverP), std::nullopt, ParticleHypothesis::pion());
 
     // Obtain propagation direction
     intersection = perigeeSurface
                        .intersect(gctx, paramVecCopy.template head<3>(),
                                   wiggledDir, BoundaryTolerance::Infinite())
                        .closest();
     pOptions.direction =
         Direction::fromScalarZeroAsPositive(intersection.pathLength());
 
     // Propagate to the new PCA and extract Perigee parameters
     auto newResult = m_cfg.propagator->propagateToSurface(
         wiggledCurvilinearParams, perigeeSurface, pOptions);
     if (!newResult.ok()) {
       return newResult.error();
     }
     newPerigeeParams = newResult->parameters();
 
     // Computing the numerical derivatives and filling the Jacobian
     completeJacobian.array().col(i) =
         (newPerigeeParams - perigeeParams) / m_cfg.delta;
     // We need to account for the periodicity of phi. We overwrite the
     // previously computed value for better readability.
     completeJacobian(eLinPhi, i) =
         Acts::detail::difference_periodic(newPerigeeParams(eLinPhi),
                                           perigeeParams(eLinPhi),
                                           2 * std::numbers::pi) /
         m_cfg.delta;
   }
 
   // Extracting positionJacobian and momentumJacobian from the complete Jacobian
   ActsMatrix<eBoundSize, eLinPosSize> positionJacobian =
       completeJacobian.block<eBoundSize, eLinPosSize>(0, 0);
   ActsMatrix<eBoundSize, eLinMomSize> momentumJacobian =
       completeJacobian.block<eBoundSize, eLinMomSize>(0, eLinPosSize);
 
   // Constant term of Taylor expansion (Eq. 5.38 in Ref. (1))
   BoundVector constTerm =
       perigeeParams - positionJacobian * pca - momentumJacobian * momentumAtPCA;
 
   Vector4 linPoint;
   linPoint.head<3>() = perigeeSurface.center(gctx);
   linPoint[3] = linPointTime;
 
   return LinearizedTrack(perigeeParams, parCovarianceAtPCA, weightAtPCA,
                          linPoint, positionJacobian, momentumJacobian, pca,
                          momentumAtPCA, constTerm);
 }

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