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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/HelicalTrackLinearizer.hpp"
 
 #include "Acts/Propagator/PropagatorOptions.hpp"
 #include "Acts/Utilities/Intersection.hpp"
 #include "Acts/Utilities/MathHelpers.hpp"
 #include "Acts/Vertexing/LinearizerTrackParameters.hpp"
 
 Acts::Result<Acts::LinearizedTrack>
 Acts::HelicalTrackLinearizer::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
   const auto res =
       m_cfg.propagator->propagateToSurface(params, perigeeSurface, pOptions);
   if (!res.ok()) {
     return res.error();
   }
   const auto& endParams = *res;
 
   // Extracting the track parameters at said PCA - this corresponds to the
   // Perigee representation of the track wrt the reference point
   BoundVector paramsAtPCA = endParams.parameters();
 
   // Extracting the 4D position of the PCA in global coordinates
   Vector4 pca = Vector4::Zero();
   {
     auto pos = endParams.position(gctx);
     pca[ePos0] = pos[ePos0];
     pca[ePos1] = pos[ePos1];
     pca[ePos2] = pos[ePos2];
     pca[eTime] = endParams.time();
   }
   BoundSquareMatrix parCovarianceAtPCA = endParams.covariance().value();
 
   // Extracting Perigee parameters and compute functions of them for later
   // usage
   double d0 = paramsAtPCA(BoundIndices::eBoundLoc0);
 
   double phi = paramsAtPCA(BoundIndices::eBoundPhi);
   double sinPhi = std::sin(phi);
   double cosPhi = std::cos(phi);
 
   double theta = paramsAtPCA(BoundIndices::eBoundTheta);
   double sinTheta = std::sin(theta);
   double tanTheta = std::tan(theta);
 
   // q over p
   double qOvP = paramsAtPCA(BoundIndices::eBoundQOverP);
   // Rest mass
   double m0 = params.particleHypothesis().mass();
   // Momentum
   double p = params.particleHypothesis().extractMomentum(qOvP);
 
   // Speed in units of c
   double beta = p / fastHypot(p, m0);
   // Transverse speed (i.e., speed in the x-y plane)
   double betaT = beta * sinTheta;
 
   // Momentum direction at the PCA
   Vector3 momentumAtPCA(phi, theta, qOvP);
 
   // Particle charge
   double absoluteCharge = params.particleHypothesis().absoluteCharge();
 
   // get the z-component of the B-field at the PCA
   auto field = m_cfg.bField->getField(VectorHelpers::position(pca), fieldCache);
   if (!field.ok()) {
     return field.error();
   }
   double Bz = (*field)[eZ];
 
   // Complete Jacobian (consists of positionJacobian and momentumJacobian)
   ActsMatrix<eBoundSize, eLinSize> completeJacobian =
       ActsMatrix<eBoundSize, eLinSize>::Zero(eBoundSize, eLinSize);
 
   // The particle moves on a straight trajectory if its charge is 0 or if there
   // is no B field. Conversely, if it has a charge and the B field is constant,
   // it moves on a helical trajectory.
   if (absoluteCharge == 0. || Bz == 0.) {
     // Derivatives can be found in Eqs. 5.39 and 5.40 of Ref. (1).
     // Since we propagated to the PCA (point P in Ref. (1)), we evaluate the
     // Jacobians there. One can show that, in this case, RTilde = 0 and QTilde =
     // -d0.
 
     // Derivatives of d0
     completeJacobian(eBoundLoc0, eLinPos0) = -sinPhi;
     completeJacobian(eBoundLoc0, eLinPos1) = cosPhi;
 
     // Derivatives of z0
     completeJacobian(eBoundLoc1, eLinPos0) = -cosPhi / tanTheta;
     completeJacobian(eBoundLoc1, eLinPos1) = -sinPhi / tanTheta;
     completeJacobian(eBoundLoc1, eLinPos2) = 1.;
     completeJacobian(eBoundLoc1, eLinPhi) = -d0 / tanTheta;
 
     // Derivatives of phi
     completeJacobian(eBoundPhi, eLinPhi) = 1.;
 
     // Derivatives of theta
     completeJacobian(eBoundTheta, eLinTheta) = 1.;
 
     // Derivatives of q/p
     completeJacobian(eBoundQOverP, eLinQOverP) = 1.;
 
     // Derivatives of time
     completeJacobian(eBoundTime, eLinPos0) = -cosPhi / betaT;
     completeJacobian(eBoundTime, eLinPos1) = -sinPhi / betaT;
     completeJacobian(eBoundTime, eLinTime) = 1.;
     completeJacobian(eBoundTime, eLinPhi) = -d0 / betaT;
   } else {
     // Helix radius
     double rho = sinTheta * (1. / qOvP) / Bz;
     // Sign of helix radius
     double h = (rho < 0.) ? -1 : 1;
 
     // Quantities from Eq. 5.34 in Ref. (1) (see .hpp)
     double X = pca(0) - perigeeSurface.center(gctx).x() + rho * sinPhi;
     double Y = pca(1) - perigeeSurface.center(gctx).y() - rho * cosPhi;
     double S2 = (X * X + Y * Y);
     // S is the 2D distance from the helix center to the reference point
     // in the x-y plane
     double S = std::sqrt(S2);
 
     double XoverS2 = X / S2;
     double YoverS2 = Y / S2;
     double rhoCotTheta = rho / tanTheta;
     double rhoOverBetaT = rho / betaT;
     // Absolute value of rho over S
     double absRhoOverS = h * rho / S;
 
     // Derivatives can be found in Eq. 5.36 in Ref. (1)
     // Since we propagated to the PCA (point P in Ref. (1)), the points
     // P and V coincide, and thus deltaPhi = 0.
     // One can show that if deltaPhi = 0 --> R = 0 and Q = h * S.
     // As a consequence, many terms of the B matrix vanish.
 
     // Derivatives of d0
     completeJacobian(eBoundLoc0, eLinPos0) = -h * X / S;
     completeJacobian(eBoundLoc0, eLinPos1) = -h * Y / S;
 
     // Derivatives of z0
     completeJacobian(eBoundLoc1, eLinPos0) = rhoCotTheta * YoverS2;
     completeJacobian(eBoundLoc1, eLinPos1) = -rhoCotTheta * XoverS2;
     completeJacobian(eBoundLoc1, eLinPos2) = 1.;
     completeJacobian(eBoundLoc1, eLinPhi) = rhoCotTheta * (1. - absRhoOverS);
 
     // Derivatives of phi
     completeJacobian(eBoundPhi, eLinPos0) = -YoverS2;
     completeJacobian(eBoundPhi, eLinPos1) = XoverS2;
     completeJacobian(eBoundPhi, eLinPhi) = absRhoOverS;
 
     // Derivatives of theta
     completeJacobian(eBoundTheta, eLinTheta) = 1.;
 
     // Derivatives of q/p
     completeJacobian(eBoundQOverP, eLinQOverP) = 1.;
 
     // Derivatives of time
     completeJacobian(eBoundTime, eLinPos0) = rhoOverBetaT * YoverS2;
     completeJacobian(eBoundTime, eLinPos1) = -rhoOverBetaT * XoverS2;
     completeJacobian(eBoundTime, eLinTime) = 1.;
     completeJacobian(eBoundTime, eLinPhi) = rhoOverBetaT * (1. - absRhoOverS);
   }
 
   // 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);
 
   // const term in Taylor expansion from Eq. 5.38 in Ref. (1)
   BoundVector constTerm =
       paramsAtPCA - positionJacobian * pca - momentumJacobian * momentumAtPCA;
 
   // The parameter weight
   BoundSquareMatrix weightAtPCA = parCovarianceAtPCA.inverse();
 
   Vector4 linPoint;
   linPoint.head<3>() = perigeeSurface.center(gctx);
   linPoint[3] = linPointTime;
 
   return LinearizedTrack(paramsAtPCA, parCovarianceAtPCA, weightAtPCA, linPoint,
                          positionJacobian, momentumJacobian, pca, momentumAtPCA,
                          constTerm);
 }

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