Track.h

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/**
 * @file    lardataobj/RecoBase/Track.h
 * @brief   Provides `recob::Track` data product.
 * @author  Brian Rebel (brebel@fnal.gov)
 * @ingroup DataProductRecoBase
 * @see     lardataobj/RecoBase/Track.cxx
 */

#ifndef LARDATAOBJ_RECOBASE_TRACK_H
#define LARDATAOBJ_RECOBASE_TRACK_H

#include "lardataobj/RecoBase/TrackTrajectory.h"
#include "lardataobj/RecoBase/TrackingTypes.h"
#include "larcoreobj/SimpleTypesAndConstants/PhysicalConstants.h"

#include <iosfwd>
#include <stddef.h>

namespace recob {

  /**
   * @brief Track from a non-cascading particle.
   * @ingroup DataProductRecoBase
   *
   * A `recob::Track` consists of a `recob::TrackTrajectory`, plus additional members relevant for a "fitted" track:
   *
   * * fit &chi;&sup2;
   * * number of degrees of freedom
   * * particle ID hypothesis used in the fit (if any)
   * * covariance matrices at start (vertex) and end positions.
   *
   * Please refer to the `recob::TrackTrajectory` documentation for more information about it;
   * for a discussion on the object type for coordinates see recob::tracking::Coord_t.
   *
   * In terms of interface, `recob::Track` extends `recob::TrackTrajectory`, so that methods of the stored `recob::TrackTrajectory` can be called directly from the `recob::Track interface`,
   * e.g.:
   * ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~{.cpp}
   * size_t       NumberTrajectoryPoints()         const { return fTraj.NumberTrajectoryPoints(); }
   * ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
   *
   * Two different parameter conventions are used in a `recob::Track`, and functions to convert from one to the other are provided:
   *
   * 1. Trajectory points and momenta (or directions) are in form of 3-vectors, corresponding to a global Cartesian 6D representation
   * 2. Covariance matrices are stored in a Local 5D representation (so that the covariance matrix is invertible),
   *    where the parameters are defined on the plane orthogonal to the track direction at a given track point.
   *    By construction the local parameters of the track itself are (0,0,0,0,1/p).
   * See `lardataobj/RecoBase/TrackingPlane.h` for more information.
   */
  class Track {

  public:

    using Point_t           = tracking::Point_t;
    using Vector_t          = tracking::Vector_t;
    using Positions_t       = tracking::Positions_t;
    using Momenta_t         = tracking::Momenta_t;
    using Rotation_t        = tracking::Rotation_t;
    using TrajectoryPoint_t = tracking::TrajectoryPoint_t;

    using SMatrixSym55 = tracking::SMatrixSym55;
    using SMatrixSym66 = tracking::SMatrixSym66;
    using SMatrix65    = tracking::SMatrix65;
    using SMatrix56    = tracking::SMatrix56;
    using SVector6     = tracking::SVector6;
    using SVector5     = tracking::SVector5;

    using PointFlags_t = TrackTrajectory::PointFlags_t;
    using Flags_t      = TrackTrajectory::Flags_t;

  protected:

    TrackTrajectory fTraj;                         ///< Stored trajectory data member
    int fPId                = 0;                   ///< Particle ID hypothesis used in the fit (if any)
    float fChi2             = -1.;                 ///< Fit chi2
    int fNdof               = 0.;                  ///< Number of degrees of freedom of the fit
    SMatrixSym55 fCovVertex;                       ///< Covariance matrix (local 5D representation) at start point (vertex)
    SMatrixSym55 fCovEnd;                          ///< Covariance matrix (local 5D representation) at end point
    int              fID    = -1;                  ///< track's ID

  public:

    //Default constructor
    Track() = default;

    Track(TrackTrajectory const& Traj,
          int PId, float Chi2, int Ndof, SMatrixSym55 const& CovVertex, SMatrixSym55 const& CovEnd, int tkID)
      : fTraj(Traj), fPId(PId), fChi2(Chi2), fNdof(Ndof), fCovVertex(CovVertex), fCovEnd(CovEnd),fID(tkID) { };

    Track(TrackTrajectory&& Traj,
          int PId, float Chi2, int Ndof, SMatrixSym55&& CovVertex, SMatrixSym55&& CovEnd, int tkID)
      : fTraj(std::move(Traj)), fPId(PId), fChi2(Chi2), fNdof(Ndof), fCovVertex(std::move(CovVertex)), fCovEnd(std::move(CovEnd)),fID(tkID) { };

    Track(Positions_t&& positions, Momenta_t&& momenta, Flags_t&& flags, bool hasMomenta,
          int PId, float Chi2, int Ndof, SMatrixSym55&& CovVertex, SMatrixSym55&& CovEnd, int tkID)
      : fTraj(std::move(positions),std::move(momenta),std::move(flags),hasMomenta), fPId(PId), fChi2(Chi2), fNdof(Ndof), fCovVertex(std::move(CovVertex)), fCovEnd(std::move(CovEnd)),fID(tkID) { };

    /// Access to the stored recob::TrackTrajectory
    inline const recob::TrackTrajectory& Trajectory()  const { return fTraj; }

    //@{
    /// Various functions related to the presence and the number of (valid) points
    inline size_t       NumberTrajectoryPoints()         const { return fTraj.NumberTrajectoryPoints(); }
    inline size_t       NPoints()                        const { return fTraj.NPoints(); }
    inline size_t       FirstPoint()                     const { return fTraj.FirstPoint(); }
    inline size_t       LastPoint()                      const { return fTraj.LastPoint(); }
    inline size_t       FirstValidPoint()                const { return fTraj.FirstValidPoint(); }
    inline size_t       NextValidPoint(size_t index)     const { return fTraj.NextValidPoint(index); }
    inline size_t       PreviousValidPoint(size_t index) const { return fTraj.PreviousValidPoint(index); }
    inline size_t       LastValidPoint()                 const { return fTraj.LastValidPoint(); }
    inline bool         HasPoint(size_t i)               const { return fTraj.HasPoint(i); }
    inline bool         HasValidPoint(size_t i)          const { return fTraj.HasValidPoint(i); }
    inline unsigned int CountValidPoints()               const { return fTraj.CountValidPoints(); }
    //@}

    //@{
    /// Access to i-th TrajectoryPoint or its Flags
    inline TrajectoryPoint_t   TrajectoryPoint(size_t i) const { return fTraj.TrajectoryPoint(i); }
    inline PointFlags_t const& FlagsAtPoint(size_t i)    const { return fTraj.FlagsAtPoint(i); }
    //@}

    //@{
    /// Access to track position at different points
    inline Point_t const& Start()  const { return fTraj.Start(); }
    inline Point_t const& Vertex() const { return fTraj.Vertex(); }
    inline Point_t const& End()    const { return fTraj.End(); }
    inline Point_t const& LocationAtPoint(size_t i) const { return fTraj.LocationAtPoint(i); }
    //@}

    //@{
    /// Access to track direction at different points
    inline Vector_t StartDirection()  const { return fTraj.StartDirection(); }
    inline Vector_t VertexDirection() const { return fTraj.VertexDirection(); }
    inline Vector_t EndDirection()    const { return fTraj.EndDirection(); }
    inline Vector_t DirectionAtPoint(size_t i) const { return fTraj.DirectionAtPoint(i); }
    //@}

    //@{
    /// Access to track momentum at different points.
    /// The user must check that HasMomentum() returns true to ensure the validity of the result of these functions.
    inline bool            HasMomentum()                   const { return fTraj.HasMomentum(); }
    inline double          MomentumAtPoint(unsigned int p) const { return fTraj.MomentumAtPoint(p); }
    inline double          VertexMomentum()                const { return fTraj.VertexMomentum(); }
    inline double          StartMomentum()                 const { return fTraj.StartMomentum(); }
    inline double          EndMomentum()                   const { return fTraj.EndMomentum();  }
    inline Vector_t const& VertexMomentumVector()          const { return fTraj.VertexMomentumVector() ; }
    inline Vector_t const& StartMomentumVector()           const { return fTraj.StartMomentumVector(); }
    inline Vector_t const& EndMomentumVector()             const { return fTraj.EndMomentumVector(); }
    inline Vector_t const& MomentumVectorAtPoint(size_t i) const { return fTraj.MomentumVectorAtPoint(i); }
    //@}

    //@{
    /// Access to covariance matrices
    const SMatrixSym55& StartCovariance() const { return fCovVertex; }
    const SMatrixSym55& VertexCovariance() const { return fCovVertex; }
    const SMatrixSym55& EndCovariance()    const { return fCovEnd; }
    //@}

    //@{
    /// Access to position, momentum or covariance at the start and end of the track
    inline std::pair<Point_t, Point_t>           Extent()      const { return fTraj.Extent(); }
    inline std::pair<Vector_t, Vector_t>         Direction()   const { return fTraj.Direction(); }
    inline std::pair<SMatrixSym55, SMatrixSym55> Covariances() const { return std::pair<SMatrixSym55, SMatrixSym55>(fCovVertex,fCovEnd); }
    //@}

    //@{
    /// Access to various track properties
    inline double  Length(size_t p=0) const { return fTraj.Length(p); }
    inline float   Chi2()             const { return fChi2; }
    inline float   Chi2PerNdof()      const { return fNdof>0 ? fChi2/float(fNdof) : util::kBogusF; }
    inline int     Ndof()             const { return fNdof; }
    inline int     ParticleId()       const { return fPId; }
    //@}

    //@{
    /// Access to spherical or geographical angles at vertex or at any point
    inline double  Theta()                const { return fTraj.Theta(); }
    inline double  Theta(size_t p)        const { return fTraj.Theta(p); }
    inline double  Phi()                  const { return fTraj.Phi(); }
    inline double  Phi(size_t p)          const { return fTraj.Phi(p); }
    inline double  ZenithAngle()          const { return fTraj.ZenithAngle(); }
    inline double  ZenithAngle(size_t p)  const { return fTraj.ZenithAngle(p); }
    inline double  AzimuthAngle()         const { return fTraj.AzimuthAngle(); }
    inline double  AzimuthAngle(size_t p) const { return fTraj.AzimuthAngle(p); }
    //@}

    //@{
    // Calculate rotation matrices between global (x,y,z) and local (u,v,w)
    // coordinate systems based on track direction (fDir).
    // The local w-axis points along the track direction.
    inline Rotation_t GlobalToLocalRotationAtPoint(size_t p) const { return fTraj.GlobalToLocalRotationAtPoint(p); }
    inline Rotation_t LocalToGlobalRotationAtPoint(size_t p) const { return fTraj.LocalToGlobalRotationAtPoint(p); }
    //@}

    //@{
    /// Track ID number, needed to relate a track to its possible track parent (e.g. in case of a refit).
    /// Note that art Assns to the same object are not currently supported.
    /// The < operator is based on the track ID.
    inline int  ID()       const { return fID; }
    friend bool operator < (const Track & a, const Track & b);
    //@}

    //@{
    /// Accessors to track parameters and covariance matrices in Local5D and Global6D coordinates
    SVector5            VertexParametersLocal5D()  const;
    SVector5            EndParametersLocal5D()     const;
    const SMatrixSym55& VertexCovarianceLocal5D()  const { return fCovVertex; }
    const SMatrixSym55& EndCovarianceLocal5D()     const { return fCovEnd; }
    SVector6            VertexParametersGlobal6D() const;
    SVector6            EndParametersGlobal6D()    const;
    SMatrixSym66        VertexCovarianceGlobal6D() const;
    SMatrixSym66        EndCovarianceGlobal6D()    const;
    //@}

    /// @{
    /// @name Templated version of homonymous functions to access to position, direction, momentum information, and covariances.

    /// Start position. Use e.g. as: @code{.cpp} TVector3 start = track.Start<TVector3>(); @endcode.
    template<typename T> inline T Start()                         const { return fTraj.Start<T>(); }

    /// Start position. Use e.g. as: @code{.cpp} TVector3 vertex = track.Vertex<TVector3>(); @endcode.
    template<typename T> inline T Vertex()                        const { return fTraj.Vertex<T>(); }

    /// End position. Use e.g. as: @code{.cpp} TVector3 end = track.End<TVector3>(); @endcode.
    template<typename T> inline T End()                           const { return fTraj.End<T>(); }

    /// Position at point p. Use e.g. as: @code{.cpp} TVector3 pos = track.LocationAtPoint<TVector3>(p); @endcode.
    template<typename T> inline T LocationAtPoint(unsigned int p) const { return fTraj.LocationAtPoint<T>(p); }

    /// Start direction. Use e.g. as: @code{.cpp} TVector3 startdir = track.StartDirection<TVector3>(); @endcode.
    template<typename T> inline T StartDirection()                 const { return fTraj.StartDirection<T>(); }

    /// Start direction. Use e.g. as: @code{.cpp} TVector3 vertexdir = track.VertexDirection<TVector3>(); @endcode.
    template<typename T> inline T VertexDirection()                const { return fTraj.VertexDirection<T>(); }

    /// End direction. Use e.g. as: @code{.cpp} TVector3 enddir = track.EndDirection<TVector3>(); @endcode.
    template<typename T> inline T EndDirection()                   const { return fTraj.EndDirection<T>(); }

    /// Direction at point p. Use e.g. as: @code{.cpp} TVector3 dir = track.DirectionAtPoint<TVector3>(p); @endcode.
    template<typename T> inline T DirectionAtPoint(unsigned int p) const { return fTraj.DirectionAtPoint<T>(p); }

    /// Momentum vector at start point. Use e.g. as: @code{.cpp} TVector3 startmom = track.StartMomentumVector<TVector3>(); @endcode.
    template<typename T> inline T StartMomentumVector()                 const { return fTraj.StartMomentumVector<T>(); }

    /// Momentum vector at start point. Use e.g. as: @code{.cpp} TVector3 vertexmom = track.VertexMomentumVector<TVector3>(); @endcode.
    template<typename T> inline T VertexMomentumVector()                const { return fTraj.VertexMomentumVector<T>(); }

    /// Momentum vector at end point. Use e.g. as: @code{.cpp} TVector3 endmom = track.EndMomentumVector<TVector3>(); @endcode.
    template<typename T> inline T EndMomentumVector()                   const { return fTraj.EndMomentumVector<T>(); }

    /// Momentum vector at point p. Use e.g. as: @code{.cpp} TVector3 mom = track.MomentumVectorAtPoint<TVector3>(p); @endcode.
    template<typename T> inline T MomentumVectorAtPoint(unsigned int p) const { return fTraj.MomentumVectorAtPoint<T>(p); }

    /// Covariance matrix at start point. Use e.g. as: @code{.cpp} TMatrixD startcov = track.StartCovariance<TMatrixD>(); @endcode.
    template<typename T> inline T StartCovariance() const;

    /// Covariance matrix at start point. Use e.g. as: @code{.cpp} TMatrixD vertexcov = track.VertexCovariance<TMatrixD>(); @endcode.
    template<typename T> inline T VertexCovariance() const { return StartCovariance<T>(); }

    /// Covariance matrix at end point. Use e.g. as: @code{.cpp} TMatrixD endcov = track.EndCovariance<TMatrixD>(); @endcode.
    template<typename T> inline T EndCovariance() const;

    /// Position at start and end points. Use e.g. as: @code{.cpp} TVector3 start, end; std::tie(start, end) = track.Extent<TVector3>(); @endcode.
    template<typename T> inline std::pair<T, T>  Extent()      const { return fTraj.Extent<T>(); }

    /// Direction at start and end points. Use e.g. as: @code{.cpp} TVector3 startdir, enddir; std::tie(startdir, enddir) = track.Direction<TVector3>(); @endcode.
    template<typename T> inline std::pair<T, T>  Direction()   const { return fTraj.Direction<T>(); }

    /// Returns a rotation matrix that brings trajectory direction along _z_. Use e.g. as: @code{.cpp} TMatrixD rot = track.GlobalToLocalRotationAtPoint<TMatrixD>(p); @endcode.
    template<typename T> inline T GlobalToLocalRotationAtPoint(unsigned int p) const { return fTraj.GlobalToLocalRotationAtPoint<T>(p); }

    /// Returns a rotation matrix bringing relative directions to global. Use e.g. as: @code{.cpp} TMatrixD rot = track.LocalToGlobalRotationAtPoint<TMatrixD>(p); @endcode.
    template<typename T> inline T LocalToGlobalRotationAtPoint(unsigned int p) const { return fTraj.LocalToGlobalRotationAtPoint<T>(p); }
    /// @}


  protected:

    friend std::ostream& operator << (std::ostream& stream, Track const& a);

  };
}

template<typename T> inline T recob::Track::StartCovariance() const {
  T result = T(5,5);
  for (unsigned int i=0; i<5; i++) {
    for (unsigned int j=0; j<5; j++) {
      result(i,j) = fCovVertex.At(i,j);
    }
  }
  return result;
}

template<typename T> inline T recob::Track::EndCovariance() const {
  T result = T(5,5);
  for (unsigned int i=0; i<5; i++) {
    for (unsigned int j=0; j<5; j++) {
      result(i,j) = fCovEnd.At(i,j);
    }
  }
  return result;
}

#endif // LARDATAOBJ_RECOBASE_TRACK_H