class AliTRDseedV1: public AliTRDtrackletBase

 Constructor

 Copy Constructor performing a deep copy

 Assignment Operator using the copy function

 Destructor. The RecoParam object belongs to the underlying tracker.

 Copy function

 Initialize this tracklet using the riemann fit information

 Initialize this tracklet using the track information

 Parameters:
   track - the TRD track used to initialize the tracklet

 Detailed description
 The function sets the starting point and direction of the
 tracklet according to the information from the TRD track.

 Caution
 The TRD track has to be propagated to the beginning of the
 chamber where the tracklet will be constructed

 Reset seed. If option opt="c" is given only cluster arrays are cleared.

 update tracklet reference position from the TRD track

 Calculate number of used clusers in the tracklet

 Use clusters

 In stand alone mode:
 Clusters which are marked as used or shared from another track are
 removed from the tracklet

 In barrel mode:
 - Clusters which are used by another track become shared
 - Clusters which are attached to a kink track become shared

 Calculates average dE/dx for all slices and store them in the internal array fdEdx.

 Parameters:
  nslices : number of slices for which dE/dx should be calculated
 Output:
  store results in the internal array fdEdx. This can be accessed with the method
  AliTRDseedV1::GetdEdx()

 Detailed description
 Calculates average dE/dx for all slices. Depending on the PID methode
 the number of slices can be 3 (LQ) or 8(NN).
 The calculation of dQ/dl are done using the tracklet fit results (see AliTRDseedV1::GetdQdl(Int_t))

 The following effects are included in the calculation:
 1. calibration values for t0 and vdrift (using x coordinate to calculate slice)
 2. cluster sharing (optional see AliTRDrecoParam::SetClusterSharing())
 3. cluster size

 Cook 2 labels for seed

 Find position inside the amplification cell for reading drift velocity map

 Computes total charge attached to tracklet. If "useOutliers" is set clusters
 which are not in chamber are also used (default false)

 Find number, size and position of charge gaps (consecutive missing time bins).
 Returns the number of gaps and fills their size in input array "sz" and position in array "pos"

 Algorithm to estimate cross point in the x-z plane for pad row cross tracklets or the z coordinate of pad row without pad row cross in the local chamber coordinates.
 Returns variance of the radial offset from anode wire in case of raw cross or 0 otherwise.

 correct dzdx for the bias in z according to MC

 correct y coordinate for tail cancellation. This should be fixed by considering TC as a function of q/pt.
  rc : TRUE if tracklet crosses rows
 bz : magnetic field z component

 Charge of the clusters at timebin

 Calculate total charge / tracklet length for 1D PID

 Using the linear approximation of the track inside one TRD chamber (TRD tracklet)
 the charge per unit length can be written as:


 where qc is the total charge collected in the current time bin and dx is the length
 of the time bin.
 The following correction are applied :
   - charge : pad row cross corrections
              [diffusion and TRF assymetry] TODO
   - dx     : anisochronity, track inclination - see Fit and AliTRDcluster::GetXloc()
              and AliTRDcluster::GetYloc() for the effects taken into account

 In the picture the energy loss measured on the tracklet as a function of drift time [left] and respectively
 drift length [right] for different particle species is displayed.
 Author : Alex Bercuci <A.Bercuci@gsi.de>

 Returns momentum of the track after update with the current tracklet as:


 and optionally the momentum error (if err is not null).
 The estimated variance of the momentum is given by:


 which can be simplified to

 Returns no. of TB occupied by clusters

 Returns no. of TB occupied by 2 clusters for pad row cross tracklets

 Fill probability array for tracklet from the DB.

 Parameters

 Output
   returns pointer to the probability array and NULL if missing DB access

 Retrieve PID probabilities for e+-, mu+-, K+-, pi+- and p+- from the DB according to tracklet information:
 - estimated momentum at tracklet reference point
 - dE/dx measurements
 - tracklet length
 - TRD layer
 According to the steering settings specified in the reconstruction one of the following methods are used
 - Neural Network [default] - option "nn"
 - 2D Likelihood - option "!nn"

 Returns a quality measurement of the current seed

 Computes covariance in the y-z plane at radial point x (in tracking coordinates)
 and returns the results in the preallocated array cov[3] as :
   cov[0] = Var(y)
   cov[1] = Cov(yz)
   cov[2] = Var(z)

 Details

 For the linear transformation


   The error propagation has the general form


  We apply this formula 2 times. First to calculate the covariance of the tracklet
 at point x we consider:


 and secondly to take into account the tilt angle



 using simple trigonometrics one can write for this last case


 which can be aproximated for small alphas (2 deg) with



 before applying the tilt rotation we also apply systematic uncertainties to the tracklet
 position which can be tunned from outside via the AliTRDrecoParam::SetSysCovMatrix(). They might
 account for extra misalignment/miscalibration uncertainties.

 Author :
 Alex Bercuci <A.Bercuci@gsi.de>
 Date : Jan 8th 2009

 Helper function to calculate the square root of the covariance matrix.
 The input matrix is stored in the vector c and the result in the vector d.
 Both arrays have to be initialized by the user with at least 3 elements. Return negative in case of failure.

 For calculating the square root of the symmetric matrix c
 the following relation is used:


 with V being the matrix with the n eigenvectors as columns.
 In case C is symmetric the followings are true:
   - matrix D is diagonal with the diagonal given by the eigenvalues of C
   - V = V^{-1}

 Author A.Bercuci <A.Bercuci@gsi.de>
 Date   Mar 19 2009

 Helper function to calculate the inverse of the covariance matrix.
 The input matrix is stored in the vector c and the result in the vector d.
 Both arrays have to be initialized by the user with at least 3 elements
 The return value is the determinant or 0 in case of singularity.

 Author A.Bercuci <A.Bercuci@gsi.de>
 Date   Mar 19 2009

 Returns geometry volume id by delegation

 Retrieve calibration and position parameters from OCDB.
 The following information are used
  - detector index
  - column and row position of first attached cluster. If no clusters are attached
 to the tracklet a random central chamber position (c=70, r=7) will be used.

 The following information is cached in the tracklet
   t0 (trigger delay)
   drift velocity
   PRF width
   omega*tau = tg(a_L)
   diffusion coefficients (longitudinal and transversal)

 Author :
 Alex Bercuci <A.Bercuci@gsi.de>
 Date : Jan 8th 2009

AliInfo(Form("own [%s] fOwner[%s]", own?"YES":"NO", fOwner?"YES":"NO"));

 Shortcut method to initialize pad geometry.

 Projective algorithm to attach clusters to seeding tracklets. The following steps are performed :
 1. Collapse x coordinate for the full detector plane
 2. truncated mean on y (r-phi) direction
 3. purge clusters
 4. truncated mean on z direction
 5. purge clusters

 Parameters
  - chamber : pointer to tracking chamber container used to search the tracklet
  - tilt    : switch for tilt correction during road building [default true]
  - chgPos  : mark same[kFALSE] and opposite[kTRUE] sign tracks with respect to Bz field sign [default true]
  - ev      : event number for debug purposes [default = -1]
 Output
  - true    : if tracklet found successfully. Failure can happend because of the following:
      -
 Detailed description

 We start up by defining the track direction in the xy plane and roads. The roads are calculated based
 on tracking information (variance in the r-phi direction) and estimated variance of the standard
 clusters (see AliTRDcluster::SetSigmaY2()) corrected for tilt (see GetCovAt()). From this the road is



 Author : Alexandru Bercuci <A.Bercuci@gsi.de>
 Debug  : level = 2 for calibration
          level = 3 for visualization in the track SR
          level = 4 for full visualization including digit level

   Fill in all derived information. It has to be called after recovery from file or HLT.
   The primitive data are
   - list of clusters
   - detector (as the detector will be removed from clusters)
   - position of anode wire (fX0) - temporary
   - track reference position and direction
   - momentum of the track
   - time bin length [cm]

   A.Bercuci <A.Bercuci@gsi.de> Oct 30th 2008

 Linear fit of the clusters attached to the tracklet

 Parameters :
   - opt : switch for tilt pad correction of cluster y position. Options are
           0 no correction [default]
           1 full tilt correction [dz/dx and z0]
           2 pseudo tilt correction [dz/dx from pad-chamber geometry]

 Output :
  True if successful

 Detailed description

            Fit in the xy plane

 The fit is performed to estimate the y position of the tracklet and the track
 angle in the bending plane. The clusters are represented in the chamber coordinate
 system (with respect to the anode wire - see AliTRDtrackerV1::FollowBackProlongation()
 on how this is set). The x and y position of the cluster and also their variances
 are known from clusterizer level (see AliTRDcluster::GetXloc(), AliTRDcluster::GetYloc(),
 AliTRDcluster::GetSX() and AliTRDcluster::GetSY()).
 If gaussian approximation is used to calculate y coordinate of the cluster the position
 is recalculated taking into account the track angle. The general formula to calculate the
 error of cluster position in the gaussian approximation taking into account diffusion and track
 inclination is given for TRD by:



 Since errors are calculated only in the y directions, radial errors (x direction) are mapped to y
 by projection i.e.


 and also by the lorentz angle correction

            Fit in the xz plane

 The "fit" is performed to estimate the radial position (x direction) where pad row cross happens.
 If no pad row crossing the z position is taken from geometry and radial position is taken from the xy
 fit (see below).

 There are two methods to estimate the radial position of the pad row cross:
   1. leading cluster radial position : Here the lower part of the tracklet is considered and the last
 cluster registered (at radial x0) on this segment is chosen to mark the pad row crossing. The error
 of the z estimate is given by :


 The systematic errors for this estimation are generated by the following sources:
   - no charge sharing between pad rows is considered (sharp cross)
   - missing cluster at row cross (noise peak-up, under-threshold signal etc.).

   2. charge fit over the crossing point : Here the full energy deposit along the tracklet is considered
 to estimate the position of the crossing by a fit in the qx plane. The errors in the q directions are
 parameterized as s_q = q^2. The systematic errors for this estimation are generated by the following sources:
   - no general model for the qx dependence
   - physical fluctuations of the charge deposit
   - gain calibration dependence

            Estimation of the radial position of the tracklet

 For pad row cross the radial position is taken from the xz fit (see above). Otherwise it is taken as the
 interpolation point of the tracklet i.e. the point where the error in y of the fit is minimum. The error
 in the y direction of the tracklet is (see AliTRDseedV1::GetCovAt()):


 and thus the radial position is:



            Estimation of tracklet position error

 The error in y direction is the error of the linear fit at the radial position of the tracklet while in the z
 direction is given by the cluster error or pad row cross error. In case of no pad row cross this is given by:


 For pad row cross the full error is calculated at the radial position of the crossing (see above) and the error
 in z by the width of the crossing region - being a matter of parameterization.


 In case of no tilt correction (default in the barrel tracking) the tilt is taken into account by the rotation of
 the covariance matrix. See AliTRDseedV1::GetCovAt() for details.

 Author
 A.Bercuci <A.Bercuci@gsi.de>

 Linear fit of the clusters attached to the tracklet
   The fit is performed in local chamber coordinates (27.11.2013) to take into account correctly the misalignment
   Also the pad row cross is checked here and some background is removed

 Author
 A.Bercuci <A.Bercuci@gsi.de>

 Apply alignment to the local position of tracklet
 A.Bercuci @ 27.11.2013

 Printing the seedstatus

 Checks if current instance of the class has the same essential members
 as the given one

   void      SetUsabilityMap(Long_t um)  { fUsable = um; }