class AliTPCCorrection: public TNamed

 default constructor

 default constructor, that set the name and title

 virtual destructor

 Add correction  and make them compact
 Assumptions:
  - origin of distortion/correction are additive
  - only correction ot the same type supported ()

 Corrects the initial coordinates x (cartesian coordinates)
 according to the given effect (inherited classes)
 roc represents the TPC read out chamber (offline numbering convention)

 Corrects the initial coordinates x (cartesian coordinates) and stores the new
 (distorted) coordinates in xp. The distortion is set according to the given effect (inherited classes)
 roc represents the TPC read out chamber (offline numbering convention)

 Distorts the initial coordinates x (cartesian coordinates)
 according to the given effect (inherited classes)
 roc represents the TPC read out chamber (offline numbering convention)

 Distorts the initial coordinates x (cartesian coordinates)
 according to the given effect (inherited classes)
 roc represents the TPC read out chamber (offline numbering convention)

 Distorts the initial coordinates x (cartesian coordinates)
 according to the given effect (inherited classes)
 roc represents the TPC read out chamber (offline numbering convention)

 Distorts the initial coordinates x (cartesian coordinates) and stores the new
 (distorted) coordinates in xp. The distortion is set according to the given effect (inherited classes)
 roc represents the TPC read out chamber (offline numbering convention)

 This function delivers the correction values dx in respect to the inital coordinates x
 roc represents the TPC read out chamber (offline numbering convention)
 Note: The dx is overwritten by the inherited effectice class ...

 This function delivers the distortion values dx in respect to the inital coordinates x
 roc represents the TPC read out chamber (offline numbering convention)

 author: marian.ivanov@cern.ch

 In this (virtual)function calculates the dx'/dz,  dy'/dz  and dz'/dz at given point (x,y,z)
 Generic implementation. Better precision can be acchieved knowing the internal structure
 of underlying trasnformation. Derived classes can reimplement it.
 To calculate correction is fitted in small neighberhood:
 (x+-delta,y+-delta,z+-delta) where delta is an argument

 Input parameters:
   x[]   - space point corrdinate
   roc   - readout chamber identifier (important e.g to do not miss the side of detector)
   delta - define the size of neighberhood
 Output parameter:
   dx[] - array {dx'/dz,  dy'/dz ,  dz'/dz }

 author: marian.ivanov@cern.ch

 In this (virtual)function calculates the dx'/dz,  dy'/dz  and dz'/dz at given point (x,y,z)
 Generic implementation. Better precision can be acchieved knowing the internal structure
 of underlying trasnformation. Derived classes can reimplement it.
 To calculate distortion is fitted in small neighberhood:
 (x+-delta,y+-delta,z+-delta) where delta is an argument

 Input parameters:
   x[]   - space point corrdinate
   roc   - readout chamber identifier (important e.g to do not miss the side of detector)
   delta - define the size of neighberhood
 Output parameter:
   dx[] - array {dx'/dz,  dy'/dz ,  dz'/dz }

 Integrate 3D distortion along drift lines starting from the roc plane
   to the expected z position of the point, this assumes that dz is small
   and the error propagating to z' instead of the correct z is negligible
 To define the drift lines virtual function  AliTPCCorrection::GetCorrectionDz is used

 Input parameters:
   x[]   - space point corrdinate
   roc   - readout chamber identifier (important e.g to do not miss the side of detector)
   delta - define the size of neighberhood
 Output parameter:
   dx[] - array { integral(dx'/dz),  integral(dy'/dz) ,  integral(dz'/dz) }

 Integrate 3D distortion along drift lines
 To define the drift lines virtual function  AliTPCCorrection::GetCorrectionDz is used

 Input parameters:
   x[]   - space point corrdinate
   roc   - readout chamber identifier (important e.g to do not miss the side of detector)
   delta - define the size of neighberhood
 Output parameter:
   dx[] - array { integral(dx'/dz),  integral(dy'/dz) ,  integral(dz'/dz) }

 Initialization funtion (not used at the moment)

 Update function

 Print function to check which correction classes are used
 option=="d" prints details regarding the setted magnitude
 option=="a" prints the C0 and C1 coefficents for calibration purposes

 Simple plot functionality.
 Returns a 2d hisogram which represents the corrections in radial direction (dr)
 in respect to position z within the XY plane.
 The histogramm has nx times ny entries.

 Simple plot functionality.
 Returns a 2d hisogram which represents the corrections in rphi direction (drphi)
 in respect to position z within the XY plane.
 The histogramm has nx times ny entries.

 Simple plot functionality.
 Returns a 2d hisogram which represents the corrections in longitudinal direction (dz)
 in respect to position z within the XY plane.
 The histogramm has nx times ny entries.

 Simple plot functionality.
 Returns a 2d hisogram which represents the corrections in r direction (dr)
 in respect to angle phi within the ZR plane.
 The histogramm has nx times ny entries.

 Simple plot functionality.
 Returns a 2d hisogram which represents the corrections in rphi direction (drphi)
 in respect to angle phi within the ZR plane.
 The histogramm has nx times ny entries.

 Simple plot functionality.
 Returns a 2d hisogram which represents the corrections in longitudinal direction (dz)
 in respect to angle phi within the ZR plane.
 The histogramm has nx times ny entries.

 Helper function to create a 2d histogramm of given size

 Interpolate table - 2D interpolation

 Interpolate table - 3D interpolation

 Interpolate table (TMatrix format) - 2D interpolation

 Interpolate table (TMatrix format) - 3D interpolation

 Interpolate function Y(x) using linear (order=1) or quadratic (order=2) interpolation.

 Interpolate table (TMatrix format) - 2D interpolation
 Float version (in order to decrease the OCDB size)

 Interpolate table (TMatrix format) - 3D interpolation
 Float version (in order to decrease the OCDB size)

 Interpolate function Y(x) using linear (order=1) or quadratic (order=2) interpolation.
 Float version (in order to decrease the OCDB size)

 Search an ordered table by starting at the most recently used point

 Initialization of interpolation points - for main look up table
   (course grid in the middle, fine grid on the borders)

 Solve Poisson's Equation by Relaxation Technique in 2D (assuming cylindrical symmetry)

 Solve Poissons equation in a cylindrical coordinate system. The arrayV matrix must be filled with the
 boundary conditions on the first and last rows, and the first and last columns.  The remainder of the
 array can be blank or contain a preliminary guess at the solution.  The Charge density matrix contains
 the enclosed spacecharge density at each point. The charge density matrix can be full of zero's if
 you wish to solve Laplaces equation however it should not contain random numbers or you will get
 random numbers back as a solution.
 Poisson's equation is solved by iteratively relaxing the matrix to the final solution.  In order to
 speed up the convergence to the best solution, this algorithm does a binary expansion of the solution
 space.  First it solves the problem on a very sparse grid by skipping rows and columns in the original
 matrix.  Then it doubles the number of points and solves the problem again.  Then it doubles the
 number of points and solves the problem again.  This happens several times until the maximum number
 of points has been included in the array.

 NOTE: In order for this algorithmto work, the number of rows and columns must be a power of 2 plus one.
 So rows == 2**M + 1 and columns == 2**N + 1.  The number of rows and columns can be different.

 NOTE: rocDisplacement is used to include (or ignore) the ROC misalignment in the dz calculation

 Original code by Jim Thomas (STAR TPC Collaboration)

 3D - Solve Poisson's Equation in 3D by Relaxation Technique

    NOTE: In order for this algorith to work, the number of rows and columns must be a power of 2 plus one.
    The number of rows and COLUMNS can be different.

    ROWS       ==  2**M + 1
    COLUMNS    ==  2**N + 1
    PHISLICES  ==  Arbitrary but greater than 3

    DeltaPhi in Radians

    SYMMETRY = 0 if no phi symmetries, and no phi boundary conditions
             = 1 if we have reflection symmetry at the boundaries (eg. sector symmetry or half sector symmetries).

 NOTE: rocDisplacement is used to include (or ignore) the ROC misalignment in the dz calculation

 Helperfunction: Check if integer is a power of 2

 Fit the track parameters - without and with distortion
 1. Space points in the TPC are simulated along the trajectory
 2. Space points distorted
 3. Fits  the non distorted and distroted track to the reference plane at refX
 4. For visualization and debugging  purposes the space points and tracks can be stored  in the tree - using the TTreeSRedirector functionality

 trackIn   - input track parameters
 refX     - reference X to fit the track
 dir      - direction - out=1 or in=-1
 pcstream -  debug streamer to check the results

 see AliExternalTrackParam.h documentation:
 track1.fP[0] - local y (rphi)
 track1.fP[1] - z
 track1.fP[2] - sinus of local inclination angle
 track1.fP[3] - tangent of deep angle
 track1.fP[4] - 1/pt

 create the distortion tree on a mesh with granularity given by step
 return the tree with distortions at given position
 Map is created on the mesh with given step size

 Make a fit tree:
 For each partial correction (specified in array) and given track topology (phi, theta, snp, refX)
 calculates partial distortions
 Partial distortion is stored in the resulting tree
 Output is storred in the file distortion_<dettype>_<partype>.root
 Partial  distortion is stored with the name given by correction name


 Parameters of function:
 input     - input tree
 dtype     - distortion type 0 - ITSTPC,  1 -TPCTRD, 2 - TPCvertex , 3 - TPC-TOF,  4 - TPCTPC track crossing
 ppype     - parameter type
 corrArray - array with partial corrections
 step      - skipe entries  - if 1 all entries processed - it is slow
 debug     0 if debug on also space points dumped - it is slow

 Make a fit tree:
 For each partial correction (specified in array) and given track topology (phi, theta, snp, refX)
 calculates partial distortions
 Partial distortion is stored in the resulting tree
 Output is storred in the file distortion_<dettype>_<partype>.root
 Partial  distortion is stored with the name given by correction name


 Parameters of function:
 input     - input tree
 dtype     - distortion type 10 - IROC-OROC
 ppype     - parameter type
 corrArray - array with partial corrections
 step      - skipe entries  - if 1 all entries processed - it is slow
 debug     0 if debug on also space points dumped - it is slow

 Make a laser fit tree for global minimization

 make a distortion map out ou fthe residual histogram
 Results are written to the debug streamer - pcstream
 Parameters:
   his0       - input (4D) residual histogram
   pcstream   - file to write the tree
   run        - run number
   refX       - track matching reference X
   type       - 0- y 1-z,2 -snp, 3-theta, 4=1/pt
 THnSparse axes:
 OBJ: TAxis     #Delta  #Delta
 OBJ: TAxis     tanTheta        tan(#Theta)
 OBJ: TAxis     phi     #phi
 OBJ: TAxis     snp     snp

 make a distortion map out ou fthe residual histogram
 Results are written to the debug streamer - pcstream
 Parameters:
   his0       - input (4D) residual histogram
   pcstream   - file to write the tree
   run        - run number
   refX       - track matching reference X
   type       - 0- y 1-z,2 -snp, 3-theta, 4=1/pt
 marian.ivanov@cern.ch

  Histo axeses
   Collection name='TObjArray', class='TObjArray', size=16
  0. OBJ: TAxis     #Delta  #Delta
  1. OBJ: TAxis     N_{cl}  N_{cl}
  2. OBJ: TAxis     dca_{r} (cm)    dca_{r} (cm)
  3. OBJ: TAxis     z (cm)  z (cm)
  4. OBJ: TAxis     sin(#phi)       sin(#phi)
  5. OBJ: TAxis     tan(#theta)     tan(#theta)
  6. OBJ: TAxis     1/pt (1/GeV)    1/pt (1/GeV)
  7. OBJ: TAxis     pt (GeV)        pt (GeV)
  8. OBJ: TAxis     alpha   alpha

 make a distortion map out of the residual histogram
 Results are written to the debug streamer - pcstream
 Parameters:
   his0       - input (4D) residual histogram
   pcstream   - file to write the tree
   run        - run number
   type       - 0- y 1-z,2 -snp, 3-theta
 marian.ivanov@cern.ch

 Store object in the OCDB
 By default the object is stored in the current directory
 default comment consit of user name and the date

 Fast method to simulate the influence of the given distortion on the vertex reconstruction

 make correction available for visualization using
 TFormula, TFX and TTree::Draw
 important in order to check corrections and also compute dervied variables
 e.g correction partial derivatives

 NOTE - class is not owner of correction

 Get visula correction registered at index=position

 calculate the correction at given position - check the geffCorr

 corrType return values
 0 - delta R
 1 - delta RPhi
 2 - delta Z
 3 - delta RPHI

 return correction at given x,y,z

 return correction at given x,y,z

 return correction at given x,y,z

 return correction at given x,y,z

 return correction at given x,y,z

 return correction at given x,y,z

 Make a laser fit tree for global minimization

 map scaling

 normally called directly in the correction classes which inherit from this class