class HMdcAligner3M: public HReconstructor

 Default constructor.

 Constructor including module election (and name and title, which
 seems to be very important). Alignment procedure
 proyects hits of modA in modB coordinate system and compares

 Constructor including module election (and name and title, which
 seems to be very important). This constructor deals with modules in
 TWO DIFFERENT sectors: selects module A in sector A and modules B and C
 in sector B
 mode takes values 1 or 2 for cosmics or pp ...

 Inits common defaults

 Destructor.

 Minimization defaults

 Serves pointers to the relative transformation parameters

 Sets ascii output for debugging.

 Sets root output

 Sets number of sigmas in cuts.

 Inits histograms

Fits to a gaussian the four relevant histograms
and obtains the fit parameters for further data selection

 Inits TNtuple

 Inits hitaux category and calls setParContainers()

 Call the functions returning auxiliar geometrical parameters

Turn on the automatic geometrical parameter input
Use it for inserting manually the parameters in the macro

 Disables control histograms output (saving memory)

 Selects minimization strategy. Only valids in this reduction!

 select = 100 (fcnalign3) Chi square sum in minimization
 select = 101 (fcnalign3) Distances line-hit

 select = 105 (fcnalign3) Minimizing angles between 2 lines
              made from Hits (testing)
 select = 106 (fcnalign3) Error with MINOS!

 introduce unit errors in Hits

 Sets off the covariance in the translationFinder() function

 Sets off the covariance in fitHistograms()

 Fix a parameter set in minimization
 New scheme: 18 bits (binary number) specifying the parameters
 fixed (1) and released (0). Lower bit is first parameter

 Disables the cuts after fitting the histograms

 Enables the Slope cuts after fitting the histograms.
 This cut makes the sample near indep. of Z translations
 and results useful for X and Y minimization.
 For 2 MDCs: the cut is effective only in MDCB, because fTranslation
 is represented in MDCB coordinates. Then, tracks passing
 the cut are almost parallel to Z direction if fSlopeCut is positive
 For 3 MDCs: a mean value for the three slopes. tracks passing
 the cut are almost parallel to Z direction if fSlopeCut is positive

 Loads the parameter containers it uses later

 Defines the parameter containers it uses later

 The transformations are:  X = R X' + T
 in the geometrical parameters.
 To obtain relative transformations: X(B) = M X(A) + V
 we follow:
   X = R(A) X(A) + T(A)
   X = R(B) X(B) + T(B)

   X(B) = [R(B)]E-1 R(A) X(A) + [R(B)]E-1 [T(A)-T(B)]

   M = [R(B)]E-1 R(A)
   V = [R(B)]E-1 [T(A)-T(B)]

 From M it is easy to get the relative Euler angles

 CONVENTION: fRotMat[i] and fTranslation[i] store the
 matrix M and vector V of the transformations made like this:
 4 modules: [0]  X(D) = fRotMat[0] X(C) + fTranslation[0]
            [1]  X(D) = fRotMat[1] X(B) + fTranslation[1]
            [2]  X(D) = fRotMat[2] X(A) + fTranslation[2]

 3 modules: [0]  X(C) = fRotMat[0] X(B) + fTranslation[0]
            [1]  X(C) = fRotMat[1] X(A) + fTranslation[1]

 2 modules: [0]  X(B) = fRotMat[0] X(A) + fTranslation[0]

 From the relative rotation, get the euler angles (radians)

 From an Euler rotation (see Dahlinger paper for the convention)
 the euler angles are:
 euler[0] = atan2(rot(5)/sin(euler[1]),rot(2)/sin(euler[1]))
 euler[1] = acos (rot(8))    with possible change of sign
 euler[2] = atan2(rot(7)/sin(euler[1]),-rot(6)/sin(euler[1]))

 Entering geometrical parameters.

 To be used introducing in the macro the parameters for
 testing, optimization ...

 Iteration in the hit category. Fills histograms
 and TTree and calculates relevant quantities

 New execute for more than two MDCs
 UPDATED TO COSMICS AND pp REACTIONS (fMode>0)

 Find the projection point of a Hit on another MDC

 Given a relative rotation and translation from MDC A to MDC B
 (see CONVENTION in HMdcAligner3M::setGeomAuxPar())
  X(B) = rot X(A) + tra
 this function obtains the projection in MDC B of a Hit in MDC A

 When the user wants to obtain the projection in MDC A of a Hit in
 MDC B, should provide the inverse transformations
 Example: X(A) = rot-1 * X(B) - rot-1 * tra
               = newrot * X(B) + newtra
 where:
    newrot = rot-1
    newtra = - (rot-1 * tra)
 The function returns also the slopes in the new coordinate system

Check if the hit is inside a window around point and slope
old check based on square cuts
New one based on equiprobability elipse (Beatriz paper)

 Propagates hitA in hitB coordinate system and merges
 the information in a new hit in hitB coordinate system
 The rot and tra verifies the CONVENTION
 (see HMdcAligner3M::setGeomAuxPar()), that is:
     X(B) = rot X(A) + tra
 Normally B is reference MDC, which is farther from target
Testing a merge in function of the coordinates

Transform hit angular components in slopes

 Getting module A parameters from module B parameters (fRotLab fTransLab)
 and from relative parameters (fRotMat and fTranslation)
 The transformations are:  X = R X' + T
 in the geometrical parameters. We have here:
   X = R(B) X(B) + T(B)
 and we know
   X(B) = M x(A) + V
 where
   M = [R(B)]E-1 R(A)
   V = [R(B)]E-1 [T(A)-T(B)]
 are the relative transformations we know (see HMdcAligner3M)
 We want to find out the transformation
   X = R(A) X(A) + T(A)
 using:
   X = R(B) X(B) + T(B) = R(B) (M x(A) + V)  + T(B) =>
   X = R(B) M x(A) + R(B) V  + T(B) =>
   R(A) = R(B) M  and
   T(A) = R(B) V  + T(B)

 Statistical information and Minimization procedure

 Performs the graphical output from obtained parameters

 Stores all histos and tree in the Root file

 Fill a matrix using the Euler angles of the relative transformation

OLD
    fRotMat[0][0]=(cos(prim) * cos(segu) * cos(terc)) - (sin(prim) * sin(terc));
    fRotMat[1][0]=( - cos(prim) * cos(segu) * sin(terc)) - (sin(prim) * cos(terc));
    fRotMat[2][0]=(cos(prim) * sin(segu));
    fRotMat[0][1]=(sin(prim) * cos(segu) * cos(terc)) + (cos(prim) * sin(terc));
    fRotMat[1][1]=( - sin(prim) * cos(segu) * sin(terc)) + (cos(prim) * cos(terc));
    fRotMat[2][1]=(sin(prim) * sin(segu));
    fRotMat[0][2]=( - sin(segu) * cos(terc));
    fRotMat[1][2]=(sin(segu) * sin(terc));
    fRotMat[2][2]=(cos(segu));

ATT! Correspondencia entre HGeomRotation y la antigua transf. arriba

  rot(0) rot(1) rot(2)     fRotMat[0][0] fRotMat[1][0] fRotMat[2][0]
  rot(3) rot(4) rot(5)  =  fRotMat[0][1] fRotMat[1][1] fRotMat[2][1]
  rot(6) rot(7) rot(8)     fRotMat[0][2] fRotMat[1][2] fRotMat[2][2]

 Translation from MDC A to MDC B

 Euler angles in transformation from MDC A to MDC B

 Limits of the square defined in the search procedure

 Set the criteria for iteration in the minimization (see finalize())

 Set the weights in the fcn()

 Set the module errors in the fcn()

 Set the steps in the minimization

 Set the criteria for iteration in the minimization (see finalize())

 Minuit menu
 Argument fix correspon to fFix value (see setFix())
 Other arguments are init values for the parameters!

 For fast minimization, a Hit array with only relevant information
 (x,y coordinates) for the Hits in accepted track combinations

 For fast minimization, a Hit array with only relevant information
 (x,y coordinates) for the Hits in accepted track combinations