class TUnfold: public TObject

 reset all data members

 delete old results (if any)
 this function is virtual, so derived classes may implement their own
 method to flag results as non-valid

 set all matrix pointers to zero

 main unfolding algorithm. Declared virtual, because other algorithms
 could be implemented

 Purpose: unfold y -> x
 Data members required:
     fA:  matrix to relate x and y
     fY:  measured data points
     fX0: bias on x
     fBiasScale: scale factor for fX0
     fVyy:  covariance matrix for y
     fL: regularisation conditions
     fTauSquared: regularisation strength
     fConstraint: whether the constraint is applied
 Data members modified:
     fVyyInv: inverse of input data covariance matrix
     fNdf: number of dgerres of freedom
     fEinv: inverse of the matrix needed for unfolding calculations
     fE:    the matrix needed for unfolding calculations
     fX:    unfolded data points
     fDXDY: derivative of x wrt y (for error propagation)
     fVxx:  error matrix (covariance matrix) on x
     fAx:   estimate of distribution y from unfolded data
     fChi2A:  contribution to chi**2 from y-Ax
     fChi2L:  contribution to chi**2 from L*(x-x0)
     fDXDtauSquared: derivative of x wrt tau
     fDXDAM[0,1]: matrix parts of derivative x wrt A
     fDXDAZ[0,1]: vector parts of derivative x wrt A
     fRhoMax: maximum global correlation coefficient
     fRhoAvg: average global correlation coefficient
 return code:
     fRhoMax   if(fRhoMax>=1.0) then the unfolding has failed!

 calculate the product of two sparse matrices
    a,b: pointers to sparse matrices, where a->GetNcols()==b->GetNrows()
 this is a replacement for the call
    new TMatrixDSparse(*a,TMatrixDSparse::kMult,*b);

 multiply a Sparse matrix with a non-sparse matrix
    a:  pointer to sparse matrix
    b:  pointer to non-sparse matrix
 this is a replacement for the call
    new TMatrixDSparse(*a,TMatrixDSparse::kMult,*b);

 a replacement for
     (*dest) += f*(*src)

 given a bin number, return the name of the output bin
 this method makes more sense for the class TUnfoldDnesity
 where it gets overwritten

 set up unfolding matrix and initial regularisation scheme
    hist_A:  matrix that describes the migrations
    histmap: mapping of the histogram axes to the unfolding output
    regmode: global regularisation mode
    constraint: type of constraint to use
 data members initialized to something different from zero:
    fA: filled from hist_A
    fDA: filled from hist_A
    fX0: filled from hist_A
    fL: filled depending on the regularisation scheme
 Treatment of overflow bins
    Bins where the unfolding input (Detector level) is in overflow
    are used for the efficiency correction. They have to be filled
    properly!
    Bins where the unfolding output (Generator level) is in overflow
    are treated as a part of the generator level distribution.
    I.e. the unfolding output could have non-zero overflow bins if the
    input matrix does have such bins.

 delete all data members

 initialize alternative bias from histogram
 modifies data member fX0

 add regularisation on the size of bin i
    bin: bin number
    scale: size of the regularisation
 return value: number of conditions which have been skipped
 modifies data member fL

 add regularisation on the difference of two bins
   left_bin: 1st bin
   right_bin: 2nd bin
   scale: size of the regularisation
 return value: number of conditions which have been skipped
 modifies data member fL

 add regularisation on the curvature through 3 bins (2nd derivative)
   left_bin: 1st bin
   center_bin: 2nd bin
   right_bin: 3rd bin
   scale_left: scale factor on center-left difference
   scale_right: scale factor on right-center difference
 return value: number of conditions which have been skipped
 modifies data member fL

 set regulatisation on a 1-dimensional curve
   start: first bin
   step:  distance between neighbouring bins
   nbin:  total number of bins
   regmode:  regularisation mode
 return value:
   number of errors (i.e. conditions which have been skipped)
 modifies data member fL

 set regularisation on a 2-dimensional grid of bins
     start: first bin
     step1: distance between bins in 1st direction
     nbin1: number of bins in 1st direction
     step2: distance between bins in 2nd direction
     nbin2: number of bins in 2nd direction
 return value:
   number of errors (i.e. conditions which have been skipped)
 modifies data member fL

 Do unfolding of an input histogram
   tau_reg: regularisation parameter
   input:   input distribution with errors
   scaleBias:  scale factor applied to the bias
 Data members required:
   fA, fX0, fL
 Data members modified:
   those documented in SetInput()
   and those documented in DoUnfold(Double_t)
 Return value:
   maximum global correlation coefficient
   NOTE!!! return value >=1.0 means error, and the result is junk

 Overflow bins of the input distribution are ignored!

 Define the input data for subsequent calls to DoUnfold(Double_t)
   input:   input distribution with errors
   scaleBias:  scale factor applied to the bias
   oneOverZeroError: for bins with zero error, this number defines 1/error.
   hist_vyy: if non-zero, defines the data covariance matrix
             otherwise it is calculated from the data errors
   hist_vyy_inv: if non-zero and if hist_vyy  is set, defines the inverse of the data covariance matrix
 Return value: number of bins with bad error
                 +10000*number of unconstrained output bins
         Note: return values>=10000 are fatal errors,
               for the given input, the unfolding can not be done!
 Data members modified:
   fY, fVyy, , fBiasScale
 Data members cleared
   fVyyInv, fNdf
   + see ClearResults

 Unfold with given value of regularisation parameter tau
     tau: new tau parameter
 required data members:
     fA:  matrix to relate x and y
     fY:  measured data points
     fX0: bias on x
     fBiasScale: scale factor for fX0
     fV:  inverse of covariance matrix for y
     fL: regularisation conditions
 modified data members:
     fTauSquared and those documented in DoUnfold(void)

 scan the L curve
   nPoint: number of points on the resulting curve
   tauMin: smallest tau value to study
   tauMax: largest tau value to study
   lCurve: the L curve as graph
   logTauX: output spline of x-coordinates vs tau for the L curve
   logTauY: output spline of y-coordinates vs tau for the L curve
 return value: the coordinate number (0..nPoint-1) with the "best" choice
     of tau

 get vector of normalisation factors
   out: output histogram
   binMap: for each bin of the original output distribution
           specify the destination bin. A value of -1 means that the bin
           is discarded. 0 means underflow bin, 1 first bin, ...
        binMap[0] : destination of underflow bin
        binMap[1] : destination of first bin

 get bias distribution, possibly with bin remapping
   out: output histogram
   binMap: for each bin of the original output distribution
           specify the destination bin. A value of -1 means that the bin
           is discarded. 0 means underflow bin, 1 first bin, ...
        binMap[0] : destination of underflow bin
        binMap[1] : destination of first bin

 get unfolding result, folded back trough the matrix
   out: output histogram
   binMap: for each bin of the original output distribution
           specify the destination bin. A value of -1 means that the bin
           is discarded. 0 means underflow bin, 1 first bin, ...
        binMap[0] : destination of underflow bin
        binMap[1] : destination of first bin

 retreive matrix of probabilities
    histmap: on which axis to arrange the input/output vector
    A: histogram to store the probability matrix

 retreive input distribution
   out: output histogram
   binMap: for each bin of the original output distribution
           specify the destination bin. A value of -1 means that the bin
           is discarded. 0 means underflow bin, 1 first bin, ...
        binMap[0] : destination of underflow bin
        binMap[1] : destination of first bin

 calculate the inverse of the contribution to the error matrix
 corresponding to the input data

 retreive matrix of regularisation conditions squared
   out: prebooked matrix

 retreive matrix of regularisation conditions
   out: prebooked matrix

 set type of constraint for the next unfolding

 return regularisation parameter

 return chi**2 contribution from regularisation conditions

 return number of parameters

 return value on x axis of L curve

 return value on y axis of L curve

 get output distribution, cumulated over several bins
   output: output histogram
   binMap: for each bin of the original output distribution
           specify the destination bin. A value of -1 means that the bin
           is discarded. 0 means underflow bin, 1 first bin, ...
        binMap[0] : destination of underflow bin
        binMap[1] : destination of first bin

 get an error matrix, cumulated over several bins
   ematrix: output error matrix histogram
   emat: error matrix
   binMap: for each bin of the original output distribution
           specify the destination bin. A value of -1 means that the bin
           is discarded. 0 means underflow bin, 1 first bin, ...
        binMap[0] : destination of underflow bin
        binMap[1] : destination of first bin

 get output error matrix, cumulated over several bins
   ematrix: output error matrix histogram
   binMap: for each bin of the original output distribution
           specify the destination bin. A value of -1 means that the bin
           is discarded. 0 means underflow bin, 1 first bin, ...
        binMap[0] : destination of underflow bin
        binMap[1] : destination of first bin

 get correlation coefficient matrix, cumulated over several bins
   rhoij:  correlation coefficient matrix histogram
   binMap: for each bin of the original output distribution
           specify the destination bin. A value of -1 means that the bin
           is discarded. 0 means underflow bin, 1 first bin, ...
        binMap[0] : destination of underflow bin
        binMap[1] : destination of first bin

 get global correlation coefficients with arbitrary min map
   rhoi: global correlation histogram
   binMap: for each bin of the original output distribution
           specify the destination bin. A value of -1 means that the bin
           is discarded. 0 means underflow bin, 1 first bin, ...
        binMap[0] : destination of underflow bin
        binMap[1] : destination of first bin

 return value: maximum global correlation

 get global correlation coefficients with arbitrary min map
   rhoi: global correlation histogram
   emat: error matrix
   binMap: for each bin of the original output distribution
           specify the destination bin. A value of -1 means that the bin
           is discarded. 0 means underflow bin, 1 first bin, ...
        binMap[0] : destination of underflow bin
        binMap[1] : destination of first bin

 return value: maximum global correlation

 clear histogram contents and error

 set accuracy for matrix inversion

 Int_t IsNotSymmetric(TMatrixDSparse const &m) const;