    // @(#)root/hist:$Name:  $:$Id: TProfile2D.cxx,v 1.24 2004/05/26 11:32:00 brun Exp $
    // Author: Rene Brun   16/04/2000

    /*************************************************************************
     * Copyright (C) 1995-2000, Rene Brun and Fons Rademakers.               *
     * All rights reserved.                                                  *
     *                                                                       *
     * For the licensing terms see $ROOTSYS/LICENSE.                         *
     * For the list of contributors see $ROOTSYS/README/CREDITS.             *
     *************************************************************************/

    #include "TProfile2D.h"
    #include "TMath.h"
    #include "THLimitsFinder.h"
    #include "Riostream.h"

    Bool_t TProfile2D::fgApproximate = kFALSE;

    ClassImp(TProfile2D)

    //______________________________________________________________________________
    //
    //  Profile2D histograms are used to display the mean
    //  value of Z and its RMS for each cell in X,Y.
    //  Profile2D histograms are in many cases an
    //  elegant replacement of three-dimensional histograms : the inter-relation of three
    //  measured quantities X, Y and Z can always be visualized by a three-dimensional
    //  histogram or scatter-plot; its representation on the line-printer is not particularly
    //  satisfactory, except for sparse data. If Z is an unknown (but single-valued)
    //  approximate function of X,Y this function is displayed by a profile2D histogram with
    //  much better precision than by a scatter-plot.
    //
    //  The following formulae show the cumulated contents (capital letters) and the values
    //  displayed by the printing or plotting routines (small letters) of the elements for cell I, J.
    //
    //                                                        2
    //      H(I,J)  =  sum Z                  E(I,J)  =  sum Z
    //      l(I,J)  =  sum l                  L(I,J)  =  sum l
    //      h(I,J)  =  H(I,J)/L(I,J)          s(I,J)  =  sqrt(E(I,J)/L(I,J)- h(I,J)**2)
    //      e(I,J)  =  s(I,J)/sqrt(L(I,J))
    //
    //  In the special case where s(I,J) is zero (eg, case of 1 entry only in one cell)
    //  e(I,J) is computed from the average of the s(I,J) for all cells.
    //  This simple/crude approximation was suggested in order to keep the cell
    //  during a fit operation.
    //
    //           Example of a profile2D histogram
    //{
    //  TCanvas *c1 = new TCanvas("c1","Profile histogram example",200,10,700,500);
    //  hprof2d  = new TProfile2D("hprof2d","Profile of pz versus px and py",40,-4,4,40,-4,4,0,20);
    //  Float_t px, py, pz;
    //  for ( Int_t i=0; i<25000; i++) {
    //     gRandom->Rannor(px,py);
    //     pz = px*px + py*py;
    //     hprof2d->Fill(px,py,pz,1);
    //  }
    //  hprof2d->Draw();
    //}
    //

    //______________________________________________________________________________
     TProfile2D::TProfile2D() : TH2D()
    {
    //*-*-*-*-*-*Default constructor for Profile2D histograms*-*-*-*-*-*-*-*-*
    //*-*        ============================================
       fTsumwz = fTsumwz2 = 0;
    }

    //______________________________________________________________________________
     TProfile2D::~TProfile2D()
    {
    //*-*-*-*-*-*Default destructor for Profile2D histograms*-*-*-*-*-*-*-*-*
    //*-*        ===========================================

    }

    //______________________________________________________________________________
     TProfile2D::TProfile2D(const char *name,const char *title,Int_t nx,Axis_t xlow,Axis_t xup,Int_t ny,Axis_t ylow,Axis_t yup,Option_t *option)
        : TH2D(name,title,nx,xlow,xup,ny,ylow,yup)
    {
    //*-*-*-*-*-*Normal Constructor for Profile histograms*-*-*-*-*-*-*-*-*-*
    //*-*        ==========================================
    //
    //  The first eight parameters are similar to TH2D::TH2D.
    //  All values of z are accepted at filling time.
    //  To fill a profile2D histogram, one must use TProfile2D::Fill function.
    //
    //  Note that when filling the profile histogram the function Fill
    //  checks if the variable z is betyween fZmin and fZmax.
    //  If a minimum or maximum value is set for the Z scale before filling,
    //  then all values below zmin or above zmax will be discarded.
    //  Setting the minimum or maximum value for the Z scale before filling
    //  has the same effect as calling the special TProfile2D constructor below
    //  where zmin and zmax are specified.
    //
    //  H(I,J) is printed as the cell contents. The errors computed are s(I,J) if CHOPT='S'
    //  (spread option), or e(I,J) if CHOPT=' ' (error on mean).
    //
    //        See TProfile2D::BuildOptions for explanation of parameters
    //
    //   see other constructors below with all possible combinations of
    //   fix and variable bin size like in TH2D.

       BuildOptions(0,0,option);
    }

    //______________________________________________________________________________
     TProfile2D::TProfile2D(const char *name,const char *title,Int_t nx,const Double_t *xbins,Int_t ny,Axis_t ylow,Axis_t yup,Option_t *option)
        : TH2D(name,title,nx,xbins,ny,ylow,yup)
    {
    //  Create a 2-D Profile with variable bins in X and fix bins in Y

       BuildOptions(0,0,option);
    }

    //______________________________________________________________________________
     TProfile2D::TProfile2D(const char *name,const char *title,Int_t nx,Axis_t xlow,Axis_t xup,Int_t ny,const Double_t *ybins,Option_t *option)
        : TH2D(name,title,nx,xlow,xup,ny,ybins)
    {
    //  Create a 2-D Profile with fix bins in X and variable bins in Y

       BuildOptions(0,0,option);
    }

    //______________________________________________________________________________
     TProfile2D::TProfile2D(const char *name,const char *title,Int_t nx,const Double_t *xbins,Int_t ny,const Double_t *ybins,Option_t *option)
        : TH2D(name,title,nx,xbins,ny,ybins)
    {
    //  Create a 2-D Profile with variable bins in X and variable bins in Y

       BuildOptions(0,0,option);
    }

    //______________________________________________________________________________
     TProfile2D::TProfile2D(const char *name,const char *title,Int_t nx,Axis_t xlow,Axis_t xup,Int_t ny, Axis_t ylow,Axis_t yup,Axis_t zlow,Axis_t zup,Option_t *option)
        : TH2D(name,title,nx,xlow,xup,ny,ylow,yup)
    {
    //*-*-*-*-*-*Constructor for Profile2D histograms with range in z*-*-*-*-*-*
    //*-*        ====================================================
    //  The first eight parameters are similar to TH2D::TH2D.
    //  Only the values of Z between ZMIN and ZMAX will be considered at filling time.
    //  zmin and zmax will also be the maximum and minimum values
    //  on the z scale when drawing the profile2D.
    //
    //        See TProfile2D::BuildOptions for more explanations on errors
    //

       BuildOptions(zlow,zup,option);
    }

    //______________________________________________________________________________
     void TProfile2D::BuildOptions(Double_t zmin, Double_t zmax, Option_t *option)
    {
    //*-*-*-*-*-*-*Set Profile2D histogram structure and options*-*-*-*-*-*-*-*-*
    //*-*          =============================================
    //
    //    If a cell has N data points all with the same value Z (especially
    //    possible when dealing with integers), the spread in Z for that cell
    //    is zero, and the uncertainty assigned is also zero, and the cell is
    //    ignored in making subsequent fits. If SQRT(Z) was the correct error
    //    in the case above, then SQRT(Z)/SQRT(N) would be the correct error here.
    //    In fact, any cell with non-zero number of entries N but with zero spread
    //    should have an uncertainty SQRT(Z)/SQRT(N).
    //
    //    Now, is SQRT(Z)/SQRT(N) really the correct uncertainty?
    //    that it is only in the case where the Z variable is some sort
    //    of counting statistics, following a Poisson distribution. This should
    //    probably be set as the default case. However, Z can be any variable
    //    from an original NTUPLE, not necessarily distributed "Poissonly".
    //    The computation of errors is based on the parameter option:
    //    option:
    //     ' '  (Default) Errors are Spread/SQRT(N) for Spread.ne.0. ,
    //                      "     "  SQRT(Z)/SQRT(N) for Spread.eq.0,N.gt.0 ,
    //                      "     "  0.  for N.eq.0
    //     's'            Errors are Spread  for Spread.ne.0. ,
    //                      "     "  SQRT(Z)  for Spread.eq.0,N.gt.0 ,
    //                      "     "  0.  for N.eq.0
    //     'i'            Errors are Spread/SQRT(N) for Spread.ne.0. ,
    //                      "     "  1./SQRT(12.*N) for Spread.eq.0,N.gt.0 ,
    //                      "     "  0.  for N.eq.0
    //
    //    The third case above corresponds to Integer Z values for which the
    //    uncertainty is +-0.5, with the assumption that the probability that Z
    //    takes any value between Z-0.5 and Z+0.5 is uniform (the same argument
    //    goes for Z uniformly distributed between Z and Z+1); this would be
    //    useful if Z is an ADC measurement, for example. Other, fancier options
    //    would be possible, at the cost of adding one more parameter to the PROFILE2D
    //    For example, if all Z variables are distributed according to some
    //    known Gaussian of standard deviation Sigma, then:
    //     'G'            Errors are Spread/SQRT(N) for Spread.ne.0. ,
    //                      "     "  Sigma/SQRT(N) for Spread.eq.0,N.gt.0 ,
    //                      "     "  0.  for N.eq.0
    //    For example, this would be useful when all Z's are experimental quantities
    //    measured with the same instrument with precision Sigma.
    //
    //

       SetErrorOption(option);

       fBinEntries.Set(fNcells);  //*-* create number of entries per cell array

       Sumw2();                   //*-* create sum of squares of weights array

       fZmin = zmin;
       fZmax = zmax;
       fScaling = kFALSE;
       fTsumwz  = fTsumwz2 = 0;
    }

    //______________________________________________________________________________
     TProfile2D::TProfile2D(const TProfile2D &profile) : TH2D()
    {
       ((TProfile2D&)profile).Copy(*this);
    }

    //______________________________________________________________________________
     void TProfile2D::Add(TF1 *, Double_t , Option_t*)
    {
       // Performs the operation: this = this + c1*f1

       Error("Add","Function not implemented for TProfile2D");
       return;
    }

    //______________________________________________________________________________
     void TProfile2D::Add(const TH1 *h1, Double_t c1)
    {
       // Performs the operation: this = this + c1*h1

       if (!h1) {
          Error("Add","Attempt to add a non-existing profile");
          return;
       }
       if (!h1->InheritsFrom("TProfile2D")) {
          Error("Add","Attempt to add a non-profile2D object");
          return;
       }
       TProfile2D *p1 = (TProfile2D*)h1;

    //*-*- Check profile compatibility
       Int_t nx = GetNbinsX();
       if (nx != p1->GetNbinsX()) {
          Error("Add","Attempt to add profiles with different number of bins");
          return;
       }
       Int_t ny = GetNbinsY();
       if (ny != p1->GetNbinsY()) {
          Error("Add","Attempt to add profiles with different number of bins");
          return;
       }

    //*-*- Add statistics
       Double_t ac1 = TMath::Abs(c1);
       fEntries += ac1*p1->GetEntries();
       fTsumw   += ac1*p1->fTsumw;
       fTsumw2  += ac1*p1->fTsumw2;
       fTsumwx  += ac1*p1->fTsumwx;
       fTsumwx2 += ac1*p1->fTsumwx2;
       fTsumwy  += ac1*p1->fTsumwy;
       fTsumwy2 += ac1*p1->fTsumwy2;
       fTsumwxy += ac1*p1->fTsumwxy;
       fTsumwz  += ac1*p1->fTsumwz;
       fTsumwz2 += ac1*p1->fTsumwz2;

    //*-*- Loop on bins (including underflows/overflows)
       Int_t bin,binx,biny;
       Double_t *cu1 = p1->GetW();
       Double_t *er1 = p1->GetW2();
       Double_t *en1 = p1->GetB();
       for (binx =0;binx<=nx+1;binx++) {
          for (biny =0;biny<=ny+1;biny++) {
             bin   = biny*(fXaxis.GetNbins()+2) + binx;
             fArray[bin]             +=  c1*cu1[bin];
             fSumw2.fArray[bin]      += ac1*er1[bin];
             if (!fScaling) fBinEntries.fArray[bin] += ac1*en1[bin];
          }
       }
    }

    //______________________________________________________________________________
     void TProfile2D::Add(const TH1 *h1, const TH1 *h2, Double_t c1, Double_t c2)
    {
    //*-*-*-*-*Replace contents of this profile2D by the addition of h1 and h2*-*-*
    //*-*      ===============================================================
    //
    //   this = c1*h1 + c2*h2
    //

       if (!h1 || !h2) {
          Error("Add","Attempt to add a non-existing profile");
          return;
       }
       if (!h1->InheritsFrom("TProfile2D")) {
          Error("Add","Attempt to add a non-profile2D object");
          return;
       }
       TProfile2D *p1 = (TProfile2D*)h1;
       if (!h2->InheritsFrom("TProfile2D")) {
          Error("Add","Attempt to add a non-profile2D object");
          return;
       }
       TProfile2D *p2 = (TProfile2D*)h2;

    //*-*- Check profile compatibility
       Int_t nx = GetNbinsX();
       if (nx != p1->GetNbinsX() || nx != p2->GetNbinsX()) {
          Error("Add","Attempt to add profiles with different number of bins");
          return;
       }
       Int_t ny = GetNbinsY();
       if (ny != p1->GetNbinsY() || ny != p2->GetNbinsY()) {
          Error("Add","Attempt to add profiles with different number of bins");
          return;
       }

    //*-*- Add statistics
       Double_t ac1 = TMath::Abs(c1);
       Double_t ac2 = TMath::Abs(c2);
       fEntries = ac1*p1->GetEntries() + ac2*p2->GetEntries();
       fTsumw   = ac1*p1->fTsumw       + ac2*p2->fTsumw;
       fTsumw2  = ac1*p1->fTsumw2      + ac2*p2->fTsumw2;
       fTsumwx  = ac1*p1->fTsumwx      + ac2*p2->fTsumwx;
       fTsumwx2 = ac1*p1->fTsumwx2     + ac2*p2->fTsumwx2;
       fTsumwy  = ac1*p1->fTsumwy      + ac2*p2->fTsumwy;
       fTsumwy2 = ac1*p1->fTsumwy2     + ac2*p2->fTsumwy2;
       fTsumwxy = ac1*p1->fTsumwxy     + ac2*p2->fTsumwxy;
       fTsumwz  = ac1*p1->fTsumwz      + ac2*p2->fTsumwz;
       fTsumwz2 = ac1*p1->fTsumwz2     + ac2*p2->fTsumwz2;

    //*-*- Loop on bins (including underflows/overflows)
       Int_t bin,binx,biny;
       Double_t *cu1 = p1->GetW();
       Double_t *cu2 = p2->GetW();
       Double_t *er1 = p1->GetW2();
       Double_t *er2 = p2->GetW2();
       Double_t *en1 = p1->GetB();
       Double_t *en2 = p2->GetB();
       for (binx =0;binx<=nx+1;binx++) {
          for (biny =0;biny<=ny+1;biny++) {
             bin   = biny*(fXaxis.GetNbins()+2) + binx;
             fArray[bin]             =  c1*cu1[bin] +  c2*cu2[bin];
             fSumw2.fArray[bin]      = ac1*er1[bin] + ac2*er2[bin];
             if (fScaling) {
                fBinEntries.fArray[bin] = en1[bin];
             } else {
                fBinEntries.fArray[bin] = ac1*en1[bin] + ac2*en2[bin];
             }
          }
       }
    }

    //______________________________________________________________________________
     void TProfile2D::Approximate(Bool_t approx)
    {
    //     static function
    // set the fgApproximate flag. When the flag is true, the function GetBinError
    // will approximate the bin error with the average profile error on all bins
    // in the following situation only
    //  - the number of bins in the profile2D is less than 10404 (eg 100x100)
    //  - the bin number of entries is small ( <5)
    //  - the estimated bin error is extremely small compared to the bin content
    //  (see TProfile2D::GetBinError)

       fgApproximate = approx;
    }

    //______________________________________________________________________________
     Int_t TProfile2D::BufferEmpty(Bool_t deleteBuffer)
    {
    // Fill histogram with all entries in the buffer.
    // The buffer is deleted if deleteBuffer is true.

       // do we need to compute the bin size?
       Int_t nbentries = (Int_t)fBuffer[0];
       if (!nbentries) return 0;
       if (fXaxis.GetXmax() <= fXaxis.GetXmin()) {
          //find min, max of entries in buffer
         Double_t xmin = fBuffer[2];
         Double_t xmax = xmin;
         Double_t ymin = fBuffer[3];
         Double_t ymax = ymin;
        for (Int_t i=1;i<nbentries;i++) {
             Double_t x = fBuffer[4*i+2];
             if (x < xmin) xmin = x;
             if (x > xmax) xmax = x;
             Double_t y = fBuffer[4*i+3];
             if (y < ymin) ymin = y;
             if (y > ymax) ymax = y;
         }
          THLimitsFinder::GetLimitsFinder()->FindGoodLimits(this,xmin,xmax,ymin,ymax);
       }

       Double_t *buffer = fBuffer; fBuffer = 0;

       for (Int_t i=0;i<nbentries;i++) {
          Fill(buffer[4*i+2],buffer[4*i+3],buffer[4*i+4],buffer[4*i+1]);
       }

       if (deleteBuffer) { delete buffer;    fBufferSize = 0;}
       else              { fBuffer = buffer; fBuffer[0] = 0;}
       return nbentries;
    }

    //______________________________________________________________________________
     Int_t TProfile2D::BufferFill(Axis_t x, Axis_t y, Axis_t z, Stat_t w)
    {
    // accumulate arguments in buffer. When buffer is full, empty the buffer
    // fBuffer[0] = number of entries in buffer
    // fBuffer[1] = w of first entry
    // fBuffer[2] = x of first entry

       Int_t nbentries = (Int_t)fBuffer[0];
       if (nbentries >= fBufferSize) {
          BufferEmpty(kTRUE);
          return Fill(x,y,z,w);
       }
       fBuffer[4*nbentries+1] = w;
       fBuffer[4*nbentries+2] = x;
       fBuffer[4*nbentries+3] = y;
       fBuffer[4*nbentries+4] = z;
       fBuffer[0] += 1;
       return -2;
    }

    //______________________________________________________________________________
     void TProfile2D::Copy(TObject &obj) const
    {
    //*-*-*-*-*-*-*-*Copy a Profile2D histogram to a new profile2D histogram*-*-*-*
    //*-*            =======================================================

       TH2D::Copy(((TProfile2D&)obj));
       fBinEntries.Copy(((TProfile2D&)obj).fBinEntries);
       ((TProfile2D&)obj).fZmin = fZmin;
       ((TProfile2D&)obj).fZmax = fZmax;
       ((TProfile2D&)obj).fScaling = fScaling;
       ((TProfile2D&)obj).fErrorMode = fErrorMode;
       ((TProfile2D&)obj).fTsumwz  = fTsumwz;
       ((TProfile2D&)obj).fTsumwz2 = fTsumwz2;
    }

    //______________________________________________________________________________
     void TProfile2D::Divide(TF1 *, Double_t )
    {
       // Performs the operation: this = this/(c1*f1)

       Error("Divide","Function not implemented for TProfile2D");
       return;
    }

    //______________________________________________________________________________
     void TProfile2D::Divide(const TH1 *h1)
    {
    //*-*-*-*-*-*-*-*-*-*-*Divide this profile2D by h1*-*-*-*-*-*-*-*-*-*-*-*-*
    //*-*                  ===========================
    //
    //   this = this/h1
    //

       if (!h1) {
          Error("Divide","Attempt to divide a non-existing profile2D");
          return;
       }
       if (!h1->InheritsFrom("TProfile2D")) {
          Error("Divide","Attempt to divide a non-profile2D object");
          return;
       }
       TProfile2D *p1 = (TProfile2D*)h1;

    //*-*- Check profile compatibility
       Int_t nx = GetNbinsX();
       if (nx != p1->GetNbinsX()) {
          Error("Divide","Attempt to divide profiles with different number of bins");
          return;
       }
       Int_t ny = GetNbinsY();
       if (ny != p1->GetNbinsY()) {
          Error("Divide","Attempt to divide profiles with different number of bins");
          return;
       }

    //*-*- Reset statistics
       fEntries = fTsumw   = fTsumw2 = fTsumwx = fTsumwx2 = 0;

    //*-*- Loop on bins (including underflows/overflows)
       Int_t bin,binx,biny;
       Double_t *cu1 = p1->GetW();
       Double_t *er1 = p1->GetW2();
       Double_t *en1 = p1->GetB();
       Double_t c0,c1,w,z,x,y;
       for (binx =0;binx<=nx+1;binx++) {
          for (biny =0;biny<=ny+1;biny++) {
             bin   = biny*(fXaxis.GetNbins()+2) + binx;
             c0  = fArray[bin];
             c1  = cu1[bin];
             if (c1) w = c0/c1;
             else    w = 0;
             fArray[bin] = w;
             z = TMath::Abs(w);
             x = fXaxis.GetBinCenter(binx);
             y = fYaxis.GetBinCenter(biny);
             fEntries++;
             fTsumw   += z;
             fTsumw2  += z*z;
             fTsumwx  += z*x;
             fTsumwx2 += z*x*x;
             fTsumwy  += z*y;
             fTsumwy2 += z*y*y;
             fTsumwxy += z*x*y;
             fTsumwz  += z;
             fTsumwz2 += z*z;
             Double_t e0 = fSumw2.fArray[bin];
             Double_t e1 = er1[bin];
             Double_t c12= c1*c1;
             if (!c1) fSumw2.fArray[bin] = 0;
             else     fSumw2.fArray[bin] = (e0*e0*c1*c1 + e1*e1*c0*c0)/(c12*c12);
             if (!en1[bin]) fBinEntries.fArray[bin] = 0;
             else           fBinEntries.fArray[bin] /= en1[bin];
          }
       }
    }

    //______________________________________________________________________________
     void TProfile2D::Divide(const TH1 *h1, const TH1 *h2, Double_t c1, Double_t c2, Option_t *option)
    {
    //*-*-*-*-*Replace contents of this profile2D by the division of h1 by h2*-*-*
    //*-*      ==============================================================
    //
    //   this = c1*h1/(c2*h2)
    //

       TString opt = option;
       opt.ToLower();
       Bool_t binomial = kFALSE;
       if (opt.Contains("b")) binomial = kTRUE;
       if (!h1 || !h2) {
          Error("Divide","Attempt to divide a non-existing profile2D");
          return;
       }
       if (!h1->InheritsFrom("TProfile2D")) {
          Error("Divide","Attempt to divide a non-profile2D object");
          return;
       }
       TProfile2D *p1 = (TProfile2D*)h1;
       if (!h2->InheritsFrom("TProfile2D")) {
          Error("Divide","Attempt to divide a non-profile2D object");
          return;
       }
       TProfile2D *p2 = (TProfile2D*)h2;

    //*-*- Check histogram compatibility
       Int_t nx = GetNbinsX();
       if (nx != p1->GetNbinsX() || nx != p2->GetNbinsX()) {
          Error("Divide","Attempt to divide profiles with different number of bins");
          return;
       }
       Int_t ny = GetNbinsY();
       if (ny != p1->GetNbinsY() || ny != p2->GetNbinsY()) {
          Error("Divide","Attempt to divide profiles with different number of bins");
          return;
       }
       if (!c2) {
          Error("Divide","Coefficient of dividing profile cannot be zero");
          return;
       }

    //*-*- Reset statistics
       fEntries = fTsumw   = fTsumw2 = fTsumwx = fTsumwx2 = 0;

    //*-*- Loop on bins (including underflows/overflows)
       Int_t bin,binx,biny;
       Double_t *cu1 = p1->GetW();
       Double_t *cu2 = p2->GetW();
       Double_t *er1 = p1->GetW2();
       Double_t *er2 = p2->GetW2();
       Double_t *en1 = p1->GetB();
       Double_t *en2 = p2->GetB();
       Double_t b1,b2,w,z,x,y,d1,d2;
       d1 = c1*c1;
       d2 = c2*c2;
       for (binx =0;binx<=nx+1;binx++) {
          for (biny =0;biny<=ny+1;biny++) {
             bin   = biny*(fXaxis.GetNbins()+2) + binx;
             b1  = cu1[bin];
             b2  = cu2[bin];
             if (b2) w = c1*b1/(c2*b2);
             else    w = 0;
             fArray[bin] = w;
             z = TMath::Abs(w);
             x = fXaxis.GetBinCenter(binx);
             y = fYaxis.GetBinCenter(biny);
             fEntries++;
             fTsumw   += z;
             fTsumw2  += z*z;
             fTsumwx  += z*x;
             fTsumwx2 += z*x*x;
             fTsumwy  += z*y;
             fTsumwy2 += z*y*y;
             fTsumwxy += z*x*y;
             fTsumwz  += z;
             fTsumwz2 += z*z;
             Double_t e1 = er1[bin];
             Double_t e2 = er2[bin];
             Double_t b22= b2*b2*d2;
             if (!b2) fSumw2.fArray[bin] = 0;
             else {
                if (binomial) {
                   fSumw2.fArray[bin] = TMath::Abs(w*(1-w)/(c2*b2));
                } else {
                   fSumw2.fArray[bin] = d1*d2*(e1*e1*b2*b2 + e2*e2*b1*b1)/(b22*b22);
                }
             }
             if (!en2[bin]) fBinEntries.fArray[bin] = 0;
             else           fBinEntries.fArray[bin] = en1[bin]/en2[bin];
          }
       }
    }

    //______________________________________________________________________________
     TH1 *TProfile2D::DrawCopy(Option_t *option) const
    {
    //*-*-*-*-*-*-*-*Draw a copy of this profile2D histogram*-*-*-*-*-*-*-*-*-*-*
    //*-*            =======================================
       TProfile2D *newpf = new TProfile2D();
       Copy(*newpf);
       newpf->SetDirectory(0);
       newpf->SetBit(kCanDelete);
       newpf->AppendPad(option);
       return newpf;
    }

    //______________________________________________________________________________
     Int_t TProfile2D::Fill(Axis_t x, Axis_t y, Axis_t z)
    {
    //*-*-*-*-*-*-*-*-*-*-*Fill a Profile2D histogram (no weights)*-*-*-*-*-*-*-*
    //*-*                  =======================================

       if (fBuffer) return BufferFill(x,y,z,1);

       Int_t bin,binx,biny;

       if (fZmin != fZmax) {
          if (z <fZmin || z> fZmax) return -1;
       }

       fEntries++;
       binx =fXaxis.FindBin(x);
       biny =fYaxis.FindBin(y);
       bin  = biny*(fXaxis.GetNbins()+2) + binx;
       AddBinContent(bin, z);
       fSumw2.fArray[bin] += (Stat_t)z*z;
       fBinEntries.fArray[bin] += 1;
       if (binx == 0 || binx > fXaxis.GetNbins()) {
          if (!fgStatOverflows) return -1;
       }
       if (biny == 0 || biny > fYaxis.GetNbins()) {
          if (!fgStatOverflows) return -1;
       }
       ++fTsumw;
       ++fTsumw2;
       fTsumwx  += x;
       fTsumwx2 += x*x;
       fTsumwy  += y;
       fTsumwy2 += y*y;
       fTsumwxy += x*y;
       fTsumwz  += z;
       fTsumwz2 += z*z;
       return bin;
    }

    //______________________________________________________________________________
     Int_t TProfile2D::Fill(Axis_t x, const char *namey, Axis_t z)
    {
    // Fill a Profile2D histogram (no weights)
    //
       Int_t bin,binx,biny;

       if (fZmin != fZmax) {
          if (z <fZmin || z> fZmax) return -1;
       }

       fEntries++;
       binx =fXaxis.FindBin(x);
       biny =fYaxis.FindBin(namey);
       bin  = biny*(fXaxis.GetNbins()+2) + binx;
       AddBinContent(bin, z);
       fSumw2.fArray[bin] += (Stat_t)z*z;
       fBinEntries.fArray[bin] += 1;
       if (binx == 0 || binx > fXaxis.GetNbins()) {
          if (!fgStatOverflows) return -1;
       }
       if (biny == 0 || biny > fYaxis.GetNbins()) return -1;
       Axis_t y = fYaxis.GetBinCenter(biny);
       ++fTsumw;
       ++fTsumw2;
       fTsumwx  += x;
       fTsumwx2 += x*x;
       fTsumwy  += y;
       fTsumwy2 += y*y;
       fTsumwxy += x*y;
       fTsumwz  += z;
       fTsumwz2 += z*z;
       return bin;
    }

    //______________________________________________________________________________
     Int_t TProfile2D::Fill(const char *namex, const char *namey, Axis_t z)
    {
    // Fill a Profile2D histogram (no weights)
    //
       Int_t bin,binx,biny;

       if (fZmin != fZmax) {
          if (z <fZmin || z> fZmax) return -1;
       }

       fEntries++;
       binx =fXaxis.FindBin(namex);
       biny =fYaxis.FindBin(namey);
       bin  = biny*(fXaxis.GetNbins()+2) + binx;
       AddBinContent(bin, z);
       fSumw2.fArray[bin] += (Stat_t)z*z;
       fBinEntries.fArray[bin] += 1;
       if (binx == 0 || binx > fXaxis.GetNbins()) return -1;
       if (biny == 0 || biny > fYaxis.GetNbins()) return -1;
       Axis_t x = fYaxis.GetBinCenter(binx);
       Axis_t y = fYaxis.GetBinCenter(biny);
       ++fTsumw;
       ++fTsumw2;
       fTsumwx  += x;
       fTsumwx2 += x*x;
       fTsumwy  += y;
       fTsumwy2 += y*y;
       fTsumwxy += x*y;
       fTsumwz  += z;
       fTsumwz2 += z*z;
       return bin;
    }

    //______________________________________________________________________________
     Int_t TProfile2D::Fill(const char *namex, Axis_t y, Axis_t z)
    {
    // Fill a Profile2D histogram (no weights)
    //
       Int_t bin,binx,biny;

       if (fZmin != fZmax) {
          if (z <fZmin || z> fZmax) return -1;
       }

       fEntries++;
       binx =fXaxis.FindBin(namex);
       biny =fYaxis.FindBin(y);
       bin  = biny*(fXaxis.GetNbins()+2) + binx;
       AddBinContent(bin, z);
       fSumw2.fArray[bin] += (Stat_t)z*z;
       fBinEntries.fArray[bin] += 1;
       if (binx == 0 || binx > fXaxis.GetNbins()) return -1;
       if (biny == 0 || biny > fYaxis.GetNbins()) {
          if (!fgStatOverflows) return -1;
       }
       Axis_t x = fYaxis.GetBinCenter(binx);
       ++fTsumw;
       ++fTsumw2;
       fTsumwx  += x;
       fTsumwx2 += x*x;
       fTsumwy  += y;
       fTsumwy2 += y*y;
       fTsumwxy += x*y;
       fTsumwz  += z;
       fTsumwz2 += z*z;
       return bin;
    }

    //______________________________________________________________________________
     Int_t TProfile2D::Fill(Axis_t x, Axis_t y, Axis_t z, Stat_t w)
    {
    //*-*-*-*-*-*-*-*-*-*-*Fill a Profile2D histogram with weights*-*-*-*-*-*-*-*
    //*-*                  =======================================

       if (fBuffer) return BufferFill(x,y,z,w);

       Int_t bin,binx,biny;

       if (fZmin != fZmax) {
          if (z <fZmin || z> fZmax) return -1;
       }

       Stat_t u= (w > 0 ? w : -w);
       fEntries++;
       binx =fXaxis.FindBin(x);
       biny =fYaxis.FindBin(y);
       bin  = biny*(fXaxis.GetNbins()+2) + binx;
       AddBinContent(bin, u*z);
       fSumw2.fArray[bin] += u*z*z;
       fBinEntries.fArray[bin] += w;
       if (binx == 0 || binx > fXaxis.GetNbins()) {
          if (!fgStatOverflows) return -1;
       }
       if (biny == 0 || biny > fYaxis.GetNbins()) {
          if (!fgStatOverflows) return -1;
       }
       fTsumw   += u;
       fTsumw2  += u*u;
       fTsumwx  += u*x;
       fTsumwx2 += u*x*x;
       fTsumwy  += u*y;
       fTsumwy2 += u*y*y;
       fTsumwxy += u*x*y;
       fTsumwz  += u*z;
       fTsumwz2 += u*z*z;
       return bin;
    }

    //______________________________________________________________________________
     Stat_t TProfile2D::GetBinContent(Int_t bin) const
    {
    //*-*-*-*-*-*-*Return bin content of a Profile2D histogram*-*-*-*-*-*-*-*-*
    //*-*          ===========================================

       if (fBuffer) ((TProfile2D*)this)->BufferEmpty();

       if (bin < 0 || bin >= fNcells) return 0;
       if (fBinEntries.fArray[bin] == 0) return 0;
       if (!fArray) return 0;
       return fArray[bin]/fBinEntries.fArray[bin];
    }

    //______________________________________________________________________________
     Stat_t TProfile2D::GetBinEntries(Int_t bin) const
    {
    //*-*-*-*-*-*-*Return bin entries of a Profile2D histogram*-*-*-*-*-*-*-*-*
    //*-*          ===========================================

       if (fBuffer) ((TProfile2D*)this)->BufferEmpty();

       if (bin < 0 || bin >= fNcells) return 0;
       return fBinEntries.fArray[bin];
    }

    //______________________________________________________________________________
     Stat_t TProfile2D::GetBinError(Int_t bin) const
    {
    //*-*-*-*-*-*-*Return bin error of a Profile2D histogram*-*-*-*-*-*-*-*-*
    //
    // Computing errors: A moving field
    // =================================
    // The computation of errors for a TProfile2D has evolved with the versions
    // of ROOT. The difficulty is in computing errors for bins with low statistics.
    // - prior to version 3.10, we had no special treatment of low statistic bins.
    //   As a result, these bins had huge errors. The reason is that the
    //   expression eprim2 is very close to 0 (rounding problems) or 0.
    // - The algorithm is modified/protected for the case
    //   when a TProfile2D is projected (ProjectionX). The previous algorithm
    //   generated a N^2 problem when projecting a TProfile2D with a large number of
    //   bins (eg 100000).
    // - in version 3.10/02, a new static function TProfile::Approximate
    //   is introduced to enable or disable (default) the approximation.
    //   (see also comments in TProfile::GetBinError)

       if (fBuffer) ((TProfile2D*)this)->BufferEmpty();

       if (bin < 0 || bin >= fNcells) return 0;
       Stat_t cont = fArray[bin];
       Stat_t sum  = fBinEntries.fArray[bin];
       Stat_t err2 = fSumw2.fArray[bin];
       if (sum == 0) return 0;
       Stat_t eprim;
       Stat_t contsum = cont/sum;
       Stat_t eprim2  = TMath::Abs(err2/sum - contsum*contsum);
       eprim          = TMath::Sqrt(eprim2);
       Double_t test = 1;
       if (err2 != 0 && sum < 5) test = eprim2*sum/err2;
       //if (eprim <= 0) { //was in 3.10/01
       if (fgApproximate && fNcells <=10404 && (test < 1.e-4 || eprim2 < 1e-6)) { //in 3.10/02
          Stat_t scont, ssum, serr2;
          scont = ssum = serr2 = 0;
          for (Int_t i=1;i<fNcells;i++) {
             if (fSumw2.fArray[i] <= 0) continue; //added in 3.10/02
             scont += fArray[i];
             ssum  += fBinEntries.fArray[i];
             serr2 += fSumw2.fArray[i];
          }
          Stat_t scontsum = scont/ssum;
          Stat_t seprim2  = TMath::Abs(serr2/ssum - scontsum*scontsum);
          eprim           = TMath::Sqrt(seprim2);
       }
       if (fErrorMode == kERRORMEAN) return eprim/TMath::Sqrt(sum);
       else if (fErrorMode == kERRORSPREAD) return eprim;
       else if (fErrorMode == kERRORSPREADI) {
          if (eprim != 0) return eprim/TMath::Sqrt(sum);
          return 1/TMath::Sqrt(12*sum);
       }
       else if (fErrorMode == kERRORSPREADG) {
          return eprim/TMath::Sqrt(sum);
       }
       else return eprim;
    }

    //______________________________________________________________________________
     Option_t *TProfile2D::GetErrorOption() const
    {
    //*-*-*-*-*-*-*-*-*-*Return option to compute profile2D errors*-*-*-*-*-*-*-*
    //*-*                =========================================

       if (fErrorMode == kERRORSPREAD)  return "s";
       if (fErrorMode == kERRORSPREADI) return "i";
       if (fErrorMode == kERRORSPREADG) return "g";
       return "";
    }

    //______________________________________________________________________________
     void TProfile2D::GetStats(Stat_t *stats) const
    {
       // fill the array stats from the contents of this profile
       // The array stats must be correctly dimensionned in the calling program.
       // stats[0] = sumw
       // stats[1] = sumw2
       // stats[2] = sumwx
       // stats[3] = sumwx2
       // stats[4] = sumwy
       // stats[5] = sumwy2
       // stats[6] = sumwxy
       // stats[7] = sumwz
       // stats[8] = sumwz2
       //
       // The function recomputes the statistics quantities
       // from the bin contents in the current axis range.

       // Loop on bins
       Int_t bin, binx, biny;
       Stat_t w;
       Axis_t x,y;
       for (bin=0;bin<9;bin++) stats[bin] = 0;
       if (!fBinEntries.fArray) return;
       for (biny=fYaxis.GetFirst();biny<=fYaxis.GetLast();biny++) {
          y = fYaxis.GetBinCenter(biny);
          for (binx=fXaxis.GetFirst();binx<=fXaxis.GetLast();binx++) {
             bin = GetBin(binx,biny);
             w         = fBinEntries.fArray[bin];
             x         = fXaxis.GetBinCenter(binx);
             stats[0] += w;
             stats[1] += w*w;
             stats[2] += w*x;
             stats[3] += w*x*x;
             stats[4] += w*y;
             stats[5] += w*y*y;
             stats[6] += w*x*y;
             stats[7] += fArray[bin];
             stats[8] += fSumw2.fArray[bin];
          }
       }
    }

    //___________________________________________________________________________
     void TProfile2D::LabelsDeflate(Option_t *ax)
    {
    // Reduce the number of bins for this axis to the number of bins having a label.

       TAxis *axis = GetXaxis();
       if (ax[0] == 'y' || ax[0] == 'Y') axis = GetYaxis();
       if (!axis->GetLabels()) return;
       TIter next(axis->GetLabels());
       TObject *obj;
       Int_t nbins = 0;
       while ((obj = next())) {
          if (obj->GetUniqueID()) nbins++;
       }
       if (nbins < 2) nbins = 2;
       TProfile2D *hold = (TProfile2D*)Clone();
       hold->SetDirectory(0);

       Int_t  nbxold = fXaxis.GetNbins();
       Double_t xmin = axis->GetXmin();
       Double_t xmax = axis->GetBinUpEdge(nbins);
       axis->SetRange(0,0);
       axis->Set(nbins,xmin,xmax);
       Int_t  nbinsx = fXaxis.GetNbins();
       Int_t  nbinsy = fYaxis.GetNbins();
       Int_t ncells = (nbinsx+2)*(nbinsy+2);
       SetBinsLength(ncells);
       fBinEntries.Set(ncells);
       fSumw2.Set(ncells);

       //now loop on all bins and refill
       Int_t bin,ibin,binx,biny;
       for (biny=1;biny<=nbinsy;biny++) {
          for (binx=1;binx<=nbinsx;binx++) {
             bin   = biny*(nbxold+2) + binx;
             ibin  = biny*(nbinsx+2) + binx;
             fArray[ibin] = hold->fArray[bin];
             fBinEntries.fArray[ibin] = hold->fBinEntries.fArray[bin];
             fSumw2.fArray[ibin] = hold->fSumw2.fArray[bin];
          }
       }
       delete hold;
    }

    //___________________________________________________________________________
     void TProfile2D::LabelsInflate(Option_t *ax)
    {
    // Double the number of bins for axis.
    // Refill histogram
    // This function is called by TAxis::FindBin(const char *label)

       TAxis *axis = GetXaxis();
       if (ax[0] == 'y' || ax[0] == 'Y') axis = GetYaxis();
       TProfile2D *hold = (TProfile2D*)Clone();
       hold->SetDirectory(0);

       Int_t  nbxold = fXaxis.GetNbins();
       Int_t  nbyold = fYaxis.GetNbins();
       Int_t  nbins  = axis->GetNbins();
       Double_t xmin = axis->GetXmin();
       Double_t xmax = axis->GetXmax();
       xmax = xmin + 2*(xmax-xmin);
       axis->SetRange(0,0);
       axis->Set(2*nbins,xmin,xmax);
       nbins *= 2;
       Int_t  nbinsx = fXaxis.GetNbins();
       Int_t  nbinsy = fYaxis.GetNbins();
       Int_t ncells = (nbinsx+2)*(nbinsy+2);
       SetBinsLength(ncells);
       fBinEntries.Set(ncells);
       fSumw2.Set(ncells);

       //now loop on all bins and refill
       Int_t bin,ibin,binx,biny;
       for (biny=1;biny<=nbinsy;biny++) {
          for (binx=1;binx<=nbinsx;binx++) {
             bin   = biny*(nbxold+2) + binx;
             ibin  = biny*(nbinsx+2) + binx;
             if (binx <= nbxold && biny <= nbyold) {
                fArray[ibin] = hold->fArray[bin];
                fBinEntries.fArray[ibin] = hold->fBinEntries.fArray[bin];
                fSumw2.fArray[ibin] = hold->fSumw2.fArray[bin];
             } else {
                fArray[ibin] = 0;
                fBinEntries.fArray[ibin] = 0;
                fSumw2.fArray[ibin] = 0;
             }
          }
       }
       delete hold;
    }

    //___________________________________________________________________________
     void TProfile2D::LabelsOption(Option_t *option, Option_t *ax)
    {
    //  Set option(s) to draw axis with labels
    //  option = "a" sort by alphabetic order
    //         = ">" sort by decreasing values
    //         = "<" sort by increasing values
    //         = "h" draw labels horizonthal
    //         = "v" draw labels vertical
    //         = "u" draw labels up (end of label right adjusted)
    //         = "d" draw labels down (start of label left adjusted)

       TAxis *axis = GetXaxis();
       if (ax[0] == 'y' || ax[0] == 'Y') axis = GetYaxis();
       THashList *labels = axis->GetLabels();
       if (!labels) {
          Warning("LabelsOption","Cannot sort. No labels");
          return;
       }
       TString opt = option;
       opt.ToLower();
       if (opt.Contains("h")) {
          fXaxis.SetBit(TAxis::kLabelsHori);
          fXaxis.ResetBit(TAxis::kLabelsVert);
          fXaxis.ResetBit(TAxis::kLabelsDown);
          fXaxis.ResetBit(TAxis::kLabelsUp);
       }
        if (opt.Contains("v")) {
          fXaxis.SetBit(TAxis::kLabelsVert);
          fXaxis.ResetBit(TAxis::kLabelsHori);
          fXaxis.ResetBit(TAxis::kLabelsDown);
          fXaxis.ResetBit(TAxis::kLabelsUp);
       }
       if (opt.Contains("u")) {
          fXaxis.SetBit(TAxis::kLabelsUp);
          fXaxis.ResetBit(TAxis::kLabelsVert);
          fXaxis.ResetBit(TAxis::kLabelsDown);
          fXaxis.ResetBit(TAxis::kLabelsHori);
       }
       if (opt.Contains("d")) {
          fXaxis.SetBit(TAxis::kLabelsDown);
          fXaxis.ResetBit(TAxis::kLabelsVert);
          fXaxis.ResetBit(TAxis::kLabelsHori);
          fXaxis.ResetBit(TAxis::kLabelsUp);
       }
       Int_t sort = -1;
       if (opt.Contains("a")) sort = 0;
       if (opt.Contains(">")) sort = 1;
       if (opt.Contains("<")) sort = 2;
       if (sort < 0) return;

       Int_t nx = fXaxis.GetNbins()+2;
       Int_t ny = fYaxis.GetNbins()+2;
       Int_t n = TMath::Min(axis->GetNbins(), labels->GetSize());
       Int_t *a = new Int_t[n+2];
       Int_t i,j,k,bin;
       Double_t *sumw   = new Double_t[nx*ny];
       Double_t *errors = new Double_t[nx*ny];
       Double_t *ent    = new Double_t[nx*ny];
       THashList *labold = new THashList(labels->GetSize(),1);
       TIter nextold(labels);
       TObject *obj;
       while ((obj=nextold())) {
          labold->Add(obj);
       }
       labels->Clear();
       if (sort > 0) {
          //---sort by values of bins
          Double_t *pcont = new Double_t[n+2];
          for (i=0;i<=n;i++) pcont[i] = 0;
          for (i=1;i<nx;i++) {
             for (j=1;j<ny;j++) {
                bin = i+nx*j;
                sumw[bin]   = fArray[bin];
                errors[bin] = fSumw2.fArray[bin];
                ent[bin]    = fBinEntries.fArray[bin];
                if (axis == GetXaxis()) k = i;
                else                    k = j;
                if (fBinEntries.fArray[bin] != 0) pcont[k-1] += fArray[bin]/fBinEntries.fArray[bin];
             }
          }
          if (sort ==1) TMath::Sort(n,pcont,a,kTRUE);  //sort by decreasing values
          else          TMath::Sort(n,pcont,a,kFALSE); //sort by increasing values
          delete [] pcont;
          for (i=0;i<n;i++) {
             obj = labold->At(a[i]);
             labels->Add(obj);
             obj->SetUniqueID(i+1);
          }
          for (i=1;i<nx;i++) {
             for (j=1;j<ny;j++) {
                bin = i+nx*j;
                if (axis == GetXaxis()) {
                   fArray[bin] = sumw[a[i-1]+1+nx*j];
                   fSumw2.fArray[bin] = errors[a[i-1]+1+nx*j];
                   fBinEntries.fArray[bin] = ent[a[i-1]+1+nx*j];
                } else {
                   fArray[bin] = sumw[i+nx*(a[j-1]+1)];
                   fSumw2.fArray[bin] = errors[i+nx*(a[j-1]+1)];
                   fBinEntries.fArray[bin] = ent[i+nx*(a[j-1]+1)];
                }
             }
          }
       } else {
          //---alphabetic sort
          const UInt_t kUsed = 1<<18;
          TObject *objk=0;
          a[0] = 0;
          a[n+1] = n+1;
          for (i=1;i<=n;i++) {
             const char *label = "zzzzzzzzzzzz";
             for (j=1;j<=n;j++) {
                obj = labold->At(j-1);
                if (!obj) continue;
                if (obj->TestBit(kUsed)) continue;
                //use strcasecmp for case non-sensitive sort (may be an option)
                if (strcmp(label,obj->GetName()) < 0) continue;
                objk = obj;
                a[i] = j;
                label = obj->GetName();
             }
             if (objk) {
                objk->SetUniqueID(i);
                labels->Add(objk);
                objk->SetBit(kUsed);
             }
          }
          for (i=1;i<=n;i++) {
             obj = labels->At(i-1);
             if (!obj) continue;
             obj->ResetBit(kUsed);
          }
          for (i=0;i<nx;i++) {
             for (j=0;j<ny;j++) {
                bin = i+nx*j;
                sumw[bin]   = fArray[bin];
                errors[bin] = fSumw2.fArray[bin];
                ent[bin]    = fBinEntries.fArray[bin];
             }
          }
          for (i=0;i<nx;i++) {
             for (j=0;j<ny;j++) {
                bin = i+nx*j;
                if (axis == GetXaxis()) {
                   fArray[bin] = sumw[a[i]+nx*j];
                   fSumw2.fArray[bin] = errors[a[i]+nx*j];
                   fBinEntries.fArray[bin] = ent[a[i]+nx*j];
                } else {
                   fArray[bin] = sumw[i+nx*a[j]];
                   fSumw2.fArray[bin] = errors[i+nx*a[j]];
                   fBinEntries.fArray[bin] = ent[i+nx*a[j]];
                }
             }
          }
       }
       delete labold;
       if (a)      delete [] a;
       if (sumw)   delete [] sumw;
       if (errors) delete [] errors;
       if (ent)    delete [] ent;
    }

    //______________________________________________________________________________
     Int_t TProfile2D::Merge(TCollection *list)
    {
       //Merge all histograms in the collection in this histogram.
       //This function computes the min/max for the axes,
       //compute a new number of bins, if necessary,
       //add bin contents, errors and statistics.
       //The function returns the merged number of entries if the merge is
       //successfull, -1 otherwise.
       //
       //IMPORTANT remark. The 2 axis x and y may have different number
       //of bins and different limits, BUT the largest bin width must be
       //a multiple of the smallest bin width.

       if (!list) return 0;
       TIter next(list);
       Double_t umin,umax,vmin,vmax;
       Int_t nx,ny;
       Double_t xmin  = fXaxis.GetXmin();
       Double_t xmax  = fXaxis.GetXmax();
       Double_t ymin  = fYaxis.GetXmin();
       Double_t ymax  = fYaxis.GetXmax();
       Double_t bwix  = fXaxis.GetBinWidth(1);
       Double_t bwiy  = fYaxis.GetBinWidth(1);
       Int_t    nbix  = fXaxis.GetNbins();
       Int_t    nbiy  = fYaxis.GetNbins();

       TProfile2D *h;
       Int_t nentries=0;
       Bool_t same = kTRUE;
       while ((h=(TProfile2D*)next())) {
          if (!h->InheritsFrom(TProfile2D::Class())) {
             Error("Add","Attempt to add object of class: %s to a %s",h->ClassName(),this->ClassName());
             return -1;
          }
          //import statistics
          nentries += (Int_t)h->GetEntries();

          // find min/max of the axes
          umin = h->GetXaxis()->GetXmin();
          umax = h->GetXaxis()->GetXmax();
          vmin = h->GetYaxis()->GetXmin();
          vmax = h->GetYaxis()->GetXmax();
          nx   = h->GetXaxis()->GetNbins();
          ny   = h->GetYaxis()->GetNbins();
          if (nx != nbix || ny != nbiy ||
                  umin != xmin || umax != xmax || vmin != ymin || vmax != ymax) {
             same = kFALSE;
             if (umin < xmin) xmin = umin;
             if (umax > xmax) xmax = umax;
             if (vmin < ymin) ymin = vmin;
             if (vmax > ymax) ymax = vmax;
             if (h->GetXaxis()->GetBinWidth(1) > bwix) bwix = h->GetXaxis()->GetBinWidth(1);
             if (h->GetYaxis()->GetBinWidth(1) > bwiy) bwiy = h->GetYaxis()->GetBinWidth(1);
          }
       }

       //  if different binning compute best binning
       if (!same) {
          nbix = (Int_t) ((xmax-xmin)/bwix +0.1); while(nbix > 100) nbix /= 2;
          nbiy = (Int_t) ((ymax-ymin)/bwiy +0.1); while(nbiy > 100) nbiy /= 2;
          SetBins(nbix,xmin,xmax,nbiy,ymin,ymax);
       }

       //merge bin contents and errors
       next.Reset();
       Int_t ibin, bin, binx, biny, ix, iy;
       while ((h=(TProfile2D*)next())) {
          nx   = h->GetXaxis()->GetNbins();
          ny   = h->GetYaxis()->GetNbins();
          for (biny=0;biny<=ny+1;biny++) {
             iy = fYaxis.FindBin(h->GetBinCenter(biny));
             for (binx=0;binx<=nx+1;binx++) {
                ix = fXaxis.FindBin(h->GetBinCenter(binx));
                bin = binx +(nx+2)*biny;
                ibin = ix +(nbix+2)*iy;
                fArray[ibin]             += h->GetW()[bin];
                fSumw2.fArray[ibin]      += h->GetW2()[bin];
                fBinEntries.fArray[ibin] += h->GetB()[bin];
             }
          }
          fEntries += h->GetEntries();
          fTsumw   += h->fTsumw;
          fTsumw2  += h->fTsumw2;
          fTsumwx  += h->fTsumwx;
          fTsumwx2 += h->fTsumwx2;
          fTsumwy  += h->fTsumwy;
          fTsumwy2 += h->fTsumwy2;
          fTsumwxy += h->fTsumwxy;
          fTsumwz  += h->fTsumwz;
          fTsumwz2 += h->fTsumwz2;
      }

       return nentries;
    }

    //______________________________________________________________________________
     void TProfile2D::Multiply(TF1 *, Double_t )
    {
       // Performs the operation: this = this*c1*f1

       Error("Multiply","Function not implemented for TProfile2D");
       return;
    }

    //______________________________________________________________________________
     void TProfile2D::Multiply(const TH1 *)
    {
    //*-*-*-*-*-*-*-*-*-*-*Multiply this profile2D by h1*-*-*-*-*-*-*-*-*-*-*-*
    //*-*                  =============================
    //
    //   this = this*h1
    //
       Error("Multiply","Multiplication of profile2D histograms not implemented");
    }

    //______________________________________________________________________________
     void TProfile2D::Multiply(const TH1 *, const TH1 *, Double_t, Double_t, Option_t *)
    {
    //*-*-*-*-*Replace contents of this profile2D by multiplication of h1 by h2*-*
    //*-*      ================================================================
    //
    //   this = (c1*h1)*(c2*h2)
    //

       Error("Multiply","Multiplication of profile2D histograms not implemented");
    }

    //______________________________________________________________________________
     TH2D *TProfile2D::ProjectionXY(const char *name, Option_t *option) const
    {
    //*-*-*-*-*Project this profile2D into a 2-D histogram along X,Y*-*-*-*-*-*-*
    //*-*      =====================================================
    //
    //   The projection is always of the type TH2D.
    //
    //   if option "E" is specified, the errors are computed. (default)
    //
    //

      TString opt = option;
      opt.ToLower();
      Int_t nx = fXaxis.GetNbins();
      Int_t ny = fYaxis.GetNbins();

    // Create the projection histogram
      char *pname = (char*)name;
      if (strcmp(name,"_px") == 0) {
         Int_t nch = strlen(GetName()) + 4;
         pname = new char[nch];
         sprintf(pname,"%s%s",GetName(),name);
      }
      TH2D *h1 = new TH2D(pname,GetTitle(),nx,fXaxis.GetXmin(),fXaxis.GetXmax(),ny,fYaxis.GetXmin(),fYaxis.GetXmax());
      Bool_t computeErrors = kFALSE;
      if (opt.Contains("e")) {h1->Sumw2(); computeErrors = kTRUE;}
      if (pname != name)  delete [] pname;

    // Fill the projected histogram
      Int_t bin, binx, biny;
      Double_t cont,err;
      for (binx =0;binx<=nx+1;binx++) {
         for (biny =0;biny<=ny+1;biny++) {
            bin   = biny*(fXaxis.GetNbins()+2) + binx;
            cont  = GetBinContent(bin);
            err   = GetBinError(bin);
            if (cont)          h1->Fill(fXaxis.GetBinCenter(binx),fYaxis.GetBinCenter(biny), cont);
            if (computeErrors) h1->SetBinError(bin,err);
         }
      }
      h1->SetEntries(fEntries);
      return h1;
    }

    //______________________________________________________________________________
     void TProfile2D::Reset(Option_t *option)
    {
    //*-*-*-*-*-*-*-*-*-*Reset contents of a Profile2D histogram*-*-*-*-*-*-*-*
    //*-*                =======================================
      TH2D::Reset(option);
      fBinEntries.Reset();
      fTsumwz = fTsumwz2 = 0;
    }

    //______________________________________________________________________________
     void TProfile2D::SavePrimitive(ofstream &out, Option_t *option)
    {
       // Save primitive as a C++ statement(s) on output stream out

       //Note the following restrictions in the code generated:
       // - variable bin size not implemented
       // - SetErrorOption not implemented

       char quote = '"';
       out <<"   "<<endl;
       out <<"   "<<"ClassName()"<<" *";

       out << GetName() << " = new " << ClassName() << "(" << quote
           << GetName() << quote << "," << quote<< GetTitle() << quote
           << "," << GetXaxis()->GetNbins();
       out << "," << GetXaxis()->GetXmin()
           << "," << GetXaxis()->GetXmax();
       out << "," << GetYaxis()->GetNbins();
       out << "," << GetYaxis()->GetXmin()
           << "," << GetYaxis()->GetXmax();
       out << "," << fZmin
           << "," << fZmax;
       out << ");" << endl;

       // save bin entries
       Int_t bin;
       for (bin=0;bin<fNcells;bin++) {
          Double_t bi = GetBinEntries(bin);
          if (bi) {
             out<<"   "<<GetName()<<"->SetBinEntries("<<bin<<","<<bi<<");"<<endl;
          }
       }
       //save bin contents
       for (bin=0;bin<fNcells;bin++) {
          Double_t bc = fArray[bin];
          if (bc) {
             out<<"   "<<GetName()<<"->SetBinContent("<<bin<<","<<bc<<");"<<endl;
          }
       }
       // save bin errors
       if (fSumw2.fN) {
          for (bin=0;bin<fNcells;bin++) {
             Double_t be = TMath::Sqrt(fSumw2.fArray[bin]);
             if (be) {
                out<<"   "<<GetName()<<"->SetBinError("<<bin<<","<<be<<");"<<endl;
             }
          }
       }

       TH1::SavePrimitiveHelp(out, option);
    }

    //______________________________________________________________________________
     void TProfile2D::Scale(Double_t c1)
    {
    //*-*-*-*-*Multiply this profile2D by a constant c1*-*-*-*-*-*-*-*-*
    //*-*      ========================================
    //
    //   this = c1*this
    //
    // This function uses the services of TProfile2D::Add
    //

       Double_t ent = fEntries;
       fScaling = kTRUE;
       Add(this,this,c1,0);
       fScaling = kFALSE;
       fEntries = ent;
    }

    //______________________________________________________________________________
     void TProfile2D::SetBinEntries(Int_t bin, Stat_t w)
    {
    //*-*-*-*-*-*-*-*-*Set the number of entries in bin*-*-*-*-*-*-*-*-*-*-*-*
    //*-*              ================================

       if (bin < 0 || bin >= fNcells) return;
       fBinEntries.fArray[bin] = w;
    }

    //______________________________________________________________________________
     void TProfile2D::SetBins(Int_t nx, Double_t xmin, Double_t xmax, Int_t ny, Double_t ymin, Double_t ymax)
    {
    //*-*-*-*-*-*-*-*-*Redefine  x axis parameters*-*-*-*-*-*-*-*-*-*-*-*
    //*-*              ===========================

       fXaxis.Set(nx,xmin,xmax);
       fYaxis.Set(ny,ymin,ymax);
       fNcells = (nx+2)*(ny+2);
       fBinEntries.Set(fNcells);
       fSumw2.Set(fNcells);
    }

    //______________________________________________________________________________
     void TProfile2D::SetBuffer(Int_t buffersize, Option_t *)
    {
    // set the buffer size in units of 8 bytes (double)

       if (fBuffer) {
          BufferEmpty();
          delete [] fBuffer;
          fBuffer = 0;
       }
       if (buffersize <= 0) {
          fBufferSize = 0;
          return;
       }
       if (buffersize < 100) buffersize = 100;
       fBufferSize = 1 + 4*buffersize;
       fBuffer = new Double_t[fBufferSize];
       memset(fBuffer,0,8*fBufferSize);
    }

    //______________________________________________________________________________
     void TProfile2D::SetErrorOption(Option_t *option)
    {
    //*-*-*-*-*-*-*-*-*-*Set option to compute profile2D errors*-*-*-*-*-*-*-*
    //*-*                =======================================
    //
    //    The computation of errors is based on the parameter option:
    //    option:
    //     ' '  (Default) Errors are Spread/SQRT(N) for Spread.ne.0. ,
    //                      "     "  SQRT(Z)/SQRT(N) for Spread.eq.0,N.gt.0 ,
    //                      "     "  0.  for N.eq.0
    //     's'            Errors are Spread  for Spread.ne.0. ,
    //                      "     "  SQRT(Z)  for Spread.eq.0,N.gt.0 ,
    //                      "     "  0.  for N.eq.0
    //     'i'            Errors are Spread/SQRT(N) for Spread.ne.0. ,
    //                      "     "  1./SQRT(12.*N) for Spread.eq.0,N.gt.0 ,
    //                      "     "  0.  for N.eq.0
    //   See TProfile2D::BuildOptions for explanation of all options

       TString opt = option;
       opt.ToLower();
       fErrorMode = kERRORMEAN;
       if (opt.Contains("s")) fErrorMode = kERRORSPREAD;
       if (opt.Contains("i")) fErrorMode = kERRORSPREADI;
       if (opt.Contains("g")) fErrorMode = kERRORSPREADG;
    }

    //______________________________________________________________________________
     void TProfile2D::Streamer(TBuffer &R__b)
    {
       // Stream an object of class TProfile2D.

       if (R__b.IsReading()) {
          UInt_t R__s, R__c;
          Version_t R__v = R__b.ReadVersion(&R__s, &R__c);
          if (R__v > 2) {
             TProfile2D::Class()->ReadBuffer(R__b, this, R__v, R__s, R__c);
             return;
          }
          //====process old versions before automatic schema evolution
          TH2D::Streamer(R__b);
          fBinEntries.Streamer(R__b);
          R__b >> (Int_t&)fErrorMode;
          if (R__v < 2) {
             Float_t zmin,zmax;
             R__b >> zmin; fZmin = zmin;
             R__b >> zmax; fZmax = zmax;
          } else {
             R__b >> fZmin;
             R__b >> fZmax;
          }
          R__b.CheckByteCount(R__s, R__c, TProfile2D::IsA());
          //====end of old versions

       } else {
          TProfile2D::Class()->WriteBuffer(R__b,this);
       }
    }