class TH2: public TH1

 Constructor.

 see comments in the TH1 base class constructors

 see comments in the TH1 base class constructors

 see comments in the TH1 base class constructors

 see comments in the TH1 base class constructors

 see comments in the TH1 base class constructors

 Copy constructor.
 The list of functions is not copied. (Use Clone if needed)

 Destructor.

 Fill histogram with all entries in the buffer.
 action = -1 histogram is reset and refilled from the buffer (called by THistPainter::Paint)
 action =  0 histogram is filled from the buffer
 action =  1 histogram is filled and buffer is deleted
             The buffer is automatically deleted when the number of entries
             in the buffer is greater than the number of entries in the histogram

 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
 fBuffer[3] = y of first entry

 Copy.

-*Increment cell defined by x,y by 1
*-*                  ==================================
-
*-* if x or/and y is less than the low-edge of the corresponding axis first bin,
*-*   the Underflow cell is incremented.
*-* if x or/and y is greater than the upper edge of corresponding axis last bin,
*-*   the Overflow cell is incremented.
-
*-* If the storage of the sum of squares of weights has been triggered,
*-* via the function Sumw2, then the sum of the squares of weights is incremented
*-* by 1in the cell corresponding to x,y.
-
-

-*-*-*-*-*Increment cell defined by x,y by a weight w
*-*                  ===========================================
-
*-* if x or/and y is less than the low-edge of the corresponding axis first bin,
*-*   the Underflow cell is incremented.
*-* if x or/and y is greater than the upper edge of corresponding axis last bin,
*-*   the Overflow cell is incremented.
-
*-* If the storage of the sum of squares of weights has been triggered,
*-* via the function Sumw2, then the sum of the squares of weights is incremented
*-* by w^2 in the cell corresponding to x,y.
-
-

 Increment cell defined by namex,namey by a weight w

 if x or/and y is less than the low-edge of the corresponding axis first bin,
   the Underflow cell is incremented.
 if x or/and y is greater than the upper edge of corresponding axis last bin,
   the Overflow cell is incremented.

 If the storage of the sum of squares of weights has been triggered,
 via the function Sumw2, then the sum of the squares of weights is incremented
 by w^2 in the cell corresponding to x,y.

 Increment cell defined by namex,y by a weight w

 if x or/and y is less than the low-edge of the corresponding axis first bin,
   the Underflow cell is incremented.
 if x or/and y is greater than the upper edge of corresponding axis last bin,
   the Overflow cell is incremented.

 If the storage of the sum of squares of weights has been triggered,
 via the function Sumw2, then the sum of the squares of weights is incremented
 by w^2 in the cell corresponding to x,y.

 Increment cell defined by x,namey by a weight w

 if x or/and y is less than the low-edge of the corresponding axis first bin,
   the Underflow cell is incremented.
 if x or/and y is greater than the upper edge of corresponding axis last bin,
   the Overflow cell is incremented.

 If the storage of the sum of squares of weights has been triggered,
 via the function Sumw2, then the sum of the squares of weights is incremented
 by w^2 in the cell corresponding to x,y.

-*-*-*Fill a 2-D histogram with an array of values and weights
*-*          ========================================================
-
*-* ntimes:  number of entries in arrays x and w (array size must be ntimes*stride)
*-* x:       array of x values to be histogrammed
*-* y:       array of y values to be histogrammed
*-* w:       array of weights
*-* stride:  step size through arrays x, y and w
-
*-* If the storage of the sum of squares of weights has been triggered,
*-* via the function Sumw2, then the sum of the squares of weights is incremented
*-* by w[i]^2 in the cell corresponding to x[i],y[i].
*-* if w is NULL each entry is assumed a weight=1
-
*-* NB: function only valid for a TH2x object
-
-

-*-*-*Fill histogram following distribution in function fname
*-*          =======================================================
-
*-*   The distribution contained in the function fname (TF2) is integrated
*-*   over the channel contents.
*-*   It is normalized to 1.
*-*   Getting one random number implies:
*-*     - Generating a random number between 0 and 1 (say r1)
*-*     - Look in which bin in the normalized integral r1 corresponds to
*-*     - Fill histogram channel
*-*   ntimes random numbers are generated
-
*-*  One can also call TF2::GetRandom2 to get a random variate from a function.
-
*

-*-*-*Fill histogram following distribution in histogram h
*-*          ====================================================
-
*-*   The distribution contained in the histogram h (TH2) is integrated
*-*   over the channel contents.
*-*   It is normalized to 1.
*-*   Getting one random number implies:
*-*     - Generating a random number between 0 and 1 (say r1)
*-*     - Look in which bin in the normalized integral r1 corresponds to
*-*     - Fill histogram channel
*-*   ntimes random numbers are generated
-
*

 Project slices along X in case of a 2-D histogram, then fit each slice
 with function f1 and make a histogram for each fit parameter
 Only bins along Y between firstybin and lastybin are considered.
 By default (firstybin == 0, lastybin == -1), all bins in y including
 over- and underflows are taken into account.
 If f1=0, a gaussian is assumed
 Before invoking this function, one can set a subrange to be fitted along X
 via f1->SetRange(xmin,xmax)
 The argument option (default="QNR") can be used to change the fit options.
     "Q"  means Quiet mode
     "N"  means do not show the result of the fit
     "R"  means fit the function in the specified function range
     "G2" merge 2 consecutive bins along X
     "G3" merge 3 consecutive bins along X
     "G4" merge 4 consecutive bins along X
     "G5" merge 5 consecutive bins along X

 The generated histograms are returned by adding them to arr, if arr is not NULL.
 arr's SetOwner() is called, to signal that it is the user's respponsability to
 delete the histograms, possibly by deleting the arrary.
    TObjArray aSlices;
    h2->FitSlicesX(func, 0, -1, "QNR", &aSlices);
 will already delete the histograms once aSlice goes out of scope. aSlices will
 contain the histogram for the i-th parameter of the fit function at aSlices[i];
 aSlices[n] (n being the number of parameters) contains the chi2 distribution of
 the fits.

 If arr is NULL, the generated histograms are added to the list of objects
 in the current directory. It is the user's responsability to delete
 these histograms.

  Example: Assume a 2-d histogram h2
   Root > h2->FitSlicesX(); produces 4 TH1D histograms
          with h2_0 containing parameter 0(Constant) for a Gaus fit
                    of each bin in Y projected along X
          with h2_1 containing parameter 1(Mean) for a gaus fit
          with h2_2 containing parameter 2(RMS)  for a gaus fit
          with h2_chi2 containing the chisquare/number of degrees of freedom for a gaus fit

   Root > h2->FitSlicesX(0,15,22,10);
          same as above, but only for bins 15 to 22 along Y
          and only for bins in Y for which the corresponding projection
          along X has more than cut bins filled.

  NOTE: To access the generated histograms in the current directory, do eg:
     TH1D *h2_1 = (TH1D*)gDirectory->Get("h2_1");

 Project slices along Y in case of a 2-D histogram, then fit each slice
 with function f1 and make a histogram for each fit parameter
 Only bins along X between firstxbin and lastxbin are considered.
 By default (firstxbin == 0, lastxbin == -1), all bins in x including
 over- and underflows are taken into account.
 If f1=0, a gaussian is assumed
 Before invoking this function, one can set a subrange to be fitted along Y
 via f1->SetRange(ymin,ymax)
 The argument option (default="QNR") can be used to change the fit options.
     "Q"  means Quiet mode
     "N"  means do not show the result of the fit
     "R"  means fit the function in the specified function range
     "G2" merge 2 consecutive bins along Y
     "G3" merge 3 consecutive bins along Y
     "G4" merge 4 consecutive bins along Y
     "G5" merge 5 consecutive bins along Y

 The generated histograms are returned by adding them to arr, if arr is not NULL.
 arr's SetOwner() is called, to signal that it is the user's respponsability to
 delete the histograms, possibly by deleting the arrary.
    TObjArray aSlices;
    h2->FitSlicesX(func, 0, -1, "QNR", &aSlices);
 will already delete the histograms once aSlice goes out of scope. aSlices will
 contain the histogram for the i-th parameter of the fit function at aSlices[i];
 aSlices[n] (n being the number of parameters) contains the chi2 distribution of
 the fits.

 If arr is NULL, the generated histograms are added to the list of objects
 in the current directory. It is the user's responsability to delete
 these histograms.

  Example: Assume a 2-d histogram h2
   Root > h2->FitSlicesY(); produces 4 TH1D histograms
          with h2_0 containing parameter 0(Constant) for a Gaus fit
                    of each bin in X projected along Y
          with h2_1 containing parameter 1(Mean) for a gaus fit
          with h2_2 containing parameter 2(RMS)  for a gaus fit
          with h2_chi2 containing the chisquare/number of degrees of freedom for a gaus fit

   Root > h2->FitSlicesY(0,15,22,10);
          same as above, but only for bins 15 to 22 along X
          and only for bins in X for which the corresponding projection
          along Y has more than cut bins filled.

  NOTE: To access the generated histograms in the current directory, do eg:
     TH1D *h2_1 = (TH1D*)gDirectory->Get("h2_1");

 A complete example of this function is given in 

 with the following output:

 compute first cell (binx,biny) in the range [firstxbin,lastxbin][firstybin,lastybin] for which
 diff = abs(cell_content-c) <= maxdiff
 In case several cells in the specified range with diff=0 are found
 the first cell found is returned in binx,biny.
 In case several cells in the specified range satisfy diff <=maxdiff
 the cell with the smallest difference is returned in binx,biny.
 In all cases the function returns the smallest difference.

 NOTE1: if firstxbin < 0, firstxbin is set to 1
        if (lastxbin < firstxbin then lastxbin is set to the number of bins in X
          ie if firstxbin=1 and lastxbin=0 (default) the search is on all bins in X except
          for X's under- and overflow bins.
        if firstybin < 0, firstybin is set to 1
        if (lastybin < firstybin then lastybin is set to the number of bins in Y
          ie if firstybin=1 and lastybin=0 (default) the search is on all bins in Y except
          for Y's under- and overflow bins.
 NOTE2: if maxdiff=0 (default), the first cell with content=c is returned.

-*-*-*Return correlation factor between axis1 and axis2
*-*            ====================================================

-*-*-*Return covariance between axis1 and axis2
*-*            ====================================================

 return 2 random numbers along axis x and y distributed according
 the cellcontents of a 2-dim histogram

 fill the array stats from the contents of this histogram
 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

Return integral of bin contents. Only bins in the bins range are considered.
 By default the integral is computed as the sum of bin contents in the range.
 if option "width" is specified, the integral is the sum of
 the bin contents multiplied by the bin width in x and in y.

Return integral of bin contents in range [firstxbin,lastxbin],[firstybin,lastybin]
 for a 2-D histogram
 By default the integral is computed as the sum of bin contents in the range.
 if option "width" is specified, the integral is the sum of
 the bin contents multiplied by the bin width in x and in y.

illegal for a TH2

 Given a point P(x,y), Interpolate approximates the value via bilinear
 interpolation based on the four nearest bin centers
 see Wikipedia, Bilinear Interpolation
 Andy Mastbaum 10/8/2008
 vaguely based on R.Raja 6-Sep-2008

illegal for a TH2

  Statistical test of compatibility in shape between
  THIS histogram and h2, using Kolmogorov test.
     Default: Ignore under- and overflow bins in comparison

     option is a character string to specify options
         "U" include Underflows in test
         "O" include Overflows
         "N" include comparison of normalizations
         "D" Put out a line of "Debug" printout
         "M" Return the Maximum Kolmogorov distance instead of prob

   The returned function value is the probability of test
       (much less than one means NOT compatible)

   The KS test uses the distance between the pseudo-CDF's obtained
   from the histogram. Since in 2D the order for generating the pseudo-CDF is
   arbitrary, two pairs of pseudo-CDF are used, one starting from the x axis the
   other from the y axis and the maximum distance is the average of the two maximum
   distances obtained.

  Code adapted by Rene Brun from original HBOOK routine HDIFF

Add all histograms in the collection to 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.
If overflows are present and limits are different the function will fail.
The function returns the total number of entries in the result histogram
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 and the upper limit must also
be a multiple of the bin width.

 Rebin only the X axis
 see Rebin2D

 Rebin only the Y axis
 see Rebin2D

   -*-*-*Rebin this histogram grouping nxgroup/nygroup bins along the xaxis/yaxis together*-*-*-*-

   if newname is not blank a new temporary histogram hnew is created.
   else the current histogram is modified (default)
   The parameter nxgroup/nygroup indicate how many bins along the xaxis/yaxis of this
   have to me merged into one bin of hnew
   If the original histogram has errors stored (via Sumw2), the resulting
   histograms has new errors correctly calculated.

   examples: if hpxpy is an existing TH2 histogram with 40 x 40 bins
     hpxpy->Rebin();  // merges two bins along the xaxis and yaxis in one in hpxpy
                      // Carefull: previous contents of hpxpy are lost
     hpxpy->RebinX(5); //merges five bins along the xaxis in one in hpxpy
     TH2 *hnew = hpxpy->RebinY(5,"hnew"); // creates a new histogram hnew
                                          // merging 5 bins of h1 along the yaxis in one bin

   NOTE : If nxgroup/nygroup is not an exact divider of the number of bins,
          along the xaxis/yaxis the top limit(s) of the rebinned histogram
          is changed to the upper edge of the xbin=newxbins*nxgroup resp.
          ybin=newybins*nygroup and the corresponding bins are added to
          the overflow bin.
          Statistics will be recomputed from the new bin contents.

 *-*-*-*-*Project a 2-D histogram into a profile histogram along X*-*-*-*-*-*
 *-*      ========================================================

   The projection is made from the channels along the Y axis
   ranging from firstybin to lastybin included.
   By default, bins 1 to ny are included
   When all bins are included, the number of entries in the projection
   is set to the number of entries of the 2-D histogram, otherwise
   the number of entries is incremented by 1 for all non empty cells.

   if option "d" is specified, the profile is drawn in the current pad.

   Using a TCutG object, it is possible to select a sub-range of a 2-D histogram.
   One must create a graphical cut (mouse or C++) and specify the name
   of the cut between [] in the option.
   For example, with a TCutG named "cutg", one can call:
      myhist->ProfileX(" ",firstybin,lastybin,"[cutg]");
   To invert the cut, it is enough to put a "-" in front of its name:
      myhist->ProfileX(" ",firstybin,lastybin,"[-cutg]");
   It is possible to apply several cuts ("," means logical AND):
      myhist->ProfileX(" ",firstybin,lastybin,[cutg1,cutg2]");

   NOTE that if a TProfile named name exists in the current directory or pad,
   the histogram is reset and filled again with the current contents of the TH2.
   The X axis attributes of the TH2 are copied to the X axis of the profile.

   NOTE2 that the default under- / overflow behavior differs from what ProjectionX
   does! Profiles take the bin center into account, so here the under- and overflow
   bins are ignored by default.

 *-*-*-*-*Project a 2-D histogram into a profile histogram along Y*-*-*-*-*-*
 *-*      ========================================================

   The projection is made from the channels along the X axis
   ranging from firstxbin to lastxbin included.
   By default, bins 1 to nx are included
   When all bins are included, the number of entries in the projection
   is set to the number of entries of the 2-D histogram, otherwise
   the number of entries is incremented by 1 for all non empty cells.

   if option "d" is specified, the profile is drawn in the current pad.

   Using a TCutG object, it is possible to select a sub-range of a 2-D histogram.
   One must create a graphical cut (mouse or C++) and specify the name
   of the cut between [] in the option.
   For example, with a TCutG named "cutg", one can call:
      myhist->ProfileY(" ",firstybin,lastybin,"[cutg]");
   To invert the cut, it is enough to put a "-" in front of its name:
      myhist->ProfileY(" ",firstybin,lastybin,"[-cutg]");
   It is possible to apply several cuts:
      myhist->ProfileY(" ",firstybin,lastybin,[cutg1,cutg2]");

   NOTE that if a TProfile named name exists in the current directory or pad,
   the histogram is reset and filled again with the current contents of the TH2.
   The Y axis attributes of the TH2 are copied to the X axis of the profile.

   NOTE2 that the default under- / overflow behavior differs from what ProjectionX
   does! Profiles take the bin center into account, so here the under- and overflow
   bins are ignored by default.

 internal (protected) method for performing projection on the X or Y axis
 called by ProjectionX or ProjectionY

Project a 2-D histogram into a 1-D histogram along X*-*-
*-*      ====================================================

   The projection is always of the type TH1D.
   The projection is made from the channels along the Y axis
   ranging from firstybin to lastybin included.
   By default, all bins including under- and overflow are included.
   The number of entries in the projection is estimated from the
   number of effective entries for all the cells included in the projection

   To exclude the underflow bins in Y, use firstybin=1;
   to exclude the underflow bins in Y, use lastybin=nx.

   if option "e" is specified, the errors are computed.
   if option "d" is specified, the projection is drawn in the current pad.

   Using a TCutG object, it is possible to select a sub-range of a 2-D histogram.
   One must create a graphical cut (mouse or C++) and specify the name
   of the cut between [] in the option.
   For example, with a TCutG named "cutg", one can call:
      myhist->ProjectionX(" ",firstybin,lastybin,"[cutg]");
   To invert the cut, it is enough to put a "-" in front of its name:
      myhist->ProjectionX(" ",firstybin,lastybin,"[-cutg]");
   It is possible to apply several cuts:
      myhist->ProjectionX(" ",firstybin,lastybin,[cutg1,cutg2]");

   NOTE that if a TH1D named name exists in the current directory or pad,
   the histogram is reset and filled again with the current contents of the TH2.
   The X axis attributes of the TH2 are copied to the X axis of the projection.

Project a 2-D histogram into a 1-D histogram along Y*-*-
*-*      ====================================================

   The projection is always of the type TH1D.
   The projection is made from the channels along the X axis
   ranging from firstxbin to lastxbin included.
   By default, all bins including under- and overflow are included.
   The number of entries in the projection is estimated from the
   number of effective entries for all the cells included in the projection

   To exclude the underflow bins in X, use firstxbin=1;
   to exclude the underflow bins in X, use lastxbin=nx.

   if option "e" is specified, the errors are computed.
   if option "d" is specified, the projection is drawn in the current pad.

   Using a TCutG object, it is possible to select a sub-range of a 2-D histogram.
   One must create a graphical cut (mouse or C++) and specify the name
   of the cut between [] in the option.
   For example, with a TCutG named "cutg", one can call:
      myhist->ProjectionY(" ",firstxbin,lastxbin,"[cutg]");
   To invert the cut, it is enough to put a "-" in front of its name:
      myhist->ProjectionY(" ",firstxbin,lastxbin,"[-cutg]");
   It is possible to apply several cuts:
      myhist->ProjectionY(" ",firstxbin,lastxbin,[cutg1,cutg2]");

   NOTE that if a TH1D named name exists in the current directory or pad,
   the histogram is reset and filled again with the current contents of the TH2.
   The Y axis attributes of the TH2 are copied to the X axis of the projection.

 Replace current statistics with the values in array stats

Reset this histogram: contents, errors, etc
*-*            ===========================================

 When the mouse is moved in a pad containing a 2-d view of this histogram
 a second canvas shows the projection along X corresponding to the
 mouse position along Y.
 To stop the generation of the projections, delete the canvas
 containing the projection.

 When the mouse is moved in a pad containing a 2-d view of this histogram
 a second canvas shows the projection along Y corresponding to the
 mouse position along X.
 To stop the generation of the projections, delete the canvas
 containing the projection.

   This function calculates the background spectrum in this histogram.
   The background is returned as a histogram.
   to be implemented (may be)

Interface to TSpectrum2::Search
the function finds peaks in this histogram where the width is > sigma
and the peak maximum greater than threshold*maximum bin content of this.
for more detauils see TSpectrum::Search.
note the difference in the default value for option compared to TSpectrum2::Search
option="" by default (instead of "goff")

 Smooth bin contents of this 2-d histogram using kernel algorithms
 similar to the ones used in the raster graphics community.
 Bin contents in the active range are replaced by their smooth values.
 If Errors are defined via Sumw2, they are scaled.
 3 kernels are proposed k5a, k5b and k3a.
 k5a and k5b act on 5x5 cells (i-2,i-1,i,i+1,i+2, and same for j)
 k5b is a bit more stronger in smoothing
 k3a acts only on 3x3 cells (i-1,i,i+1, and same for j).
 By default the kernel "k5a" is used. You can select the kernels "k5b" or "k3a"
 via the option argument.
 If TAxis::SetRange has been called on the x or/and y axis, only the bins
 in the specified range are smoothed.
 In the current implementation if the first argument is not used (default value=1).

 implementation by David McKee (dmckee@bama.ua.edu). Extended by Rene Brun

 Stream an object of class TH2.