class TProfile2D: public TH2D

Default constructor for Profile2D histograms*-*-*-
*-*        ============================================

Default destructor for Profile2D histograms*-*-*-
*-*        ===========================================

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.

  Create a 2-D Profile with variable bins in X and fix bins in Y

  Create a 2-D Profile with fix bins in X and variable bins in Y

  Create a 2-D Profile with variable bins in X and variable bins in Y

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

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.

 Copy constructor.

 Performs the operation: this = this + c1*f1

 Performs the operation: this = this + c1*h1

-*-*Replace contents of this profile2D by the addition of h1 and h2
*-*      ===============================================================

   this = c1*h1 + c2*h2

     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)

 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
 fBuffer[4] = z of first entry

-*-*-*-*Copy a Profile2D histogram to a new profile2D histogram
*-*            =======================================================

 Performs the operation: this = this/(c1*f1)

Divide this profile2D by h1*-*-
*-*                  ===========================

   this = this/h1

-*-*Replace contents of this profile2D by the division of h1 by h2
*-*      ==============================================================

   this = c1*h1/(c2*h2)

Draw a copy of this profile2D histogram*-*-*-
*-*            =======================================

-*-*-*Fill a Profile2D histogram (no weights)
*-*                  =======================================

 Fill a Profile2D histogram (no weights)

 Fill a Profile2D histogram (no weights)

 Fill a Profile2D histogram (no weights)

-*-*-*Fill a Profile2D histogram with weights
*-*                  =======================================

Return bin content of a Profile2D histogram*-*-
*-*          ===========================================

Return bin entries of a Profile2D histogram*-*-
*-*          ===========================================

            Return bin effective entries for a weighted filled Profile histogram.
            In case of an unweighted profile, it is equivalent to the number of entries per bin
            The effective entries is defined as the square of the sum of the weights divided by the
            sum of the weights square.
            TProfile::Sumw2() must be called before filling the profile with weights.
            Only by calling this method the  sum of the square of the weights per bin is stored.

*-*          =========================================

 *-*-*-*-*-*-*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)

-*-*Return option to compute profile2D errors
*-*                =========================================

 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

 If no axis-subrange is specified (via TAxis::SetRange), the array stats
 is simply a copy of the statistics quantities computed at filling time.
 If a sub-range is specified, the function recomputes these quantities
 from the bin contents in the current axis range.

 Reduce the number of bins for this axis to the number of bins having a label.

 Double the number of bins for axis.
 Refill histogram
 This function is called by TAxis::FindBin(const char *label)

  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)

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.
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.

 Performs the operation: this = this*c1*f1

Multiply this profile2D by h1*-
*-*                  =============================

   this = this*h1

-*-*-*Replace contents of this profile2D by multiplication of h1 by h2
*-*      ================================================================

   this = (c1*h1)*(c2*h2)

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 of the projected histogram are computed and set
      to be equal to the errors of the profile.
      Option "E" is defined as the default one in the header file.
   if option "" is specified the histogram errors are simply the sqrt of its content
   if option "B" is specified, the content of bin of the returned histogram
      will be equal to the GetBinEntries(bin) of the profile,
   if option "C=E" the bin contents of the projection are set to the
       bin errors of the profile
   if option "W" is specified the bin content of the projected histogram  is set to the
       product of the bin content of the profile and the entries.
       With this option the returned histogram will be equivalent to the one obtained by
       filling directly a TH2D using the 3-rd value as a weight.
       This option makes sense only for profile filled with all weights =1.
       When the profile is weighted (filled with weights different than 1) the
       bin error of the projected histogram (obtained using this option "W") cannot be
       correctly computed from the information stored in the profile.

 Replace current statistics with the values in array stats

-*-*Reset contents of a Profile2D histogram
*-*                =======================================

 Profile histogram is resized along axis such that x is in the axis range.
 The new axis limits are recomputed by doubling iteratively
 the current axis range until the specified value x is within the limits.
 The algorithm makes a copy of the histogram, then loops on all bins
 of the old histogram to fill the rebinned histogram.
 Takes into account errors (Sumw2) if any.
 The bit kCanRebin must be set before invoking this function.
  Ex:  h->SetBit(TH1::kCanRebin);

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

   if newname is not blank a new profile 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 be merged into one bin of hnew
   If the original profile has errors stored (via Sumw2), the resulting
   profile has new errors correctly calculated.

   examples: if hpxpy is an existing TProfile2D profile with 40 x 40 bins
     hpxpy->Rebin2D();  // merges two bins along the xaxis and yaxis in one
                        // Carefull: previous contents of hpxpy are lost
     hpxpy->Rebin2D(3,5);  // merges 3 bins along the xaxis and 5 bins along the yaxis in one
                           // Carefull: previous contents of hpxpy are lost
     hpxpy->RebinX(5); //merges five bins along the xaxis in one in hpxpy
     TProfile2D *hnew = hpxpy->RebinY(5,"hnew"); // creates a new profile hnew
                                                 // merging 5 bins of hpxpy 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 profile
          is changed to the upper edge of the xbin=newxbins*nxgroup resp.
          ybin=newybins*nygroup and the remaining bins are added to
          the overflow bin.
          Statistics will be recomputed from the new bin contents.

 Rebin only the X axis
 see Rebin2D

 Rebin only the Y axis
 see Rebin2D

 Save primitive as a C++ statement(s) on output stream out

 *-*-*-*-*Multiply this profile2D by a constant c1*-*-*-*-*-*-*-*-*
 *-*      ========================================

   this = c1*this

 This function uses the services of TProfile2D::Add

Set the number of entries in bin*-*-*-
*-*              ================================

Redefine  x axis parameters*-*-*-
*-*              ===========================

 set the buffer size in units of 8 bytes (double)

-*-*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

 Stream an object of class TProfile2D.

 Create structure to store sum of squares of weights per bin  *-*-*-*-*-*-*-*
   This is needed to compute  the correct statistical quantities
    of a profile filled with weights


  This function is automatically called when the histogram is created
  if the static function TH1::SetDefaultSumw2 has been called before.

 helper methods for the Merge unification in TProfileHelper