class TProfile: public TH1D

Default constructor for Profile histograms*-*-*-
*-*        ==========================================

Default destructor for Profile histograms*-*-*-
*-*        =========================================

Normal Constructor for Profile histograms*-*-*-*-
*-*        ==========================================

  The first five parameters are similar to TH1D::TH1D.
  All values of y are accepted at filling time.
  To fill a profile histogram, one must use TProfile::Fill function.

  Note that when filling the profile histogram the function Fill
  checks if the variable y is betyween fYmin and fYmax.
  If a minimum or maximum value is set for the Y scale before filling,
  then all values below ymin or above ymax will be discarded.
  Setting the minimum or maximum value for the Y scale before filling
  has the same effect as calling the special TProfile constructor below
  where ymin and ymax are specified.

  H(J) is printed as the channel contents. The errors displayed are s(J) if CHOPT='S'
  (spread option), or e(J) if CHOPT=' ' (error on mean).

        See TProfile::BuildOptions for explanation of parameters

 see also comments in the TH1 base class constructors

-*Constructor for Profile histograms with variable bin size
*-*        =========================================================

        See TProfile::BuildOptions for more explanations on errors

 see also comments in the TH1 base class constructors

-*Constructor for Profile histograms with variable bin size
*-*        =========================================================

        See TProfile::BuildOptions for more explanations on errors

 see also comments in the TH1 base class constructors

-*Constructor for Profile histograms with variable bin size
*-*        =========================================================

        See TProfile::BuildOptions for more explanations on errors

 see also comments in the TH1 base class constructors

Constructor for Profile histograms with range in y
*-*        ==================================================
  The first five parameters are similar to TH1D::TH1D.
  Only the values of Y between ylow and yup will be considered at filling time.
  ylow and yup will also be the maximum and minimum values
  on the y scale when drawing the profile.

        See TProfile::BuildOptions for more explanations on errors

 see also comments in the TH1 base class constructors

Set Profile histogram structure and options*-*-
*-*          ===========================================
    ymin:  minimum value allowed for y
    ymax:  maximum value allowed for y
            if (ymin = ymax = 0) there are no limits on the allowed y values (ymin = -inf, ymax = +inf)

    option:  this is the option for the computation of the y error of the profile ( TProfile::GetBinError )
             possible values for the options are:


     ' '  (Default) the bin errors are the standard error on the mean of Y  =  S(Y)/SQRT(N)
                    where S(Y) is the standard deviation (RMS) of the Y data in the bin
                    and N is the number of bin entries (from TProfile::GetBinEntries(ibin) )
                    (i.e the errors are the standard error on the bin content of the profile)

     's'            Errors are the standard deviation of Y, S(Y)

     'i'            Errors are S(Y)/SQRT(N) (standard error on the mean as in the default)
                    The only difference is only when the standard deviation in Y is zero.
                    In this  case the error a standard deviation = 1/SQRT(12) is assumed and the error is
                    1./SQRT(12*N).
                    This approximation assumes that the Y values are integer (e.g. ADC counts)
                    and have an implicit uncertainty of y +/- 0.5. With the assumption that the probability that y
                    takes any value between y-0.5 and y+0.5 is uniform, its standard error is 1/SQRT(12)

     'g'            Errors are 1./SQRT(W) where W is the sum of the weights for the bin J
                    W is obtained as from TProfile::GetBinEntries(ibin)
                    This errors corresponds to the standard deviation of weighted mean where each
                    measurement Y is uncorrelated and has an error sigma, which is expressed in the
                    weight used to fill the Profile:  w = 1/sigma^2
                    The resulting  error in TProfile is then 1./SQRT( Sum(1./sigma^2) )

 Copy constructor.

 Performs the operation: this = this + c1*f1

 Performs the operation: this = this + c1*h1

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

   this = c1*h1 + c2*h2

   c1 and c2 are considered as weights applied to the two summed profiles.
   The operation acts therefore like merging the two profiles with a weight c1 and c2

     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 profile is less than 1002
  - the bin number of entries is small ( <5)
  - the estimated bin error is extremely small compared to the bin content
  (see TProfile::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

-*-*-*Copy a Profile histogram to a new profile histogram
*-*            ===================================================

 Performs the operation: this = this/(c1*f1)
 This function is not implemented for the TProfile

Divide this profile by h1*-*-
*-*                  =========================

   this = this/h1
 This function accepts to divide a TProfile by a histogram

 The function return kFALSE if the divide operation failed

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

   this = c1*h1/(c2*h2)

 The function return kFALSE if the divide operation failed

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

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

 Fill a Profile histogram (no weights)

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

 Fill a Profile histogram with weights

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

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

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

 Computing errors: A moving field

 The computation of errors for a TProfile has evolved with the versions
 of ROOT. The difficulty is in computing errors for bins with low statistics.
 - prior to version 3.00, 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.
 - in version 3.00 (18 Dec 2000), the algorithm is protected for values of
   eprim2 very small and the bin errors set to the average bin errors, following
   recommendations from a group of users.
 - in version 3.01 (19 Apr 2001), it is realized that the algorithm above
   should be applied only to low statistic bins.
 - in version 3.02 (26 Sep 2001), the same group of users recommend instead
   to take two times the average error on all bins for these low
   statistics bins giving a very small value for eprim2.
 - in version 3.04 (Nov 2002), the algorithm is modified/protected for the case
   when a TProfile is projected (ProjectionX). The previous algorithm
   generated a N^2 problem when projecting a TProfile with a large number of
   bins (eg 100000).
 - in version 3.05/06, a new static function TProfile::Approximate
   is introduced to enable or disable (default) the approximation.

 Ideas for improvements of this algorithm are welcome. No suggestions
 received since our call for advice to roottalk in Jul 2002.
 see for instance: http://root.cern.ch/root/roottalk/roottalk02/2916.html

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

   Redefines TObject::GetObjectInfo.
   Displays the profile info (bin number, contents, eroor, entries per bin
   corresponding to cursor position px,py

 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

 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 x axis,
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 axis x 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

 The function return kFALSE if the Multiply operation failed

Multiply this profile by h1*-*-
*-*                  =============================

   this = this*h1

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

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

Project this profile into a 1-D histogram along X*-*-
*-*      =================================================

   The projection is always of the type TH1D.

   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,
      otherwise (default) it will be equal to GetBinContent(bin)
   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 TH1D using the 2-nd value as a weight.
       This makes sense only for profile filled with weights =1. If not, the error of the
        projected histogram obtained with this option will not be correct.

 Replace current statistics with the values in array stats

Rebin this profile grouping ngroup bins together*-*-*-*-
*-*      ================================================
  -case 1  xbins=0
   if newname is not blank a new temporary profile hnew is created.
   else the current profile is modified (default)
   The parameter ngroup indicates how many bins of this have to me 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 hp is an existing TProfile histogram with 100 bins
     hp->Rebin();  //merges two bins in one in hp: previous contents of hp are lost
     hp->Rebin(5); //merges five bins in one in hp
     TProfile *hnew = hp->Rebin(5,"hnew"); // creates a new profile hnew
                                       //merging 5 bins of hp in one bin

   NOTE:  If ngroup is not an exact divider of the number of bins,
          the top limit of the rebinned profile is changed
          to the upper edge of the bin=newbins*ngroup and the corresponding
          bins are added to the overflow bin.
          Statistics will be recomputed from the new bin contents.

  -case 2  xbins!=0
   a new profile is created (you should specify newname).
   The parameter ngroup is the number of variable size bins in the created profile
   The array xbins must contain ngroup+1 elements that represent the low-edge
   of the bins.
   The data of the old bins are added to the new bin which contains the bin center
   of the old bins. It is possible that information from the old binning are attached
   to the under-/overflow bins of the new binning.

   examples: if hp is an existing TProfile with 100 bins
     Double_t xbins[25] = {...} array of low-edges (xbins[25] is the upper edge of last bin
     hp->Rebin(24,"hpnew",xbins);  //creates a new variable bin size profile hpnew

 Profile histogram is resized along x 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);

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

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

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

   this = c1*this

 This function uses the services of TProfile::Add

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

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

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

 Set total number of bins including under/overflow
 Reallocate bin contents array

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

-*Set option to compute profile errors
*-*                =====================================

    The computation of the bin errors is based on the parameter option:
    option:
     ' '  (Default) The bin errors are the standard error on the mean of the bin profiled values (Y),
                    i.e. the standard error of the bin contents.
                    Note that if TProfile::Approximate()  is called, an approximation is used when
                    the spread in Y is 0 and the number of bin entries  is > 0

     's'            The bin errors are the standard deviations of the Y bin values
                    Note that if TProfile::Approximate()  is called, an approximation is used when
                    the spread in Y is 0 and the number of bin entries is > 0

     'i'            Errors are as in default case (standard errors of the bin contents)
                    The only difference is for the case when the spread in Y is zero.
                    In this case for N > 0 the error is  1./SQRT(12.*N)

     'g'            Errors are 1./SQRT(W)  for W not equal to 0 and 0 for W = 0.
                    W is the sum in the bin of the weights of the profile.
                    This option is for combining measurements y +/- dy,
                    and  the profile is filled with values y and weights w = 1/dy**2

   See TProfile::BuildOptions for a detailed explanation of all options

 Stream an object of class TProfile.

 Create/delete 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.
 If flag is false the structure is deleted

 helper methods for the Merge unification in TProfileHelper