TProfile

class TProfile : public TH1D

    private:

      virtual Int_t Fill(Axis_t)
       virtual void FillN(Int_t, const Axis_t*, const Double_t*, Int_t)
          Double_t* GetB()
          Double_t* GetW()
          Double_t* GetW2()
       virtual void SetBins(Int_t, Axis_t, Axis_t, Int_t, Axis_t, Axis_t)
       virtual void SetBins(Int_t, const Axis_t*, Int_t, const Axis_t*)
       virtual void SetBins(Int_t, Axis_t, Axis_t, Int_t, Axis_t, Axis_t, Int_t, Axis_t, Axis_t)

    protected:

      virtual Int_t BufferFill(Axis_t, Stat_t)
      virtual Int_t BufferFill(Axis_t x, Axis_t y, Stat_t w)

    public:

                       TProfile()
                       TProfile(const char* name, const char* title, Int_t nbinsx, Axis_t xlow, Axis_t xup, Option_t* option = "")
                       TProfile(const char* name, const char* title, Int_t nbinsx, Axis_t xlow, Axis_t xup, Axis_t ylow, Axis_t yup, Option_t* option = "")
                       TProfile(const char* name, const char* title, Int_t nbinsx, const Float_t* xbins, Option_t* option = "")
                       TProfile(const char* name, const char* title, Int_t nbinsx, const Double_t* xbins, Option_t* option = "")
                       TProfile(const char* name, const char* title, Int_t nbinsx, const Double_t* xbins, Axis_t ylow, Axis_t yup, Option_t* option = "")
                       TProfile(const TProfile& profile)
               virtual ~TProfile()
          virtual void Add(TF1* h1, Double_t c1 = 1, Option_t* option = "")
          virtual void Add(const TH1* h1, Double_t c1 = 1)
          virtual void Add(const TH1* h1, const TH1* h2, Double_t c1 = 1, Double_t c2 = 1)
           static void Approximate(Bool_t approx = kTRUE)
         virtual Int_t BufferEmpty(Int_t action = 0)
                  void BuildOptions(Double_t ymin, Double_t ymax, Option_t* option)
        static TClass* Class()
          virtual void Copy(TObject& hnew) const
          virtual void Divide(TF1* h1, Double_t c1 = 1)
          virtual void Divide(const TH1* h1)
          virtual void Divide(const TH1* h1, const TH1* h2, Double_t c1 = 1, Double_t c2 = 1, Option_t* option = "")
          virtual TH1* DrawCopy(Option_t* option = "") const
         virtual Int_t Fill(Axis_t x, Axis_t y)
         virtual Int_t Fill(const char* namex, Axis_t y)
         virtual Int_t Fill(Axis_t x, Axis_t y, Stat_t w)
         virtual Int_t Fill(const char* namex, Axis_t y, Stat_t w)
          virtual void FillN(Int_t ntimes, const Axis_t* x, const Axis_t* y, const Double_t* w, Int_t stride = 1)
        virtual Stat_t GetBinContent(Int_t bin) const
        virtual Stat_t GetBinContent(Int_t bin, Int_t) const
        virtual Stat_t GetBinContent(Int_t bin, Int_t, Int_t) const
        virtual Stat_t GetBinEntries(Int_t bin) const
        virtual Stat_t GetBinError(Int_t bin) const
        virtual Stat_t GetBinError(Int_t bin, Int_t) const
        virtual Stat_t GetBinError(Int_t bin, Int_t, Int_t) const
             Option_t* GetErrorOption() const
          virtual void GetStats(Stat_t* stats) const
      virtual Double_t GetYmax() const
      virtual Double_t GetYmin() const
       virtual TClass* IsA() const
          virtual void LabelsDeflate(Option_t* axis = "X")
          virtual void LabelsInflate(Option_t* axis = "X")
          virtual void LabelsOption(Option_t* option = "h", Option_t* axis = "X")
      virtual Long64_t Merge(TCollection* list)
          virtual void Multiply(TF1* h1, Double_t c1 = 1)
          virtual void Multiply(const TH1* h1)
          virtual void Multiply(const TH1* h1, const TH1* h2, Double_t c1 = 1, Double_t c2 = 1, Option_t* option = "")
             TProfile& operator=(const TProfile&)
                 TH1D* ProjectionX(const char* name = "_px", Option_t* option = "e") const
          virtual void PutStats(Stat_t* stats)
          virtual TH1* Rebin(Int_t ngroup = 2, const char* newname = "")
          virtual void RebinAxis(Axis_t x, const char* ax)
          virtual void Reset(Option_t* option = "")
          virtual void SavePrimitive(ofstream& out, Option_t* option)
          virtual void Scale(Double_t c1 = 1)
          virtual void SetBinEntries(Int_t bin, Stat_t w)
          virtual void SetBins(Int_t nbins, Axis_t xmin, Axis_t xmax)
          virtual void SetBins(Int_t nx, const Axis_t* xbins)
          virtual void SetBuffer(Int_t buffersize, Option_t* option = "")
          virtual void SetErrorOption(Option_t* option = "")
          virtual void ShowMembers(TMemberInspector& insp, char* parent)
          virtual void Streamer(TBuffer& b)
                  void StreamerNVirtual(TBuffer& b)

Data Members

    protected:

            TArrayD fBinEntries    number of entries per bin
         EErrorType fErrorMode     Option to compute errors
           Double_t fYmin          Lower limit in Y (if set)
           Double_t fYmax          Upper limit in Y (if set)
             Bool_t fScaling       !True when TProfile::Scale is called
             Stat_t fTsumwy        Total Sum of weight*Y
             Stat_t fTsumwy2       Total Sum of weight*Y*Y
      static Bool_t fgApproximate  bin error approximation option

Class Description

  Profile histograms are used to display the mean
  value of Y and its RMS for each bin in X. Profile histograms are in many cases an
  elegant replacement of two-dimensional histograms : the inter-relation of two
  measured quantities X and Y can always be visualized by a two-dimensional
  histogram or scatter-plot; its representation on the line-printer is not particularly
  satisfactory, except for sparse data. If Y is an unknown (but single-valued)
  approximate function of X, this function is displayed by a profile 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 bin J.

                                                    2
      H(J)  =  sum Y                  E(J)  =  sum Y
      l(J)  =  sum l                  L(J)  =  sum l
      h(J)  =  H(J)/L(J)              s(J)  =  sqrt(E(J)/L(J)- h(J)**2)
      e(J)  =  s(J)/sqrt(L(J))

  In the special case where s(J) is zero (eg, case of 1 entry only in one bin)
  e(J) is computed from the average of the s(J) for all bins.
  This simple/crude approximation was suggested in order to keep the bin
  during a fit operation.

           Example of a profile histogram with its graphics output
{
  TCanvas *c1 = new TCanvas("c1","Profile histogram example",200,10,700,500);
  hprof  = new TProfile("hprof","Profile of pz versus px",100,-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;
     hprof->Fill(px,pz,1);
  }
  hprof->Draw();
}

*-*-*-*-*-*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 YMIN and YMAX will be considered at filling time.
  ymin and ymax 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*-*-*-*-*-*-*-*-*
*-*          ===========================================

    If a bin has N data points all with the same value Y (especially
    possible when dealing with integers), the spread in Y for that bin
    is zero, and the uncertainty assigned is also zero, and the bin is
    ignored in making subsequent fits. If SQRT(Y) was the correct error
    in the case above, then SQRT(Y)/SQRT(N) would be the correct error here.
    In fact, any bin with non-zero number of entries N but with zero spread
    should have an uncertainty SQRT(Y)/SQRT(N).

    Now, is SQRT(Y)/SQRT(N) really the correct uncertainty?
    that it is only in the case where the Y variable is some sort
    of counting statistics, following a Poisson distribution. This should
    probably be set as the default case. However, Y 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(Y)/SQRT(N) for Spread.eq.0,N.gt.0 ,
                      "     "  0.  for N.eq.0
     's'            Errors are Spread  for Spread.ne.0. ,
                      "     "  SQRT(Y)  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 Y values for which the
    uncertainty is +-0.5, with the assumption that the probability that Y
    takes any value between Y-0.5 and Y+0.5 is uniform (the same argument
    goes for Y uniformly distributed between Y and Y+1); this would be
    useful if Y is an ADC measurement, for example. Other, fancier options
    would be possible, at the cost of adding one more parameter to the PROFILE
    command. For example, if all Y 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 Y's are experimental quantities
    measured with the same instrument with precision Sigma.

 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

     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)

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

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

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

   this = c1*h1/(c2*h2)

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

 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

*-*-*-*-*-*-*-*-*-*-*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 are computed. (default)
   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)

 Replace current statistics with the values in array stats

*-*-*-*-*Rebin this profile grouping ngroup bins together*-*-*-*-*-*-*-*-*
*-*      ================================================
   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.

 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 the buffer size in units of 8 bytes (double)

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

    The computation of errors is based on the parameter option:
    option:
     ' '  (Default) Errors are Spread/SQRT(N) for Spread.ne.0. ,
                      "     "  SQRT(Y)/SQRT(N) for Spread.eq.0,N.gt.0 ,
                      "     "  0.  for N.eq.0
     's'            Errors are Spread  for Spread.ne.0. ,
                      "     "  SQRT(Y)  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 TProfile::BuildOptions for explanation of all options

 Stream an object of class TProfile.

Inline Functions

              Int_t BufferFill(Axis_t x, Axis_t y, Stat_t w)
               void SetBins(Int_t, Axis_t, Axis_t, Int_t, Axis_t, Axis_t, Int_t, Axis_t, Axis_t)
          Double_t* GetB()
          Double_t* GetW()
          Double_t* GetW2()
              Int_t Fill(const char* namex, Axis_t y, Stat_t w)
               void FillN(Int_t ntimes, const Axis_t* x, const Axis_t* y, const Double_t* w, Int_t stride = 1)
             Stat_t GetBinContent(Int_t bin, Int_t) const
             Stat_t GetBinContent(Int_t bin, Int_t, Int_t) const
             Stat_t GetBinError(Int_t bin, Int_t) const
             Stat_t GetBinError(Int_t bin, Int_t, Int_t) const
           Double_t GetYmin() const
           Double_t GetYmax() const
               void SetBins(Int_t nbins, Axis_t xmin, Axis_t xmax)
               void SetBins(Int_t nx, const Axis_t* xbins)
            TClass* Class()
            TClass* IsA() const
               void ShowMembers(TMemberInspector& insp, char* parent)
               void StreamerNVirtual(TBuffer& b)
          TProfile& operator=(const TProfile&)