TProfile2D

class TProfile2D : public TH2D

    private:

      Double_t* GetB()
      Double_t* GetW()
      Double_t* GetW2()

    protected:

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

    public:

                       TProfile2D()
                       TProfile2D(const char* name, const char* title, Int_t nbinsx, Axis_t xlow, Axis_t xup, Int_t nbinsy, Axis_t ylow, Axis_t yup, Axis_t zlow, Axis_t zup, Option_t* option = "")
                       TProfile2D(const char* name, const char* title, Int_t nbinsx, Axis_t xlow, Axis_t xup, Int_t nbinsy, Axis_t ylow, Axis_t yup, Option_t* option = "")
                       TProfile2D(const char* name, const char* title, Int_t nbinsx, const Double_t* xbins, Int_t nbinsy, Axis_t ylow, Axis_t yup, Option_t* option = "")
                       TProfile2D(const char* name, const char* title, Int_t nbinsx, Axis_t xlow, Axis_t xup, Int_t nbinsy, const Double_t* ybins, Option_t* option = "")
                       TProfile2D(const char* name, const char* title, Int_t nbinsx, const Double_t* xbins, Int_t nbinsy, const Double_t* ybins, Option_t* option = "")
                       TProfile2D(const TProfile2D& profile)
               virtual ~TProfile2D()
          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 zmin, Double_t zmax, 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)
         virtual Int_t Fill(const char*, Stat_t)
         virtual Int_t Fill(Axis_t, Stat_t)
         virtual Int_t Fill(Axis_t x, Axis_t y, Axis_t z)
         virtual Int_t Fill(Axis_t x, const char* namey, Axis_t z)
         virtual Int_t Fill(const char* namex, Axis_t y, Axis_t z)
         virtual Int_t Fill(const char* namex, const char* namey, Axis_t z)
         virtual Int_t Fill(Axis_t x, Axis_t y, Axis_t z, Stat_t w)
        virtual Stat_t GetBinContent(Int_t bin) const
        virtual Stat_t GetBinContent(Int_t binx, Int_t biny) const
        virtual Stat_t GetBinContent(Int_t binx, Int_t biny, 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 binx, Int_t biny) const
        virtual Stat_t GetBinError(Int_t binx, Int_t biny, Int_t) const
             Option_t* GetErrorOption() const
          virtual void GetStats(Stat_t* stats) const
      virtual Double_t GetZmax() const
      virtual Double_t GetZmin() 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 = "")
           TProfile2D& operator=(const TProfile2D&)
                 TH2D* ProjectionXY(const char* name = "_pxy", Option_t* option = "e") const
          virtual void PutStats(Stat_t* stats)
          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, Axis_t, Axis_t)
          virtual void SetBins(Int_t, const Axis_t*)
          virtual void SetBins(Int_t nbinsx, Axis_t xmin, Axis_t xmax, Int_t nbinsy, Axis_t ymin, Axis_t ymax)
          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)
          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 fZmin          Lower limit in Z (if set)
           Double_t fZmax          Upper limit in Z (if set)
             Bool_t fScaling       !True when TProfile2D::Scale is called
             Stat_t fTsumwz        Total Sum of weight*Z
             Stat_t fTsumwz2       Total Sum of weight*Z*Z
      static Bool_t fgApproximate  bin error approximation option

Class Description

  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();
}

*-*-*-*-*-*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.

 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 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 are computed. (default)

 Replace current statistics with the values in array stats

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

 Profile histogram is resized along ax 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);

 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.

Inline Functions

              Int_t BufferFill(Axis_t, Axis_t, Stat_t)
              Int_t BufferFill(Axis_t x, Axis_t y, Axis_t z, Stat_t w)
          Double_t* GetB()
          Double_t* GetW()
          Double_t* GetW2()
              Int_t Fill(const char* namex, Axis_t y, Axis_t z)
              Int_t Fill(const char* namex, const char* namey, Axis_t z)
              Int_t Fill(Axis_t x, Axis_t y, Axis_t z, Stat_t w)
             Stat_t GetBinContent(Int_t binx, Int_t biny) const
             Stat_t GetBinContent(Int_t binx, Int_t biny, Int_t) const
             Stat_t GetBinError(Int_t binx, Int_t biny) const
             Stat_t GetBinError(Int_t binx, Int_t biny, Int_t) const
           Double_t GetZmin() const
           Double_t GetZmax() const
               void SetBins(Int_t, const Axis_t*)
               void SetBins(Int_t nbinsx, Axis_t xmin, Axis_t xmax, Int_t nbinsy, Axis_t ymin, Axis_t ymax)
               void SetBins(Int_t, const Axis_t*, Int_t, const Axis_t*)
               void SetBins(Int_t, Axis_t, Axis_t, Int_t, Axis_t, Axis_t, Int_t, Axis_t, Axis_t)
            TClass* Class()
            TClass* IsA() const
               void ShowMembers(TMemberInspector& insp, char* parent)
               void StreamerNVirtual(TBuffer& b)
        TProfile2D& operator=(const TProfile2D&)