TH3

class TH3 : public TH1, public TAtt3D

    protected:

      virtual Int_t BufferFill(Double_t, Double_t)
      virtual Int_t BufferFill(Double_t, Double_t, Double_t)
      virtual Int_t BufferFill(Double_t x, Double_t y, Double_t z, Double_t w)

    public:

                       TH3()
                       TH3(const char* name, const char* title, Int_t nbinsx, Double_t xlow, Double_t xup, Int_t nbinsy, Double_t ylow, Double_t yup, Int_t nbinsz, Double_t zlow, Double_t zup)
                       TH3(const char* name, const char* title, Int_t nbinsx, const Float_t* xbins, Int_t nbinsy, const Float_t* ybins, Int_t nbinsz, const Float_t* zbins)
                       TH3(const char* name, const char* title, Int_t nbinsx, const Double_t* xbins, Int_t nbinsy, const Double_t* ybins, Int_t nbinsz, const Double_t* zbins)
                       TH3(const TH3&)
               virtual ~TH3()
         virtual Int_t BufferEmpty(Int_t action = 0)
        static TClass* Class()
          virtual void Copy(TObject& hnew) const
         virtual Int_t Fill(Double_t)
         virtual Int_t Fill(Double_t, Double_t)
         virtual Int_t Fill(const char*, Double_t)
                 Int_t Fill(Double_t, const char*, Double_t)
                 Int_t Fill(const char*, Double_t, Double_t)
                 Int_t Fill(const char*, const char*, Double_t)
         virtual Int_t Fill(Double_t x, Double_t y, Double_t z)
         virtual Int_t Fill(Double_t x, Double_t y, Double_t z, Double_t w)
         virtual Int_t Fill(const char* namex, const char* namey, const char* namez, Double_t w)
         virtual Int_t Fill(const char* namex, Double_t y, const char* namez, Double_t w)
         virtual Int_t Fill(const char* namex, const char* namey, Double_t z, Double_t w)
         virtual Int_t Fill(Double_t x, const char* namey, const char* namez, Double_t w)
         virtual Int_t Fill(Double_t x, const char* namey, Double_t z, Double_t w)
         virtual Int_t Fill(Double_t x, Double_t y, const char* namez, Double_t w)
          virtual void FillRandom(const char* fname, Int_t ntimes = 5000)
          virtual void FillRandom(TH1* h, Int_t ntimes = 5000)
          virtual void FitSlicesZ(TF1* f1 = 0, Int_t binminx = 1, Int_t binmaxx = 0, Int_t binminy = 1, Int_t binmaxy = 0, Int_t cut = 0, Option_t* option = "QNR")
      virtual Double_t GetBinWithContent3(Double_t c, Int_t& binx, Int_t& biny, Int_t& binz, Int_t firstx = 0, Int_t lastx = 0, Int_t firsty = 0, Int_t lasty = 0, Int_t firstz = 0, Int_t lastz = 0, Double_t maxdiff = 0) const
      virtual Double_t GetCorrelationFactor(Int_t axis1 = 1, Int_t axis2 = 2) const
      virtual Double_t GetCovariance(Int_t axis1 = 1, Int_t axis2 = 2) const
          virtual void GetRandom3(Double_t& x, Double_t& y, Double_t& z)
          virtual void GetStats(Double_t* stats) const
      virtual Double_t Integral(Option_t* option = "") const
      virtual Double_t Integral(Int_t, Int_t, Option_t* = "") const
      virtual Double_t Integral(Int_t, Int_t, Int_t, Int_t, Option_t* = "") const
      virtual Double_t Integral(Int_t binx1, Int_t binx2, Int_t biny1, Int_t biny2, Int_t binz1, Int_t binz2, Option_t* option = "") const
       virtual TClass* IsA() const
      virtual Double_t KolmogorovTest(const TH1* h2, Option_t* option = "") const
      virtual Long64_t Merge(TCollection* list)
                  TH3& operator=(const TH3&)
                  TH1* Project3D(Option_t* option = "x") const
           TProfile2D* Project3DProfile(Option_t* option = "xy") const
                 TH1D* ProjectionZ(const char* name = "_pz", Int_t firstxbin = -1, Int_t lastxbin = 9999, Int_t firstybin = 0, Int_t lastybin = -1, Option_t* option = "") const
          virtual void PutStats(Double_t* stats)
          virtual void Reset(Option_t* option = "")
          virtual void ShowMembers(TMemberInspector& insp, char* parent)
          virtual void Streamer(TBuffer& b)
                  void StreamerNVirtual(TBuffer& b)

Data Members

    protected:

      Double_t fTsumwy   Total Sum of weight*Y
      Double_t fTsumwy2  Total Sum of weight*Y*Y
      Double_t fTsumwxy  Total Sum of weight*X*Y
      Double_t fTsumwz   Total Sum of weight*Z
      Double_t fTsumwz2  Total Sum of weight*Z*Z
      Double_t fTsumwxz  Total Sum of weight*X*Z
      Double_t fTsumwyz  Total Sum of weight*Y*Z

Class Description

*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*
*-*
*-*  The 3-D histogram classes derived from the 1-D histogram classes.
*-*  all operations are supported (fill, fit).
*-*  Drawing is currently restricted to one single option.
*-*  A cloud of points is drawn. The number of points is proportional to
*-*  cell content.
*-*

  TH3C a 3-D histogram with one byte per cell (char)
  TH3S a 3-D histogram with two bytes per cell (short integer)
  TH3I a 3-D histogram with four bytes per cell (32 bits integer)
  TH3F a 3-D histogram with four bytes per cell (float)
  TH3D a 3-D histogram with eight bytes per cell (double)

*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*

*-*-*-*-*-*-*-*-*Normal constructor for fix bin size 3-D histograms*-*-*-*-*
*-*              ==================================================

*-*-*-*-*-*-*-*Normal constructor for variable bin size 3-D histograms*-*-*-*
*-*            =======================================================

*-*-*-*-*-*-*-*Normal constructor for variable bin size 3-D histograms*-*-*-*
*-*            =======================================================

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

 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

*-*-*-*-*-*-*-*-*-*-*Increment cell defined by x,y,z by 1 *-*-*-*-*
*-*                  ====================================
*-*
*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*

*-*-*-*-*-*-*-*-*-*-*Increment cell defined by x,y,z by a weight 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^2 in the cell corresponding to x,y,z.
*-*
*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*

 Increment cell defined by namex,namey,namez by a weight 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^2 in the cell corresponding to x,y,z.

 Increment cell defined by namex,y,namez by a weight 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^2 in the cell corresponding to x,y,z.

 Increment cell defined by namex,namey,z by a weight 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^2 in the cell corresponding to x,y,z.

 Increment cell defined by x,namey,namezz by a weight 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^2 in the cell corresponding to x,y,z.

 Increment cell defined by x,namey,z by a weight 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^2 in the cell corresponding to x,y,z.

 Increment cell defined by x,y,namez by a weight 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^2 in the cell corresponding to x,y,z.

*-*-*-*-*-*-*Fill histogram following distribution in function fname*-*-*-*
*-*          =======================================================
*-*
*-*   The distribution contained in the function fname (TF1) 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 TF1::GetRandom to get a random variate from a function.
*-*
*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-**-*-*-*-*-*-*-*

*-*-*-*-*-*-*Fill histogram following distribution in histogram h*-*-*-*
*-*          ====================================================
*-*
*-*   The distribution contained in the histogram h (TH3) 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 Z in case of a 3-D histogram, then fit each slice
 with function f1 and make a 2-d histogram for each fit parameter
 Only cells in the bin range [binminx,binmaxx] and [binminy,binmaxy] are considered.
 if f1=0, a gaussian is assumed
 Before invoking this function, one can set a subrange to be fitted along Z
 via f1->SetRange(zmin,zmax)
 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

 Note that 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 3-d histogram h3
   Root > h3->FitSlicesZ(); produces 4 TH2D histograms
          with h3_0 containing parameter 0(Constant) for a Gaus fit
                    of each cell in X,Y projected along Z
          with h3_1 containing parameter 1(Mean) for a gaus fit
          with h3_2 containing parameter 2(RMS)  for a gaus fit
          with h3_chi2 containing the chisquare/number of degrees of freedom for a gaus fit

   Root > h3->Fit(0,15,22,0,0,10);
          same as above, but only for bins 15 to 22 along X
          and only for cells in X,Y for which the corresponding projection
          along Z has more than cut bins filled.

  NOTE: To access the generated histograms in the current directory, do eg:
     TH2D *h3_1 = (TH2D*)gDirectory->Get("h3_1");

 compute first cell (binx,biny,binz) in the range [firstx,lastx](firsty,lasty][firstz,lastz] 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,binz.
 In case several cells in the specified range satisfy diff <=maxdiff
 the cell with the smallest difference is returned in binx,biny,binz.
 In all cases the function returns the smallest difference.

 NOTE1: if firstx <= 0, firstx is set to bin 1
        if (lastx < firstx then firstx is set to the number of bins in X
        ie if firstx=0 and lastx=0 (default) the search is on all bins in X.
        if firsty <= 0, firsty is set to bin 1
        if (lasty < firsty then firsty is set to the number of bins in Y
        ie if firsty=0 and lasty=0 (default) the search is on all bins in Y.
        if firstz <= 0, firstz is set to bin 1
        if (lastz < firstz then firstz is set to the number of bins in Z
        ie if firstz=0 and lastz=0 (default) the search is on all bins in Z.
 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 3 random numbers along axis x , y and z distributed according
 the cellcontents of a 3-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
 stats[7] = sumwz
 stats[8] = sumwz2
 stats[9] = sumwxz
 stats[10]= sumwyz

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, y and in z.

Return integral of bin contents in range [binx1,binx2],[biny1,biny2],[binz1,binz2]
 for a 3-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, y and in z.

  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

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

        WARNING !!!! THIS FUNCTION NOT YET TESTED
  I started from TH2::KolmogorovTest, but changes are probably required
  when invoking KolmogorovProb to take into account the 3rd dimension
  It would be nice if a mathematician could look into this.

  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.

*-*-*-*-*Project a 3-D histogram into a 1-D histogram along Z*-*-*-*-*-*-*
*-*      ====================================================

   The projection is always of the type TH1D.
   The projection is made from the cells along the X axis
   ranging from ixmin to ixmax and iymin to iymax included.
   By default, bins 1 to nx and 1 to ny  are included

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

   NOTE1: 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.

   code from Paola Collins & Hans Dijkstra

   NOTE 2: The number of entries in the projected histogram is set to the
   number of entries of the parent histogram if all bins are selected,
   otherwise it is set to the sum of the bin contents.

 Project a 3-d histogram into 1 or 2-d histograms depending on the
 option parameter
 option may contain a combination of the characters x,y,z,e
 option = "x" return the x projection into a TH1D histogram
 option = "y" return the y projection into a TH1D histogram
 option = "z" return the z projection into a TH1D histogram
 option = "xy" return the x versus y projection into a TH2D histogram
 option = "yx" return the y versus x projection into a TH2D histogram
 option = "xz" return the x versus z projection into a TH2D histogram
 option = "zx" return the z versus x projection into a TH2D histogram
 option = "yz" return the y versus z projection into a TH2D histogram
 option = "zy" return the z versus y projection into a TH2D histogram

 If option contains the string "e", errors are computed

 The projection is made for the selected bins only.
 To select a bin range along an axis, use TAxis::SetRange, eg
    h3.GetYaxis()->SetRange(23,56);

 NOTE 1: The generated histogram is named th3name + option
 eg if the TH3* h histogram is named "myhist", then
 h->Project3D("xy"); produces a TH2D histogram named "myhist_xy"
 if a histogram of the same type already exists, it is overwritten.
 The following sequence
    h->Project3D("xy");
    h->Project3D("xy2");
  will generate two TH2D histograms named "myhist_xy" and "myhist_xy2"

  NOTE 2: The number of entries in the projected histogram is set to the
  number of entries of the parent histogram if all bins are selected,
  otherwise it is set to the sum of the bin contents.

 Project a 3-d histogram into a 2-d profile histograms depending
 on the option parameter
 option may contain a combination of the characters x,y,z
 option = "xy" return the x versus y projection into a TProfile2D histogram
 option = "yx" return the y versus x projection into a TProfile2D histogram
 option = "xz" return the x versus z projection into a TProfile2D histogram
 option = "zx" return the z versus x projection into a TProfile2D histogram
 option = "yz" return the y versus z projection into a TProfile2D histogram
 option = "zy" return the z versus y projection into a TProfile2D histogram

 The projection is made for the selected bins only.
 To select a bin range along an axis, use TAxis::SetRange, eg
    h3.GetYaxis()->SetRange(23,56);

 NOTE 1: The generated histogram is named th3name + _poption
 eg if the TH3* h histogram is named "myhist", then
 h->Project3D("xy"); produces a TProfile2D histogram named "myhist_pxy"
 if a histogram of the same type already exists, it is deleted.
 The following sequence
    h->Project3DProfile("xy");
    h->Project3DProfile("xy2");
  will generate two TProfile2D histograms named "myhist_pxy" and "myhist_pxy2"

  NOTE 2: The number of entries in the projected profile is set to the
  number of entries of the parent histogram if all bins are selected,
  otherwise it is set to the sum of the bin contents.

 Replace current statistics with the values in array stats

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

 Stream an object of class TH3.

Inline Functions

              Int_t BufferFill(Double_t, Double_t, Double_t)
              Int_t BufferFill(Double_t x, Double_t y, Double_t z, Double_t w)
              Int_t Fill(const char* namex, const char* namey, const char* namez, Double_t w)
              Int_t Fill(const char* namex, Double_t y, const char* namez, Double_t w)
              Int_t Fill(const char* namex, const char* namey, Double_t z, Double_t w)
              Int_t Fill(Double_t x, const char* namey, const char* namez, Double_t w)
              Int_t Fill(Double_t x, const char* namey, Double_t z, Double_t w)
              Int_t Fill(Double_t x, Double_t y, const char* namez, Double_t w)
           Double_t Integral(Int_t, Int_t, Int_t, Int_t, Option_t* = "") const
           Double_t Integral(Int_t binx1, Int_t binx2, Int_t biny1, Int_t biny2, Int_t binz1, Int_t binz2, Option_t* option = "") const
            TClass* Class()
            TClass* IsA() const
               void ShowMembers(TMemberInspector& insp, char* parent)
               void StreamerNVirtual(TBuffer& b)
               TH3& operator=(const TH3&)