library: libHist #include "TH3.h"

# TH3

class description - source file - inheritance tree (.pdf)

## class TH3 : public TH1, public TAtt3D

| Inheritance Chart:
`TObject`
| <- | `TNamed`
`TAttLine`
`TAttFill`
`TAttMarker`
| <- | `TH1`
`TAtt3D`
| <- | `TH3` |
<- |
`TH3C` |
`TH3D` |
`TH3F` |
`TH3I` |
`TH3S` |

        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:

                           TH3()
                           TH3(const char* name, const char* title, Int_t nbinsx, Axis_t xlow, Axis_t xup, Int_t nbinsy, Axis_t ylow, Axis_t yup, Int_t nbinsz, Axis_t zlow, Axis_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(Axis_t)
             virtual Int_t Fill(Axis_t, Stat_t)
             virtual Int_t Fill(const char*, Stat_t)
                     Int_t Fill(Axis_t, const char*, Stat_t)
                     Int_t Fill(const char*, Axis_t, Stat_t)
                     Int_t Fill(const char*, const char*, Stat_t)
             virtual Int_t Fill(Axis_t x, Axis_t y, Axis_t z)
             virtual Int_t Fill(Axis_t x, Axis_t y, Axis_t z, Stat_t w)
             virtual Int_t Fill(const char* namex, const char* namey, const char* namez, Stat_t w)
             virtual Int_t Fill(const char* namex, Axis_t y, const char* namez, Stat_t w)
             virtual Int_t Fill(const char* namex, const char* namey, Axis_t z, Stat_t w)
             virtual Int_t Fill(Axis_t x, const char* namey, const char* namez, Stat_t w)
             virtual Int_t Fill(Axis_t x, const char* namey, Axis_t z, Stat_t w)
             virtual Int_t Fill(Axis_t x, Axis_t y, const char* namez, Stat_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 Stat_t GetCorrelationFactor(Int_t axis1 = 1, Int_t axis2 = 2) const
            virtual Stat_t GetCovariance(Int_t axis1 = 1, Int_t axis2 = 2) const
              virtual void GetRandom3(Axis_t& x, Axis_t& y, Axis_t& z)
              virtual void GetStats(Stat_t* stats) const
            virtual Stat_t Integral(Option_t* option = "") const
            virtual Stat_t Integral(Int_t, Int_t, Option_t* = "") const
            virtual Stat_t Integral(Int_t, Int_t, Int_t, Int_t, Option_t* = "") const
            virtual Stat_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(TH1* h2, Option_t* option = "") const
          virtual Long64_t Merge(TCollection* list)
                      TH3& operator=(const TH3&)
                      TH1* Project3D(Option_t* option = "x") 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(Stat_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:

          Stat_t fTsumwy   Total Sum of weight*Y
          Stat_t fTsumwy2  Total Sum of weight*Y*Y
          Stat_t fTsumwxy  Total Sum of weight*X*Y
          Stat_t fTsumwz   Total Sum of weight*Z
          Stat_t fTsumwz2  Total Sum of weight*Z*Z
          Stat_t fTsumwxz  Total Sum of weight*X*Z
          Stat_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)

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

TH3()

TH3(const char *name,const char *title,Int_t nbinsx,Axis_t xlow,Axis_t xup ,Int_t nbinsy,Axis_t ylow,Axis_t yup ,Int_t nbinsz,Axis_t zlow,Axis_t zup) :TH1(name,title,nbinsx,xlow,xup), TAtt3D()

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

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) :TH1(name,title,nbinsx,xbins), TAtt3D()

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

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) :TH1(name,title,nbinsx,xbins), TAtt3D()

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

TH3(const TH3 &h) : TH1(), TAtt3D()

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

~TH3()

void Copy(TObject &obj) const

Int_t BufferEmpty(Int_t action)

     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

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

     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

Int_t Fill(Axis_t x, Axis_t y, Axis_t z)

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

Int_t Fill(Axis_t x, Axis_t y, Axis_t z, Stat_t w)

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

Int_t Fill(const char *namex, const char *namey, const char *namez, Stat_t w)

     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.

Int_t Fill(const char *namex, Axis_t y, const char *namez, Stat_t w)

     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.

Int_t Fill(const char *namex, const char *namey, Axis_t z, Stat_t w)

     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.

Int_t Fill(Axis_t x, const char *namey, const char *namez, Stat_t w)

     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.

Int_t Fill(Axis_t x, const char *namey, Axis_t z, Stat_t w)

     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.

Int_t Fill(Axis_t x, Axis_t y, const char *namez, Stat_t w)

     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.

void FillRandom(const char *fname, Int_t ntimes)

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

void FillRandom(TH1 *h, Int_t ntimes)

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

void FitSlicesZ(TF1 *f1, Int_t binminx, Int_t binmaxx, Int_t binminy, Int_t binmaxy, Int_t cut, Option_t *option)

     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");

Stat_t GetCorrelationFactor(Int_t axis1, Int_t axis2) const

    *-*-*-*-*-*-*-*Return correlation factor between axis1 and axis2*-*-*-*-*
    *-*            ====================================================

Stat_t GetCovariance(Int_t axis1, Int_t axis2) const

    *-*-*-*-*-*-*-*Return covariance between axis1 and axis2*-*-*-*-*
    *-*            ====================================================

void GetRandom3(Axis_t &x, Axis_t &y, Axis_t &z)

     return 3 random numbers along axis x , y and z distributed according
     the cellcontents of a 3-dim histogram

void GetStats(Stat_t *stats) const

     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

Stat_t Integral(Option_t *option) const

    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.

Stat_t Integral(Int_t binx1, Int_t binx2, Int_t biny1, Int_t biny2, Int_t binz1, Int_t binz2, Option_t *option) const

    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.

Double_t KolmogorovTest(TH1 *h2, Option_t *option) const

      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

Long64_t Merge(TCollection *list)

    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.

TH1D* ProjectionZ(const char *name, Int_t ixmin, Int_t ixmax, Int_t iymin, Int_t iymax, Option_t *option) const

    *-*-*-*-*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.

TH1* Project3D(Option_t *option) const

     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.

void PutStats(Stat_t *stats)

     Replace current statistics with the values in array stats

void Reset(Option_t *option)

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

void Streamer(TBuffer &R__b)

     Stream an object of class TH3.

### 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)
                  Int_t Fill(const char* namex, const char* namey, const char* namez, Stat_t w)
                  Int_t Fill(const char* namex, Axis_t y, const char* namez, Stat_t w)
                  Int_t Fill(const char* namex, const char* namey, Axis_t z, Stat_t w)
                  Int_t Fill(Axis_t x, const char* namey, const char* namez, Stat_t w)
                  Int_t Fill(Axis_t x, const char* namey, Axis_t z, Stat_t w)
                  Int_t Fill(Axis_t x, Axis_t y, const char* namez, Stat_t w)
                 Stat_t Integral(Int_t, Int_t, Int_t, Int_t, Option_t* = "") const
                 Stat_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&)

Author: Rene Brun 27/10/95
Last update: root/hist:$Name: $:$Id: TH3.cxx,v 1.63 2005/06/06 06:39:43 brun Exp $
Copyright (C) 1995-2000, Rene Brun and Fons Rademakers. *