# class TProfile3D: public TH3D

```
Profile3D histograms are used to display the mean
value of T and its RMS for each cell in X,Y,Z.
Profile3D histograms are in many cases an
The inter-relation of three measured quantities X, Y, Z and T can always
be visualized by a four-dimensional histogram or scatter-plot;
its representation on the line-printer is not particularly
satisfactory, except for sparse data. If T is an unknown (but single-valued)
approximate function of X,Y,Z this function is displayed by a profile3D 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,K)  =  sum T                      E(I,J,K)  =  sum T
l(I,J,K)  =  sum l                      L(I,J,K)  =  sum l
h(I,J,K)  =  H(I,J,K)/L(I,J,K)          s(I,J,K)  =  sqrt(E(I,J,K)/L(I,J,K)- h(I,J,K)**2)
e(I,J,K)  =  s(I,J,K)/sqrt(L(I,J,K))

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

Example of a profile3D histogram
{
TCanvas *c1 = new TCanvas("c1","Profile histogram example",200,10,700,500);
hprof3d  = new TProfile3D("hprof3d","Profile of pt versus px, py and pz",40,-4,4,40,-4,4,40,0,20);
Double_t px, py, pz, pt;
TRandom3 r(0);
for ( Int_t i=0; i<25000; i++) {
r.Rannor(px,py);
pz = px*px + py*py;
pt = r.Landau(0,1);
hprof3d->Fill(px,py,pz,pt,1);
}
hprof3d->Draw();
}

NOTE: A TProfile3D is drawn as it was a simple TH3
```

## Function Members (Methods)

public:
protected:
 Bool_t TArray::BoundsOk(const char* where, Int_t at) const virtual Int_t BufferFill(Double_t, Double_t) virtual Int_t BufferFill(Double_t, Double_t, Double_t) virtual Int_t BufferFill(Double_t, Double_t, Double_t, Double_t) virtual Int_t BufferFill(Double_t x, Double_t y, Double_t z, Double_t t, Double_t w) static bool TH1::CheckAxisLimits(const TAxis* a1, const TAxis* a2) static bool TH1::CheckBinLimits(const TAxis* a1, const TAxis* a2) static bool TH1::CheckConsistency(const TH1* h1, const TH1* h2) static bool TH1::CheckConsistentSubAxes(const TAxis* a1, Int_t firstBin1, Int_t lastBin1, const TAxis* a2, Int_t firstBin2 = 0, Int_t lastBin2 = 0) static bool TH1::CheckEqualAxes(const TAxis* a1, const TAxis* a2) virtual void TObject::DoError(int level, const char* location, const char* fmt, va_list va) const void TH3::DoFillProfileProjection(TProfile2D* p2, const TAxis& a1, const TAxis& a2, const TAxis& a3, Int_t bin1, Int_t bin2, Int_t bin3, Int_t inBin, Bool_t useWeights) const virtual Double_t TH1::DoIntegral(Int_t ix1, Int_t ix2, Int_t iy1, Int_t iy2, Int_t iz1, Int_t iz2, Double_t& err, Option_t* opt, Bool_t doerr = kFALSE) const TH1D* TH3::DoProject1D(const char* name, const char* title, TAxis* projX, bool computeErrors, bool originalRange, bool useUF, bool useOF) const TH2D* TH3::DoProject2D(const char* name, const char* title, TAxis* projX, TAxis* projY, bool computeErrors, bool originalRange, bool useUF, bool useOF) const TProfile2D* TH3::DoProjectProfile2D(const char* name, const char* title, TAxis* projX, TAxis* projY, bool originalRange, bool useUF, bool useOF) const Int_t Fill(const Double_t* v) virtual Bool_t TH1::FindNewAxisLimits(const TAxis* axis, const Double_t point, Double_t& newMin, Double_t& newMax) void TObject::MakeZombie() Bool_t TArray::OutOfBoundsError(const char* where, Int_t i) const static Bool_t TH1::RecomputeAxisLimits(TAxis& destAxis, const TAxis& anAxis) static Bool_t TH1::SameLimitsAndNBins(const TAxis& axis1, const TAxis& axis2) virtual void TH1::SavePrimitiveHelp(ostream& out, const char* hname, Option_t* option = "") void SetBins(const Int_t* nbins, const Double_t* range)
private:
 Double_t* GetB() Double_t* GetB2() Double_t* GetW() Double_t* GetW2() virtual void SetBins(Int_t, const Double_t*) virtual void SetBins(Int_t, Double_t, Double_t) virtual void SetBins(Int_t, const Double_t*, Int_t, const Double_t*) virtual void SetBins(Int_t, Double_t, Double_t, Int_t, Double_t, Double_t)

## Data Members

public:
 enum TH1::[unnamed] { kNoStats kUserContour kCanRebin kLogX kIsZoomed kNoTitle kIsAverage kNstat }; enum TObject::EStatusBits { kCanDelete kMustCleanup kObjInCanvas kIsReferenced kHasUUID kCannotPick kNoContextMenu kInvalidObject }; enum TObject::[unnamed] { kIsOnHeap kNotDeleted kZombie kBitMask kSingleKey kOverwrite kWriteDelete };
public:
 Double_t* TArrayD::fArray [fN] Array of fN doubles Int_t TArray::fN Number of array elements
protected:
 Short_t TH1::fBarOffset (1000*offset) for bar charts or legos Short_t TH1::fBarWidth (1000*width) for bar charts or legos TArrayD fBinEntries number of entries per bin TArrayD fBinSumw2 Array of sum of squares of weights per bin Double_t* TH1::fBuffer [fBufferSize] entry buffer Int_t TH1::fBufferSize fBuffer size TArrayD TH1::fContour Array to display contour levels Int_t TH1::fDimension !Histogram dimension (1, 2 or 3 dim) TDirectory* TH1::fDirectory !Pointer to directory holding this histogram Double_t TH1::fEntries Number of entries EErrorType fErrorMode Option to compute errors Color_t TAttFill::fFillColor fill area color Style_t TAttFill::fFillStyle fill area style TList* TH1::fFunctions ->Pointer to list of functions (fits and user) Double_t* TH1::fIntegral !Integral of bins used by GetRandom Color_t TAttLine::fLineColor line color Style_t TAttLine::fLineStyle line style Width_t TAttLine::fLineWidth line width Color_t TAttMarker::fMarkerColor Marker color index Size_t TAttMarker::fMarkerSize Marker size Style_t TAttMarker::fMarkerStyle Marker style Double_t TH1::fMaximum Maximum value for plotting Double_t TH1::fMinimum Minimum value for plotting TString TNamed::fName object identifier Int_t TH1::fNcells number of bins(1D), cells (2D) +U/Overflows Double_t TH1::fNormFactor Normalization factor TString TH1::fOption histogram options TVirtualHistPainter* TH1::fPainter !pointer to histogram painter Bool_t fScaling !True when TProfile3D::Scale is called TArrayD TH1::fSumw2 Array of sum of squares of weights TString TNamed::fTitle object title Double_t fTmax Upper limit in T (if set) Double_t fTmin Lower limit in T (if set) Double_t TH1::fTsumw Total Sum of weights Double_t TH1::fTsumw2 Total Sum of squares of weights Double_t fTsumwt Total Sum of weight*T Double_t fTsumwt2 Total Sum of weight*T*T Double_t TH1::fTsumwx Total Sum of weight*X Double_t TH1::fTsumwx2 Total Sum of weight*X*X Double_t TH3::fTsumwxy Total Sum of weight*X*Y Double_t TH3::fTsumwxz Total Sum of weight*X*Z Double_t TH3::fTsumwy Total Sum of weight*Y Double_t TH3::fTsumwy2 Total Sum of weight*Y*Y Double_t TH3::fTsumwyz Total Sum of weight*Y*Z Double_t TH3::fTsumwz Total Sum of weight*Z Double_t TH3::fTsumwz2 Total Sum of weight*Z*Z TAxis TH1::fXaxis X axis descriptor TAxis TH1::fYaxis Y axis descriptor TAxis TH1::fZaxis Z axis descriptor static Bool_t TH1::fgAddDirectory !flag to add histograms to the directory static Bool_t fgApproximate bin error approximation option static Int_t TH1::fgBufferSize !default buffer size for automatic histograms static Bool_t TH1::fgDefaultSumw2 !flag to call TH1::Sumw2 automatically at histogram creation time static Bool_t TH1::fgStatOverflows !flag to use under/overflows in statistics

## Function documentation

```Default constructor for Profile3D histograms*-*-*-
*-*        ============================================
```

```Default destructor for Profile3D histograms*-*-*-
*-*        ===========================================
```
TProfile3D(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, Option_t* option = "")
```Normal Constructor for Profile histograms*-*-*-*-
*-*        ==========================================

The first eleven parameters are similar to TH3D::TH3D.
All values of t are accepted at filling time.
To fill a profile3D histogram, one must use TProfile3D::Fill function.

Note that when filling the profile histogram the function Fill
checks if the variable t is betyween fTmin and fTmax.
If a minimum or maximum value is set for the T scale before filling,
then all values below tmin or above tmax will be discarded.
Setting the minimum or maximum value for the T scale before filling
has the same effect as calling the special TProfile3D constructor below
where tmin and tmax are specified.

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

See TProfile3D::BuildOptions for explanation of parameters

see other constructors below with all possible combinations of
fix and variable bin size like in TH3D.
```
TProfile3D(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, Option_t* option = "")
```  Create a 3-D Profile with variable bins in X , Y and Z
```
void BuildOptions(Double_t tmin, Double_t tmax, Option_t* option)
```Set Profile3D histogram structure and options*-*-
*-*          =============================================

If a cell has N data points all with the same value T (especially
possible when dealing with integers), the spread in T for that cell
is zero, and the uncertainty assigned is also zero, and the cell is
ignored in making subsequent fits. If SQRT(T) was the correct error
in the case above, then SQRT(T)/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(T)/SQRT(N).

Now, is SQRT(T)/SQRT(N) really the correct uncertainty?
that it is only in the case where the T variable is some sort
of counting statistics, following a Poisson distribution. This should
probably be set as the default case. However, T 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(T)/SQRT(N) for Spread.eq.0,N.gt.0 ,
"     "  0.  for N.eq.0
's'            Errors are Spread  for Spread.ne.0. ,
"     "  SQRT(T)  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 T values for which the
uncertainty is +-0.5, with the assumption that the probability that T
takes any value between T-0.5 and T+0.5 is uniform (the same argument
goes for T uniformly distributed between T and T+1); this would be
useful if T 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 T 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 T's are experimental quantities
measured with the same instrument with precision Sigma.

```
TProfile3D(const TProfile3D& profile)
```copy constructor
```
void Add(TF1* h1, Double_t c1 = 1, Option_t* option = "")
``` Performs the operation: this = this + c1*f1
```
void Add(const TH1* h1, Double_t c1 = 1)
``` Performs the operation: this = this + c1*h1
```
void Add(const TH1* h1, const TH1* h2, Double_t c1 = 1, Double_t c2 = 1)
```-*-*Replace contents of this profile3D by the addition of h1 and h2
*-*      ===============================================================

this = c1*h1 + c2*h2

```
void Approximate(Bool_t approx = kTRUE)
```     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 profile3D is less than 10404 (eg 100x100x100)
- the bin number of entries is small ( <5)
- the estimated bin error is extremely small compared to the bin content
(see TProfile3D::GetBinError)
```
Int_t BufferEmpty(Int_t action = 0)
``` 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
fBuffer[5] = t of first entry
```
void Copy(TObject& hnew) const
```-*-*-*-*Copy a Profile3D histogram to a new profile2D histogram
*-*            =======================================================
```
void Divide(TF1* h1, Double_t c1 = 1)
``` Performs the operation: this = this/(c1*f1)
```
void Divide(const TH1* h1)
```Divide this profile2D by h1*-*-
*-*                  ===========================

this = this/h1

```
void Divide(const TH1* h1, const TH1* h2, Double_t c1 = 1, Double_t c2 = 1, Option_t* option = "")
```-*-*Replace contents of this profile2D by the division of h1 by h2
*-*      ==============================================================

this = c1*h1/(c2*h2)

```
TH1 * DrawCopy(Option_t* option = "") const
```Draw a copy of this profile3D histogram*-*-*-
*-*            =======================================
```

```-*-*-*Fill a Profile3D histogram (no weights)
*-*                  =======================================
```

```-*-*-*Fill a Profile3D histogram with weights
*-*                  =======================================
```
Double_t GetBinContent(Int_t bin) const
```Return bin content of a Profile3D histogram*-*-
*-*          ===========================================
```
Double_t GetBinEntries(Int_t bin) const
```Return bin entries of a Profile3D 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.

*-*          =========================================
```
Double_t GetBinError(Int_t bin) const
``` *-*-*-*-*-*-*Return bin error of a Profile3D histogram*-*-*-*-*-*-*-*-*

Computing errors: A moving field

The computation of errors for a TProfile3D 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 TProfile3D is projected (ProjectionX). The previous algorithm
generated a N^2 problem when projecting a TProfile3D 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.
```
Option_t * GetErrorOption() const
```-*-*Return option to compute profile2D errors
*-*                =========================================
```
void GetStats(Double_t* stats) const
``` 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
stats[9] = sumwxz
stats[10]= sumwyz
stats[11]= sumwt
stats[12]= sumwt2

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.
```
Long64_t Merge(TCollection* list)
```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.
```
void Multiply(TF1* h1, Double_t c1 = 1)
``` Performs the operation: this = this*c1*f1
```
void Multiply(const TH1* h1)
```Multiply this profile2D by h1*-
*-*                  =============================

this = this*h1

```
void Multiply(const TH1* h1, const TH1* h2, Double_t c1 = 1, Double_t c2 = 1, Option_t* option = "")
```-*-*-*Replace contents of this profile2D by multiplication of h1 by h2
*-*      ================================================================

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

```
TH3D * ProjectionXYZ(const char* name = "_pxyz", Option_t* option = "e") const
```Project this profile3D into a 3-D histogram along X,Y,Z*-*-
*-*      =====================================================

The projection is always of the type TH3D.

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,
if option "C=E" the bin contents of the projection are set to the
bin errors of the profile

```
void PutStats(Double_t* stats)
``` Replace current statistics with the values in array stats
```
void Reset(Option_t* option = "")
```-*-*Reset contents of a Profile3D histogram
*-*                =======================================
```
void RebinAxis(Double_t x, TAxis* axis)
``` Profile histogram is resized along 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);
```
void SavePrimitive(ostream& out, Option_t* option = "")
``` Save primitive as a C++ statement(s) on output stream out
```
void Scale(Double_t c1 = 1, Option_t* option = "")
``` *-*-*-*-*Multiply this profile2D by a constant c1*-*-*-*-*-*-*-*-*
*-*      ========================================

this = c1*this

This function uses the services of TProfile3D::Add

```
void SetBinEntries(Int_t bin, Double_t w)
```Set the number of entries in bin*-*-*-
*-*              ================================
```
void SetBins(Int_t nbinsx, Double_t xmin, Double_t xmax, Int_t nbinsy, Double_t ymin, Double_t ymax, Int_t nbinsz, Double_t zmin, Double_t zmax)
```   -*-*-*-*-*-*-*Redefine  x, y and z axis parameters*-*-*-*-*-*-*-*-*-*-*-*
*-*              ===========================
```
void SetBins(Int_t nx, const Double_t* xBins, Int_t ny, const Double_t* yBins, Int_t nz, const Double_t* zBins)
```   -*-*-*-*-*-*-*Redefine  x, y and z axis parameters with variable bin sizes *-*-*-*-*-*-*-*-*

```
void SetBuffer(Int_t buffersize, Option_t* opt = "")
``` set the buffer size in units of 8 bytes (double)
```
void SetErrorOption(Option_t* option = "")
```-*-*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(T)/SQRT(N) for Spread.eq.0,N.gt.0 ,
"     "  0.  for N.eq.0
's'            Errors are Spread  for Spread.ne.0. ,
"     "  SQRT(T)  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 TProfile3D::BuildOptions for explanation of all options
```
void Sumw2()
``` Create 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.
```

`{return -2;}`

`{return -2;}`

`{return -2;}`
void SetBins(const Int_t* nbins, const Double_t* range)
``` helper methods for the Merge unification in TProfileHelper
```
Int_t Fill(const Double_t* v)
`{ return Fill(v[0], v[1], v[2], v[3], v[4]); }`
Double_t * GetB()
`{return &fBinEntries.fArray[0];}`

`{return (fBinSumw2.fN ? &fBinSumw2.fArray[0] : 0 ); }`
Double_t * GetW()
`{return &fArray[0];}`

`{return &fSumw2.fArray[0];}`
void SetBins(Int_t , Double_t , Double_t )
`{ MayNotUse("SetBins(Int_t, Double_t, Double_t"); }`
void SetBins(Int_t , const Double_t* )
`{ MayNotUse("SetBins(Int_t, const Double_t*"); }`

`{ MayNotUse("SetBins(Int_t, Double_t, Double_t, Int_t, Double_t, Double_t"); }`
void SetBins(Int_t , const Double_t* , Int_t , const Double_t* )
`{ MayNotUse("SetBins(Int_t, const Double_t*, Int_t, const Double_t*"); }`

`{return -1;}`
Int_t Fill(const char* , Double_t )
`{return -1;}`

`{return -1; }`

`{return -1; }`
Int_t Fill(const char* , const char* , const char* , Double_t )
`{return -1; }`
Int_t Fill(const char* , Double_t , const char* , Double_t )
`{return -1; }`
Int_t Fill(const char* , const char* , Double_t , Double_t )
`{return -1; }`
Int_t Fill(Double_t , const char* , const char* , Double_t )
`{return -1; }`
Int_t Fill(Double_t , const char* , Double_t , Double_t )
`{return -1; }`
Int_t Fill(Double_t , Double_t , const char* , Double_t )
`{return -1; }`
Double_t GetBinContent(Int_t bin) const
Double_t GetBinContent(Int_t , Int_t ) const
`{ MayNotUse("GetBinContent(Int_t, Int_t"); return -1; }`
Double_t GetBinError(Int_t bin) const
Double_t GetBinError(Int_t , Int_t ) const
`{ MayNotUse("GetBinError(Int_t, Int_t"); return -1; }`

`{return &fBinSumw2;}`
const TArrayD * GetBinSumw2() const
`{return &fBinSumw2;}`
Double_t GetTmin() const
`{return fTmin;}`
Double_t GetTmax() const
`{return fTmax;}`