class TH1D: public TH1, public TArrayD

The Histogram classes

ROOT supports the following histogram types:

• 1-D histograms:
  • TH1C : histograms with one byte per channel. Maximum bin content = 127
  • TH1S : histograms with one short per channel. Maximum bin content = 32767
  • TH1I : histograms with one int per channel. Maximum bin content = 2147483647
  • TH1F : histograms with one float per channel. Maximum precision 7 digits
  • TH1D : histograms with one double per channel. Maximum precision 14 digits
• 2-D histograms:
  • TH2C : histograms with one byte per channel. Maximum bin content = 127
  • TH2S : histograms with one short per channel. Maximum bin content = 32767
  • TH2I : histograms with one int per channel. Maximum bin content = 2147483647
  • TH2F : histograms with one float per channel. Maximum precision 7 digits
  • TH2D : histograms with one double per channel. Maximum precision 14 digits
• 3-D histograms:
  • TH3C : histograms with one byte per channel. Maximum bin content = 127
  • TH3S : histograms with one short per channel. Maximum bin content = 32767
  • TH3I : histograms with one int per channel. Maximum bin content = 2147483647
  • TH3F : histograms with one float per channel. Maximum precision 7 digits
  • TH3D : histograms with one double per channel. Maximum precision 14 digits
• Profile histograms: See classes TProfile and TProfile2D. 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; 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.

All histogram classes are derived from the base class TH1

                                TH1
                                 ^
                                 |
                                 |
                                 |
         -----------------------------------------------------------
                |                |       |      |      |     |     |
                |                |      TH1C   TH1S   TH1I  TH1F  TH1D
                |                |                                 |
                |                |                                 |
                |               TH2                             TProfile
                |                |
                |                |
                |                ----------------------------------
                |                        |      |      |     |     |
                |                       TH2C   TH2S   TH2I  TH2F  TH2D
                |                                                  |
               TH3                                                 |
                |                                               TProfile2D
                |
                -------------------------------------
                        |      |      |      |      |
                       TH3C   TH3S   TH3I   TH3F   TH3D
      The TH*C classes also inherit from the array class TArrayC.
      The TH*S classes also inherit from the array class TArrayS.
      The TH*I classes also inherit from the array class TArrayI.
      The TH*F classes also inherit from the array class TArrayF.
      The TH*D classes also inherit from the array class TArrayD.

Creating histograms

Histograms are created by invoking one of the constructors, eg

       TH1F *h1 = new TH1F("h1","h1 title",100,0,4.4);
       TH2F *h2 = new TH2F("h2","h2 title",40,0,4,30,-3,3);

Histograms may also be created by:

• calling the Clone function, see below
• making a projection from a 2-D or 3-D histogram, see below
• reading an histogram from a file

When an histogram is created, a reference to it is automatically added to the list of in-memory objects for the current file or directory. This default behaviour can be changed by:

       h->SetDirectory(0);          for the current histogram h
       TH1::AddDirectory(kFALSE);   sets a global switch disabling the reference

When the histogram is deleted, the reference to it is removed from the list of objects in memory. When a file is closed, all histograms in memory associated with this file are automatically deleted.

Fix or variable bin size

All histogram types support either fix or variable bin sizes. 2-D histograms may have fix size bins along X and variable size bins along Y or vice-versa. The functions to fill, manipulate, draw or access histograms are identical in both cases.

Each histogram always contains 3 objects TAxis: fXaxis, fYaxis and fZaxis To access the axis parameters, do:

        TAxis *xaxis = h->GetXaxis(); etc.
        Double_t binCenter = xaxis->GetBinCenter(bin), etc.

See class TAxis for a description of all the access functions. The axis range is always stored internally in double precision.

Convention for numbering bins

For all histogram types: nbins, xlow, xup

        bin = 0;       underflow bin
        bin = 1;       first bin with low-edge xlow INCLUDED
        bin = nbins;   last bin with upper-edge xup EXCLUDED
        bin = nbins+1; overflow bin

In case of 2-D or 3-D histograms, a "global bin" number is defined. For example, assuming a 3-D histogram with binx,biny,binz, the function

        Int_t gbin = h->GetBin(binx,biny,binz);

returns a global/linearized gbin number. This global gbin is useful to access the bin content/error information independently of the dimension. Note that to access the information other than bin content and errors one should use the TAxis object directly with eg:

         Double_t xcenter = h3->GetZaxis()->GetBinCenter(27);

returns the center along z of bin number 27 (not the global bin) in the 3-d histogram h3.

Alphanumeric Bin Labels

By default, an histogram axis is drawn with its numeric bin labels. One can specify alphanumeric labels instead with:

• call TAxis::SetBinLabel(bin,label); This can always be done before or after filling. When the histogram is drawn, bin labels will be automatically drawn. See example in $ROOTSYS/tutorials/graphs/labels1.C, labels2.C
• call to a Fill function with one of the arguments being a string, eg

             hist1->Fill(somename,weigth);
             hist2->Fill(x,somename,weight);
             hist2->Fill(somename,y,weight);
             hist2->Fill(somenamex,somenamey,weight);
  

  See example in $ROOTSYS/tutorials/hist/hlabels1.C, hlabels2.C
• via TTree::Draw. see for example $ROOTSYS/tutorials/tree/cernstaff.C

             tree.Draw("Nation::Division");
  

  where "Nation" and "Division" are two branches of a Tree.

When using the options 2 or 3 above, the labels are automatically added to the list (THashList) of labels for a given axis. By default, an axis is drawn with the order of bins corresponding to the filling sequence. It is possible to reorder the axis - alphabetically - by increasing or decreasing values The reordering can be triggered via the TAxis contextMenu by selecting the menu item "LabelsOption" or by calling directly TH1::LabelsOption(option,axis) where

• axis may be "X","Y" or "Z"
• option may be:
  • "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)

When using the option 2 above, new labels are added by doubling the current number of bins in case one label does not exist yet. When the Filling is terminated, it is possible to trim the number of bins to match the number of active labels by calling

           TH1::LabelsDeflate(axis) with axis = "X","Y" or "Z"

This operation is automatic when using TTree::Draw. Once bin labels have been created, they become persistent if the histogram is written to a file or when generating the C++ code via SavePrimitive.

Histograms with automatic bins

When an histogram is created with an axis lower limit greater or equal to its upper limit, the SetBuffer is automatically called with an argument fBufferSize equal to fgBufferSize (default value=1000). fgBufferSize may be reset via the static function TH1::SetDefaultBufferSize. The axis limits will be automatically computed when the buffer will be full or when the function BufferEmpty is called.

Filling histograms

An histogram is typically filled with statements like:

       h1->Fill(x);
       h1->Fill(x,w); fill with weight
       h2->Fill(x,y)
       h2->Fill(x,y,w)
       h3->Fill(x,y,z)
       h3->Fill(x,y,z,w)

or via one of the Fill functions accepting names described above. The Fill functions compute the bin number corresponding to the given x,y or z argument and increment this bin by the given weight. The Fill functions return the bin number for 1-D histograms or global bin number for 2-D and 3-D histograms.

If TH1::Sumw2 has been called before filling, the sum of squares of weights is also stored. One can also increment directly a bin number via TH1::AddBinContent or replace the existing content via TH1::SetBinContent. To access the bin content of a given bin, do:

       Double_t binContent = h->GetBinContent(bin);

By default, the bin number is computed using the current axis ranges. If the automatic binning option has been set via

       h->SetBit(TH1::kCanRebin);

then, the Fill Function will automatically extend the axis range to accomodate the new value specified in the Fill argument. The method used is to double the bin size until the new value fits in the range, merging bins two by two. This automatic binning options is extensively used by the TTree::Draw function when histogramming Tree variables with an unknown range.

This automatic binning option is supported for 1-d, 2-D and 3-D histograms. During filling, some statistics parameters are incremented to compute the mean value and Root Mean Square with the maximum precision.

In case of histograms of type TH1C, TH1S, TH2C, TH2S, TH3C, TH3S a check is made that the bin contents do not exceed the maximum positive capacity (127 or 32767). Histograms of all types may have positive or/and negative bin contents.

Rebinning

At any time, an histogram can be rebinned via TH1::Rebin. This function returns a new histogram with the rebinned contents. If bin errors were stored, they are recomputed during the rebinning.

Associated errors

By default, for each bin, the sum of weights is computed at fill time. One can also call TH1::Sumw2 to force the storage and computation of the sum of the square of weights per bin. If Sumw2 has been called, the error per bin is computed as the sqrt(sum of squares of weights), otherwise the error is set equal to the sqrt(bin content). To return the error for a given bin number, do:

        Double_t error = h->GetBinError(bin);

Associated functions

One or more object (typically a TF1*) can be added to the list of functions (fFunctions) associated to each histogram. When TH1::Fit is invoked, the fitted function is added to this list. Given an histogram h, one can retrieve an associated function with:

        TF1 *myfunc = h->GetFunction("myfunc");

Operations on histograms

Many types of operations are supported on histograms or between histograms

• Addition of an histogram to the current histogram
• Additions of two histograms with coefficients and storage into the current histogram
• Multiplications and Divisions are supported in the same way as additions.
• The Add, Divide and Multiply functions also exist to add,divide or multiply an histogram by a function.

If an histogram has associated error bars (TH1::Sumw2 has been called), the resulting error bars are also computed assuming independent histograms. In case of divisions, Binomial errors are also supported. One can mark a histogram to be an "average" histogram by setting its bit kIsAverage via myhist.SetBit(TH1::kIsAverage); When adding (see TH1::Add) average histograms, the histograms are averaged and not summed.

Fitting histograms

Histograms (1-D,2-D,3-D and Profiles) can be fitted with a user specified function via TH1::Fit. When an histogram is fitted, the resulting function with its parameters is added to the list of functions of this histogram. If the histogram is made persistent, the list of associated functions is also persistent. Given a pointer (see above) to an associated function myfunc, one can retrieve the function/fit parameters with calls such as:

       Double_t chi2 = myfunc->GetChisquare();
       Double_t par0 = myfunc->GetParameter(0); value of 1st parameter
       Double_t err0 = myfunc->GetParError(0);  error on first parameter

Projections of histograms

One can:

• make a 1-D projection of a 2-D histogram or Profile see functions TH2::ProjectionX,Y, TH2::ProfileX,Y, TProfile::ProjectionX
• make a 1-D, 2-D or profile out of a 3-D histogram see functions TH3::ProjectionZ, TH3::Project3D.

One can fit these projections via:

      TH2::FitSlicesX,Y, TH3::FitSlicesZ.

Random Numbers and histograms

TH1::FillRandom can be used to randomly fill an histogram using the contents of an existing TF1 function or another TH1 histogram (for all dimensions).

For example the following two statements create and fill an histogram 10000 times with a default gaussian distribution of mean 0 and sigma 1:

       TH1F h1("h1","histo from a gaussian",100,-3,3);
       h1.FillRandom("gaus",10000);

TH1::GetRandom can be used to return a random number distributed according the contents of an histogram.

Making a copy of an histogram

Like for any other ROOT object derived from TObject, one can use the Clone() function. This makes an identical copy of the original histogram including all associated errors and functions, e.g.:

       TH1F *hnew = (TH1F*)h->Clone("hnew");

Normalizing histograms

One can scale an histogram such that the bins integral is equal to the normalization parameter via TH1::Scale(Double_t norm), where norm is the desired normalization divided by the integral of the histogram.

Drawing histograms

Histograms are drawn via the THistPainter class. Each histogram has a pointer to its own painter (to be usable in a multithreaded program). Many drawing options are supported. See THistPainter::Paint() for more details.

The same histogram can be drawn with different options in different pads. When an histogram drawn in a pad is deleted, the histogram is automatically removed from the pad or pads where it was drawn. If an histogram is drawn in a pad, then filled again, the new status of the histogram will be automatically shown in the pad next time the pad is updated. One does not need to redraw the histogram. To draw the current version of an histogram in a pad, one can use

        h->DrawCopy();

This makes a clone (see Clone below) of the histogram. Once the clone is drawn, the original histogram may be modified or deleted without affecting the aspect of the clone.

One can use TH1::SetMaximum() and TH1::SetMinimum() to force a particular value for the maximum or the minimum scale on the plot.

TH1::UseCurrentStyle() can be used to change all histogram graphics attributes to correspond to the current selected style. This function must be called for each histogram. In case one reads and draws many histograms from a file, one can force the histograms to inherit automatically the current graphics style by calling before gROOT->ForceStyle().

Setting Drawing histogram contour levels (2-D hists only)

By default contours are automatically generated at equidistant intervals. A default value of 20 levels is used. This can be modified via TH1::SetContour() or TH1::SetContourLevel(). the contours level info is used by the drawing options "cont", "surf", and "lego".

Setting histogram graphics attributes

The histogram classes inherit from the attribute classes: TAttLine, TAttFill, TAttMarker and TAttText. See the member functions of these classes for the list of options.

Giving titles to the X, Y and Z axis

       h->GetXaxis()->SetTitle("X axis title");
       h->GetYaxis()->SetTitle("Y axis title");

The histogram title and the axis titles can be any TLatex string. The titles are part of the persistent histogram. It is also possible to specify the histogram title and the axis titles at creation time. These titles can be given in the "title" parameter. They must be separated by ";":

        TH1F* h=new TH1F("h","Histogram title;X Axis;Y Axis;Z Axis",100,0,1);

Any title can be omitted:

        TH1F* h=new TH1F("h","Histogram title;;Y Axis",100,0,1);
        TH1F* h=new TH1F("h",";;Y Axis",100,0,1);

The method SetTitle has the same syntax:

h->SetTitle("Histogram title;An other X title Axis");

Saving/Reading histograms to/from a ROOT file

The following statements create a ROOT file and store an histogram on the file. Because TH1 derives from TNamed, the key identifier on the file is the histogram name:

        TFile f("histos.root","new");
        TH1F h1("hgaus","histo from a gaussian",100,-3,3);
        h1.FillRandom("gaus",10000);
        h1->Write();

To Read this histogram in another Root session, do:

        TFile f("histos.root");
        TH1F *h = (TH1F*)f.Get("hgaus");

One can save all histograms in memory to the file by:

        file->Write();

Miscelaneous operations

        TH1::KolmogorovTest(): statistical test of compatibility in shape
                             between two histograms
        TH1::Smooth() smooths the bin contents of a 1-d histogram
        TH1::Integral() returns the integral of bin contents in a given bin range
        TH1::GetMean(int axis) returns the mean value along axis
        TH1::GetRMS(int axis)  returns the sigma distribution along axis
        TH1::GetEntries() returns the number of entries
        TH1::Reset() resets the bin contents and errors of an histogram