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TH1S TH1S() TH1S TH1S(const char* name, const char* title, Int_t nbinsx, Axis_t xlow, Axis_t xup) TH1S TH1S(const char* name, const char* title, Int_t nbinsx, const Float_t* xbins) TH1S TH1S(const char* name, const char* title, Int_t nbinsx, const Double_t* xbins) TH1S TH1S(const TH1S& h1s) virtual void ~TH1S() virtual void AddBinContent(Int_t bin) virtual void AddBinContent(Int_t bin, Stat_t w) static TClass* Class() virtual void Copy(TObject& hnew) virtual TH1* DrawCopy(Option_t* option) virtual Stat_t GetBinContent(Int_t bin) const virtual Stat_t GetBinContent(Int_t bin, Int_t) const virtual Stat_t GetBinContent(Int_t bin, Int_t, Int_t) const virtual TClass* IsA() const TH1S& operator=(const TH1S& h1) virtual void Reset(Option_t* option) virtual void SetBinContent(Int_t bin, Stat_t content) virtual void SetBinContent(Int_t bin, Int_t, Stat_t content) virtual void SetBinContent(Int_t bin, Int_t, Int_t, Stat_t content) virtual void SetBinsLength(Int_t nx) virtual void ShowMembers(TMemberInspector& insp, char* parent) virtual void Streamer(TBuffer& b) void StreamerNVirtual(TBuffer& b)

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The H I S T O G R A M Classes =============================== ROOT supports the following histogram types: 1-D histograms: TH1C : histograms with one byte per channel. Maximum bin content = 255 TH1S : histograms with one short per channel. Maximum bin content = 65535 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 = 255 TH2S : histograms with one short per channel. Maximum bin content = 65535 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 = 255 TH3S : histograms with one short per channel. Maximum bin content = 65535 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 TH1F TH1D | | | | | | | TH2 TProfile | | | | | ----------------------------- | | | | | | TH2C TH2S TH2F TH2D | | TH3 | | TProfile2D | ------------------------------ | | | | TH3C TH3S 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*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 bin = h->GetBin(binx,biny,binz); returns a global/linearized bin number. This global bin is useful to access the bin information independently of the dimension. Alphanumeric Bin Labels ======================= By default, an histogram axis is drawn with its numeric bin labels. One can specify alphanumeric labels instead with: 1- 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/labels1.C, labels2.C 2- 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/hlabels1.C, hlabels2.C 3- via TTree::Draw. see for example $ROOTSYS/tutorials/cern.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: 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) 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. 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 65535). 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. 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, eg: TH1F *hnew = (TH1F*)h->Clone(); hnew->SetName("hnew"); //recommended, otherwise you get 2 histograms //with the same name Normalizing histograms ====================== One can scale an histogram such that the bins integral is equal to to the normalization parameter via TH1::Scale(Double_t norm); 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. 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 Root Mean Square along axis TH1::GetEntries returns the number of entries TH1::Reset() resets the bin contents and errors of an histogram. /* */ -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*

TH1S(): TH1(), TArrayS()

TH1S(const char *name,const char *title,Int_t nbins,Axis_t xlow,Axis_t xup) : TH1(name,title,nbins,xlow,xup)

Create a 1-Dim histogram with fix bins of type short ==================================================== (see TH1::TH1 for explanation of parameters)

TH1S(const char *name,const char *title,Int_t nbins,const Float_t *xbins) : TH1(name,title,nbins,xbins)

Create a 1-Dim histogram with variable bins of type short ========================================================= (see TH1::TH1 for explanation of parameters)

TH1S(const char *name,const char *title,Int_t nbins,const Double_t *xbins) : TH1(name,title,nbins,xbins)

Create a 1-Dim histogram with variable bins of type short ========================================================= (see TH1::TH1 for explanation of parameters)

~TH1S()

TH1S(const TH1S &h1s)

void AddBinContent(Int_t bin)

-*-*-*-*-*-*-*-*Increment bin content by 1*-*-*-*-*-*-*-*-*-*-*-*-*-* ==========================

void AddBinContent(Int_t bin, Stat_t w)

Increment bin content by w ==========================

void Copy(TObject &newth1)

TH1* DrawCopy(Option_t *option)

Stat_t GetBinContent(Int_t bin) const

void Reset(Option_t *option)

void SetBinContent(Int_t bin, Stat_t content)

Set bin content In case the bin number is greater than the number of bins and the timedisplay option is set or the kCanRebin bit is set, the number of bins is automatically doubled to accomodate the new bin

Stat_t GetBinContent(Int_t bin, Int_t) const Stat_t GetBinContent(Int_t bin, Int_t, Int_t) const void SetBinContent(Int_t bin, Int_t, Stat_t content) void SetBinContent(Int_t bin, Int_t, Int_t, Stat_t content) void SetBinsLength(Int_t nx) TH1S& operator=(const TH1S& h1) TClass* Class() TClass* IsA() const void ShowMembers(TMemberInspector& insp, char* parent) void Streamer(TBuffer& b) void StreamerNVirtual(TBuffer& b)

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