// @(#)root/hist:$Id: TH1.cxx 29184 2009-06-24 06:40:45Z brun $ // Author: Rene Brun 26/12/94 /************************************************************************* * Copyright (C) 1995-2000, Rene Brun and Fons Rademakers. * * All rights reserved. * * * * For the licensing terms see $ROOTSYS/LICENSE. * * For the list of contributors see $ROOTSYS/README/CREDITS. * *************************************************************************/ #include <stdlib.h> #include <string.h> #include <stdio.h> #include <ctype.h> #include "Riostream.h" #include "TROOT.h" #include "TClass.h" #include "TMath.h" #include "THashList.h" #include "TH1.h" #include "TH2.h" #include "TF2.h" #include "TF3.h" #include "TPluginManager.h" #include "TVirtualPad.h" #include "TRandom.h" #include "TVirtualFitter.h" #include "THLimitsFinder.h" #include "TProfile.h" #include "TStyle.h" #include "TVectorF.h" #include "TVectorD.h" #include "TBrowser.h" #include "TObjString.h" #include "TError.h" #include "TVirtualHistPainter.h" #include "TVirtualFFT.h" #include "TSystem.h" //______________________________________________________________________________ /* Begin_Html <center><h2>The Histogram classes</h2></center> ROOT supports the following histogram types: <ul> <li>1-D histograms: <ul> <li>TH1C : histograms with one byte per channel. Maximum bin content = 127 <li>TH1S : histograms with one short per channel. Maximum bin content = 32767 <li>TH1I : histograms with one int per channel. Maximum bin content = 2147483647 <li>TH1F : histograms with one float per channel. Maximum precision 7 digits <li>TH1D : histograms with one double per channel. Maximum precision 14 digits </ul> <li>2-D histograms: <ul> <li>TH2C : histograms with one byte per channel. Maximum bin content = 127 <li>TH2S : histograms with one short per channel. Maximum bin content = 32767 <li>TH2I : histograms with one int per channel. Maximum bin content = 2147483647 <li>TH2F : histograms with one float per channel. Maximum precision 7 digits <li>TH2D : histograms with one double per channel. Maximum precision 14 digits </ul> <li>3-D histograms: <ul> <li>TH3C : histograms with one byte per channel. Maximum bin content = 127 <li>TH3S : histograms with one short per channel. Maximum bin content = 32767 <li>TH3I : histograms with one int per channel. Maximum bin content = 2147483647 <li>TH3F : histograms with one float per channel. Maximum precision 7 digits <li>TH3D : histograms with one double per channel. Maximum precision 14 digits </ul> <li>Profile histograms: See classes TProfile, TProfile2D and TProfile3D. 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. </ul> All histogram classes are derived from the base class TH1 <pre> TH1 ^ | | | ----------------------------------------------------------- | | | | | | | | | TH1C TH1S TH1I TH1F TH1D | | | | | | | TH2 TProfile | | | | | ---------------------------------- | | | | | | | TH2C TH2S TH2I TH2F TH2D | | TH3 | | TProfile2D | ------------------------------------- | | | | | TH3C TH3S TH3I TH3F TH3D | | TProfile3D 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. </pre> <h4>Creating histograms</h4> <p> Histograms are created by invoking one of the constructors, e.g. <pre> TH1F *h1 = new TH1F("h1", "h1 title", 100, 0, 4.4); TH2F *h2 = new TH2F("h2", "h2 title", 40, 0, 4, 30, -3, 3); </pre> <p> Histograms may also be created by: <ul> <li> calling the Clone function, see below <li> making a projection from a 2-D or 3-D histogram, see below <li> reading an histogram from a file </ul> <p> 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: <pre> h->SetDirectory(0); for the current histogram h TH1::AddDirectory(kFALSE); sets a global switch disabling the reference </pre> 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. <h4>Fix or variable bin size</h4> 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. <p> Each histogram always contains 3 objects TAxis: fXaxis, fYaxis and fZaxis To access the axis parameters, do: <pre> TAxis *xaxis = h->GetXaxis(); etc. Double_t binCenter = xaxis->GetBinCenter(bin), etc. </pre> See class TAxis for a description of all the access functions. The axis range is always stored internally in double precision. <h4>Convention for numbering bins</h4> For all histogram types: nbins, xlow, xup <pre> 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 </pre> <p> 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 <pre> Int_t gbin = h->GetBin(binx, biny, binz); </pre> 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 e.g.: <pre> Double_t xcenter = h3->GetZaxis()->GetBinCenter(27); </pre> returns the center along z of bin number 27 (not the global bin) in the 3-D histogram h3. <h4>Alphanumeric Bin Labels</h4> By default, an histogram axis is drawn with its numeric bin labels. One can specify alphanumeric labels instead with: <ul> <li> 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 <li> call to a Fill function with one of the arguments being a string, e.g. <pre> hist1->Fill(somename, weigth); hist2->Fill(x, somename, weight); hist2->Fill(somename, y, weight); hist2->Fill(somenamex, somenamey, weight); </pre> See example in $ROOTSYS/tutorials/hist/hlabels1.C, hlabels2.C <li> via TTree::Draw. see for example $ROOTSYS/tutorials/tree/cernstaff.C <pre> tree.Draw("Nation::Division"); </pre> where "Nation" and "Division" are two branches of a Tree. </ul> <p> 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 <ul> <li>alphabetically <li>by increasing or decreasing values </ul> <p> The reordering can be triggered via the TAxis context menu by selecting the menu item "LabelsOption" or by calling directly TH1::LabelsOption(option, axis) where <ul> <li>axis may be "X", "Y" or "Z" <li>option may be: <ul> <li>"a" sort by alphabetic order <li>">" sort by decreasing values <li>"<" sort by increasing values <li>"h" draw labels horizonthal <li>"v" draw labels vertical <li>"u" draw labels up (end of label right adjusted) <li>"d" draw labels down (start of label left adjusted) </ul> </ul> <p> 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 <pre> TH1::LabelsDeflate(axis) with axis = "X", "Y" or "Z" </pre> 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. <h4>Histograms with automatic bins</h4> 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. <h4>Filling histograms</h4> An histogram is typically filled with statements like: <pre> 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) </pre> 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. <p> 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: <pre> Double_t binContent = h->GetBinContent(bin); </pre> <p> By default, the bin number is computed using the current axis ranges. If the automatic binning option has been set via <pre> h->SetBit(TH1::kCanRebin); </pre> 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. <p> 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. <p> 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. <h4>Rebinning</h4> 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. <h4>Associated errors</h4> 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: <pre> Double_t error = h->GetBinError(bin); </pre> <h4>Associated functions</h4> 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: <pre> TF1 *myfunc = h->GetFunction("myfunc"); </pre> <h4>Operations on histograms</h4> Many types of operations are supported on histograms or between histograms <ul> <li> Addition of an histogram to the current histogram. <li> Additions of two histograms with coefficients and storage into the current histogram. <li> Multiplications and Divisions are supported in the same way as additions. <li> The Add, Divide and Multiply functions also exist to add, divide or multiply an histogram by a function. </ul> 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. <h4>Fitting histograms</h4> 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: <pre> 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 </pre> <h4>Projections of histograms</h4> <p> One can: <ul> <li> make a 1-D projection of a 2-D histogram or Profile see functions TH2::ProjectionX,Y, TH2::ProfileX,Y, TProfile::ProjectionX <li> make a 1-D, 2-D or profile out of a 3-D histogram see functions TH3::ProjectionZ, TH3::Project3D. </ul> <p> One can fit these projections via: <pre> TH2::FitSlicesX,Y, TH3::FitSlicesZ. </pre> <h4>Random Numbers and histograms</h4> 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). <p> For example the following two statements create and fill an histogram 10000 times with a default gaussian distribution of mean 0 and sigma 1: <pre> TH1F h1("h1", "histo from a gaussian", 100, -3, 3); h1.FillRandom("gaus", 10000); </pre> TH1::GetRandom can be used to return a random number distributed according the contents of an histogram. <h4>Making a copy of an histogram</h4> 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.: <pre> TH1F *hnew = (TH1F*)h->Clone("hnew"); </pre> <h4>Normalizing histograms</h4> 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. <h4>Drawing histograms</h4> 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. <p> 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 <pre> h->DrawCopy(); </pre> 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. <p> One can use TH1::SetMaximum() and TH1::SetMinimum() to force a particular value for the maximum or the minimum scale on the plot. <p> 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(). <h4>Setting Drawing histogram contour levels (2-D hists only)</h4> 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". <h4>Setting histogram graphics attributes</h4> 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. <h4>Giving titles to the X, Y and Z axis</h4> <pre> h->GetXaxis()->SetTitle("X axis title"); h->GetYaxis()->SetTitle("Y axis title"); </pre> 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 ";": <pre> TH1F* h=new TH1F("h", "Histogram title;X Axis;Y Axis;Z Axis", 100, 0, 1); </pre> Any title can be omitted: <pre> TH1F* h=new TH1F("h", "Histogram title;;Y Axis", 100, 0, 1); TH1F* h=new TH1F("h", ";;Y Axis", 100, 0, 1); </pre> The method SetTitle has the same syntax: <pre> </pre> h->SetTitle("Histogram title;Another X title Axis"); <h4>Saving/Reading histograms to/from a ROOT file</h4> 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: <pre> TFile f("histos.root", "new"); TH1F h1("hgaus", "histo from a gaussian", 100, -3, 3); h1.FillRandom("gaus", 10000); h1->Write(); </pre> To read this histogram in another Root session, do: <pre> TFile f("histos.root"); TH1F *h = (TH1F*)f.Get("hgaus"); </pre> One can save all histograms in memory to the file by: <pre> file->Write(); </pre> <h4>Miscelaneous operations</h4> <pre> 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 </pre> End_Html */ TF1 *gF1=0; //left for back compatibility (use TVirtualFitter::GetUserFunc instead) Int_t TH1::fgBufferSize = 1000; Bool_t TH1::fgAddDirectory = kTRUE; Bool_t TH1::fgDefaultSumw2 = kFALSE; Bool_t TH1::fgStatOverflows= kFALSE; extern void H1InitGaus(); extern void H1InitExpo(); extern void H1InitPolynom(); extern void H1LeastSquareFit(Int_t n, Int_t m, Double_t *a); extern void H1LeastSquareLinearFit(Int_t ndata, Double_t &a0, Double_t &a1, Int_t &ifail); extern void H1LeastSquareSeqnd(Int_t n, Double_t *a, Int_t idim, Int_t &ifail, Int_t k, Double_t *b); ClassImp(TH1) //______________________________________________________________________________ TH1::TH1(): TNamed(), TAttLine(), TAttFill(), TAttMarker() { // -*-*-*-*-*-*-*-*-*Histogram default constructor*-*-*-*-*-*-*-*-*-*-*-*-* // ============================= fDirectory = 0; fFunctions = new TList; fNcells = 0; fIntegral = 0; fPainter = 0; fEntries = 0; fNormFactor = 0; fTsumw = fTsumw2=fTsumwx=fTsumwx2=0; fMaximum = -1111; fMinimum = -1111; fBufferSize = 0; fBuffer = 0; fXaxis.SetName("xaxis"); fYaxis.SetName("yaxis"); fZaxis.SetName("zaxis"); fXaxis.SetParent(this); fYaxis.SetParent(this); fZaxis.SetParent(this); UseCurrentStyle(); } //______________________________________________________________________________ TH1::~TH1() { // -*-*-*-*-*-*-*-*-*Histogram default destructor*-*-*-*-*-*-*-*-*-*-*-*-*-* // ============================ if (!TestBit(kNotDeleted)) { return; } delete[] fIntegral; fIntegral = 0; delete[] fBuffer; fBuffer = 0; if (fFunctions) { fFunctions->SetBit(kInvalidObject); TObject* obj = 0; //special logic to support the case where the same object is //added multiple times in fFunctions. //This case happens when the same object is added with different //drawing modes //In the loop below we must be careful with objects (eg TCutG) that may // have been added to the list of functions of several histograms //and may have been already deleted. while ((obj = fFunctions->First())) { while(fFunctions->Remove(obj)) { } if (!obj->TestBit(kNotDeleted)) { break; } delete obj; obj = 0; } delete fFunctions; fFunctions = 0; } if (fDirectory) { fDirectory->Remove(this); fDirectory = 0; } delete fPainter; fPainter = 0; } //______________________________________________________________________________ TH1::TH1(const char *name,const char *title,Int_t nbins,Double_t xlow,Double_t xup) :TNamed(name,title), TAttLine(), TAttFill(), TAttMarker() { // -*-*-*-*-*-*-*Normal constructor for fix bin size histograms*-*-*-*-*-*-* // ============================================== // // Creates the main histogram structure: // name : name of histogram (avoid blanks) // title : histogram title // if title is of the form "stringt;stringx;stringy;stringz" // the histogram title is set to stringt, // the x axis title to stringy, the y axis title to stringy, etc. // nbins : number of bins // xlow : low edge of first bin // xup : upper edge of last bin (not included in last bin) // // When an histogram is created, it is automatically added to the list // of special objects in the current directory. // To find the pointer to this histogram in the current directory // by its name, do: // TH1F *h1 = (TH1F*)gDirectory->FindObject(name); // // -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* Build(); if (nbins <= 0) nbins = 1; fXaxis.Set(nbins,xlow,xup); fNcells = fXaxis.GetNbins()+2; } //______________________________________________________________________________ TH1::TH1(const char *name,const char *title,Int_t nbins,const Float_t *xbins) :TNamed(name,title), TAttLine(), TAttFill(), TAttMarker() { // -*-*-*-*-*Normal constructor for variable bin size histograms*-*-*-*-*-*-* // =================================================== // // Creates the main histogram structure: // name : name of histogram (avoid blanks) // title : histogram title // if title is of the form "stringt;stringx;stringy;stringz" // the histogram title is set to stringt, // the x axis title to stringx, the y axis title to stringy, etc. // nbins : number of bins // xbins : array of low-edges for each bin // This is an array of size nbins+1 // // -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* Build(); if (nbins <= 0) nbins = 1; if (xbins) fXaxis.Set(nbins,xbins); else fXaxis.Set(nbins,0,1); fNcells = fXaxis.GetNbins()+2; if (fgDefaultSumw2) Sumw2(); } //______________________________________________________________________________ TH1::TH1(const char *name,const char *title,Int_t nbins,const Double_t *xbins) :TNamed(name,title), TAttLine(), TAttFill(), TAttMarker() { // -*-*-*-*-*Normal constructor for variable bin size histograms*-*-*-*-*-*-* // =================================================== // // Creates the main histogram structure: // name : name of histogram (avoid blanks) // title : histogram title // if title is of the form "stringt;stringx;stringy;stringz" // the histogram title is set to stringt, // the x axis title to stringx, the y axis title to stringy, etc. // nbins : number of bins // xbins : array of low-edges for each bin // This is an array of size nbins+1 // // -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* Build(); if (nbins <= 0) nbins = 1; if (xbins) fXaxis.Set(nbins,xbins); else fXaxis.Set(nbins,0,1); fNcells = fXaxis.GetNbins()+2; if (fgDefaultSumw2) Sumw2(); } //______________________________________________________________________________ TH1::TH1(const TH1 &h) : TNamed(), TAttLine(), TAttFill(), TAttMarker() { // Copy constructor. // The list of functions is not copied. (Use Clone if needed) ((TH1&)h).Copy(*this); } //______________________________________________________________________________ Bool_t TH1::AddDirectoryStatus() { //static function: cannot be inlined on Windows/NT return fgAddDirectory; } //______________________________________________________________________________ void TH1::Browse(TBrowser *b) { // Browe the Histogram object. Draw(b ? b->GetDrawOption() : ""); gPad->Update(); } //______________________________________________________________________________ void TH1::Build() { // -*-*-*-*-*-*-*-*Creates histogram basic data structure*-*-*-*-*-*-*-*-*-* // ====================================== fDirectory = 0; fPainter = 0; fIntegral = 0; fEntries = 0; fNormFactor = 0; fTsumw = fTsumw2=fTsumwx=fTsumwx2=0; fMaximum = -1111; fMinimum = -1111; fBufferSize = 0; fBuffer = 0; fXaxis.SetName("xaxis"); fYaxis.SetName("yaxis"); fZaxis.SetName("zaxis"); fYaxis.Set(1,0.,1.); fZaxis.Set(1,0.,1.); fXaxis.SetParent(this); fYaxis.SetParent(this); fZaxis.SetParent(this); SetTitle(fTitle.Data()); fFunctions = new TList; UseCurrentStyle(); if (TH1::AddDirectoryStatus()) { fDirectory = gDirectory; if (fDirectory) { fDirectory->Append(this,kTRUE); } } } //______________________________________________________________________________ void TH1::Add(TF1 *f1, Double_t c1, Option_t *option) { // Performs the operation: this = this + c1*f1 // if errors are defined (see TH1::Sumw2), errors are also recalculated. // // By default, the function is computed at the centre of the bin. // if option "I" is specified (1-d histogram only), the integral of the // function in each bin is used instead of the value of the function at // the centre of the bin. // Only bins inside the function range are recomputed. // IMPORTANT NOTE: If you intend to use the errors of this histogram later // you should call Sumw2 before making this operation. // This is particularly important if you fit the histogram after TH1::Add if (!f1) { Error("Add","Attempt to add a non-existing function"); return; } TString opt = option; opt.ToLower(); Bool_t integral = kFALSE; if (opt.Contains("i") && fDimension ==1) integral = kTRUE; Int_t nbinsx = GetNbinsX(); Int_t nbinsy = GetNbinsY(); Int_t nbinsz = GetNbinsZ(); if (fDimension < 2) nbinsy = -1; if (fDimension < 3) nbinsz = -1; // - Add statistics Double_t s1[10]; Int_t i; for (i=0;i<10;i++) {s1[i] = 0;} PutStats(s1); SetMinimum(); SetMaximum(); // - Loop on bins (including underflows/overflows) Int_t bin, binx, biny, binz; Double_t cu=0; Double_t xx[3]; Double_t *params = 0; f1->InitArgs(xx,params); for (binz=0;binz<=nbinsz+1;binz++) { xx[2] = fZaxis.GetBinCenter(binz); for (biny=0;biny<=nbinsy+1;biny++) { xx[1] = fYaxis.GetBinCenter(biny); for (binx=0;binx<=nbinsx+1;binx++) { xx[0] = fXaxis.GetBinCenter(binx); if (!f1->IsInside(xx)) continue; TF1::RejectPoint(kFALSE); bin = binx +(nbinsx+2)*(biny + (nbinsy+2)*binz); if (integral) { xx[0] = fXaxis.GetBinLowEdge(binx); cu = c1*f1->EvalPar(xx); cu += c1*f1->Integral(fXaxis.GetBinLowEdge(binx),fXaxis.GetBinUpEdge(binx))*fXaxis.GetBinWidth(binx); } else { cu = c1*f1->EvalPar(xx); } if (TF1::RejectedPoint()) continue; Double_t error1 = GetBinError(bin); AddBinContent(bin,cu); if (fSumw2.fN) { //errors are unchanged: error on f1 assumed 0 fSumw2.fArray[bin] = error1*error1; } } } } } //______________________________________________________________________________ void TH1::Add(const TH1 *h1, Double_t c1) { // Performs the operation: this = this + c1*h1 // if errors are defined (see TH1::Sumw2), errors are also recalculated. // Note that if h1 has Sumw2 set, Sumw2 is automatically called for this // if not already set. // // SPECIAL CASE (Average/Efficiency histograms) // For histograms representing averages or efficiencies, one should compute the average // of the two histograms and not the sum. One can mark a histogram to be an average // histogram by setting its bit kIsAverage with // myhist.SetBit(TH1::kIsAverage); // Note that the two histograms must have their kIsAverage bit set // // IMPORTANT NOTE1: If you intend to use the errors of this histogram later // you should call Sumw2 before making this operation. // This is particularly important if you fit the histogram after TH1::Add // // IMPORTANT NOTE2: if h1 has a normalisation factor, the normalisation factor // is used , ie this = this + c1*factor*h1 // Use the other TH1::Add function if you do not want this feature if (!h1) { Error("Add","Attempt to add a non-existing histogram"); return; } Int_t nbinsx = GetNbinsX(); Int_t nbinsy = GetNbinsY(); Int_t nbinsz = GetNbinsZ(); // - Check histogram compatibility if (nbinsx != h1->GetNbinsX() || nbinsy != h1->GetNbinsY() || nbinsz != h1->GetNbinsZ()) { Error("Add","Attempt to add histograms with different number of bins"); return; } // - Issue a Warning if histogram limits are different if (fXaxis.GetXmin() != h1->fXaxis.GetXmin() || fXaxis.GetXmax() != h1->fXaxis.GetXmax() || fYaxis.GetXmin() != h1->fYaxis.GetXmin() || fYaxis.GetXmax() != h1->fYaxis.GetXmax() || fZaxis.GetXmin() != h1->fZaxis.GetXmin() || fZaxis.GetXmax() != h1->fZaxis.GetXmax()) { Warning("Add","Attempt to add histograms with different axis limits"); } if (fDimension < 2) nbinsy = -1; if (fDimension < 3) nbinsz = -1; // Create Sumw2 if h1 has Sumw2 set if (fSumw2.fN == 0 && h1->GetSumw2N() != 0) Sumw2(); // - Add statistics fEntries += c1*h1->GetEntries(); Double_t s1[kNstat], s2[kNstat]; Int_t i; for (i=0;i<kNstat;i++) {s1[i] = s2[i] = 0;} GetStats(s1); h1->GetStats(s2); for (i=0;i<kNstat;i++) { if (i == 1) s1[i] += c1*c1*s2[i]; else s1[i] += TMath::Abs(c1)*s2[i]; } SetMinimum(); SetMaximum(); // - Loop on bins (including underflows/overflows) Int_t bin, binx, biny, binz; Double_t cu; Double_t factor =1; if (h1->GetNormFactor() != 0) factor = h1->GetNormFactor()/h1->GetSumOfWeights();; for (binz=0;binz<=nbinsz+1;binz++) { for (biny=0;biny<=nbinsy+1;biny++) { for (binx=0;binx<=nbinsx+1;binx++) { bin = binx +(nbinsx+2)*(biny + (nbinsy+2)*binz); //special case where histograms have the kIsAverage bit set if (this->TestBit(kIsAverage) && h1->TestBit(kIsAverage)) { Double_t y1 = h1->GetBinContent(bin); Double_t y2 = this->GetBinContent(bin); Double_t e1 = h1->GetBinError(bin); Double_t e2 = this->GetBinError(bin); Double_t w1 = 1., w2 = 1.; if (e1 > 0) w1 = 1./(e1*e1); if (e2 > 0) w2 = 1./(e2*e2); SetBinContent(bin, (w1*y1 + w2*y2)/(w1 + w2)); if (fSumw2.fN) fSumw2.fArray[bin] = 1./(w1 + w2); } else { cu = c1*factor*h1->GetBinContent(bin); AddBinContent(bin,cu); if (fSumw2.fN) { Double_t e1 = factor*h1->GetBinError(bin); fSumw2.fArray[bin] += c1*c1*e1*e1; } } } } } // update statistics (do here to avoid changes by SetBinContent) PutStats(s1); } //______________________________________________________________________________ void TH1::Add(const TH1 *h1, const TH1 *h2, Double_t c1, Double_t c2) { // -*-*-*Replace contents of this histogram by the addition of h1 and h2*-*-* // =============================================================== // // this = c1*h1 + c2*h2 // if errors are defined (see TH1::Sumw2), errors are also recalculated // Note that if h1 or h2 have Sumw2 set, Sumw2 is automatically called for this // if not already set. // // SPECIAL CASE (Average/Efficiency histograms) // For histograms representing averages or efficiencies, one should compute the average // of the two histograms and not the sum. One can mark a histogram to be an average // histogram by setting its bit kIsAverage with // myhist.SetBit(TH1::kIsAverage); // Note that the two histograms must have their kIsAverage bit set // // IMPORTANT NOTE: If you intend to use the errors of this histogram later // you should call Sumw2 before making this operation. // This is particularly important if you fit the histogram after TH1::Add if (!h1 || !h2) { Error("Add","Attempt to add a non-existing histogram"); return; } Bool_t normWidth = kFALSE; if (h1 == h2 && c2 < 0) {c2 = 0; normWidth = kTRUE;} Int_t nbinsx = GetNbinsX(); Int_t nbinsy = GetNbinsY(); Int_t nbinsz = GetNbinsZ(); // - Check histogram compatibility if (nbinsx != h1->GetNbinsX() || nbinsy != h1->GetNbinsY() || nbinsz != h1->GetNbinsZ() || nbinsx != h2->GetNbinsX() || nbinsy != h2->GetNbinsY() || nbinsz != h2->GetNbinsZ()) { Error("Add","Attempt to add histograms with different number of bins"); return; } // - Issue a Warning if histogram limits are different if (fXaxis.GetXmin() != h1->fXaxis.GetXmin() || fXaxis.GetXmax() != h1->fXaxis.GetXmax() || fYaxis.GetXmin() != h1->fYaxis.GetXmin() || fYaxis.GetXmax() != h1->fYaxis.GetXmax() || fZaxis.GetXmin() != h1->fZaxis.GetXmin() || fZaxis.GetXmax() != h1->fZaxis.GetXmax()) { Warning("Add","Attempt to add histograms with different axis limits"); } if (fXaxis.GetXmin() != h2->fXaxis.GetXmin() || fXaxis.GetXmax() != h2->fXaxis.GetXmax() || fYaxis.GetXmin() != h2->fYaxis.GetXmin() || fYaxis.GetXmax() != h2->fYaxis.GetXmax() || fZaxis.GetXmin() != h2->fZaxis.GetXmin() || fZaxis.GetXmax() != h2->fZaxis.GetXmax()) { Warning("Add","Attempt to add histograms::Add with different axis limits"); } if (fDimension < 2) nbinsy = -1; if (fDimension < 3) nbinsz = -1; if (fDimension < 3) nbinsz = -1; // Create Sumw2 if h1 or h2 have Sumw2 set if (fSumw2.fN == 0 && (h1->GetSumw2N() != 0 || h2->GetSumw2N() != 0)) Sumw2(); // - Add statistics Double_t nEntries = c1*h1->GetEntries() + c2*h2->GetEntries(); Double_t s1[kNstat], s2[kNstat], s3[kNstat]; Int_t i; for (i=0;i<kNstat;i++) {s1[i] = s2[i] = s3[i] = 0;} h1->GetStats(s1); h2->GetStats(s2); for (i=0;i<kNstat;i++) { if (i == 1) s3[i] = c1*c1*s1[i] + c2*c2*s2[i]; else s3[i] = TMath::Abs(c1)*s1[i] + TMath::Abs(c2)*s2[i]; } SetMinimum(); SetMaximum(); // Reset the kCanRebin option. Otherwise SetBinContent on the overflow bin // would resize the axis limits! ResetBit(kCanRebin); // - Loop on bins (including underflows/overflows) Int_t bin, binx, biny, binz; Double_t cu; for (binz=0;binz<=nbinsz+1;binz++) { Double_t wz = h1->GetZaxis()->GetBinWidth(binz); for (biny=0;biny<=nbinsy+1;biny++) { Double_t wy = h1->GetYaxis()->GetBinWidth(biny); for (binx=0;binx<=nbinsx+1;binx++) { Double_t wx = h1->GetXaxis()->GetBinWidth(binx); bin = binx +(nbinsx+2)*(biny + (nbinsy+2)*binz); //special case where histograms have the kIsAverage bit set if (h1->TestBit(kIsAverage) && h2->TestBit(kIsAverage)) { Double_t y1 = h1->GetBinContent(bin); Double_t y2 = h2->GetBinContent(bin); Double_t e1 = h1->GetBinError(bin); Double_t e2 = h2->GetBinError(bin); Double_t w1 = 1., w2 = 1.; if (e1 > 0) w1 = 1./(e1*e1); if (e2 > 0) w2 = 1./(e2*e2); SetBinContent(bin, (w1*y1 + w2*y2)/(w1 + w2)); if (fSumw2.fN) fSumw2.fArray[bin] = 1./(w1 + w2); } else { if (normWidth) { Double_t w = wx*wy*wz; cu = c1*h1->GetBinContent(bin)/w; SetBinContent(bin,cu); if (fSumw2.fN) { Double_t e1 = h1->GetBinError(bin)/w; fSumw2.fArray[bin] = c1*c1*e1*e1; } } else { cu = c1*h1->GetBinContent(bin)+ c2*h2->GetBinContent(bin); SetBinContent(bin,cu); if (fSumw2.fN) { Double_t e1 = h1->GetBinError(bin); Double_t e2 = h2->GetBinError(bin); fSumw2.fArray[bin] = c1*c1*e1*e1 + c2*c2*e2*e2; } } } } } } // update statistics (do here to avoid changes by SetBinContent) PutStats(s3); SetEntries(nEntries); } //______________________________________________________________________________ void TH1::AddBinContent(Int_t) { // -*-*-*-*-*-*-*-*Increment bin content by 1*-*-*-*-*-*-*-*-*-*-*-*-*-* // ========================== AbstractMethod("AddBinContent"); } //______________________________________________________________________________ void TH1::AddBinContent(Int_t, Double_t) { // -*-*-*-*-*-*-*-*Increment bin content by a weight w*-*-*-*-*-*-*-*-*-*-* // =================================== AbstractMethod("AddBinContent"); } //______________________________________________________________________________ void TH1::AddDirectory(Bool_t add) { // Sets the flag controlling the automatic add of histograms in memory // // By default (fAddDirectory = kTRUE), histograms are automatically added // to the list of objects in memory. // Note that one histogram can be removed from its support directory // by calling h->SetDirectory(0) or h->SetDirectory(dir) to add it // to the list of objects in the directory dir. // // NOTE that this is a static function. To call it, use; // TH1::AddDirectory fgAddDirectory = add; } //______________________________________________________________________________ Int_t TH1::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 // do we need to compute the bin size? if (!fBuffer) return 0; Int_t nbentries = (Int_t)fBuffer[0]; if (!nbentries) return 0; Double_t *buffer = fBuffer; if (nbentries < 0) { if (action == 0) return 0; nbentries = -nbentries; fBuffer=0; Reset(); fBuffer = buffer; } if (TestBit(kCanRebin) || (fXaxis.GetXmax() <= fXaxis.GetXmin())) { //find min, max of entries in buffer Double_t xmin = fBuffer[2]; Double_t xmax = xmin; for (Int_t i=1;i<nbentries;i++) { Double_t x = fBuffer[2*i+2]; if (x < xmin) xmin = x; if (x > xmax) xmax = x; } if (fXaxis.GetXmax() <= fXaxis.GetXmin()) { THLimitsFinder::GetLimitsFinder()->FindGoodLimits(this,xmin,xmax); } else { fBuffer = 0; Int_t keep = fBufferSize; fBufferSize = 0; if (xmin < fXaxis.GetXmin()) RebinAxis(xmin,&fXaxis); if (xmax >= fXaxis.GetXmax()) RebinAxis(xmax,&fXaxis); fBuffer = buffer; fBufferSize = keep; } } FillN(nbentries,&fBuffer[2],&fBuffer[1],2); if (action > 0) { delete [] fBuffer; fBuffer = 0; fBufferSize = 0;} else { if (nbentries == (Int_t)fEntries) fBuffer[0] = -nbentries; else fBuffer[0] = 0; } return nbentries; } //______________________________________________________________________________ Int_t TH1::BufferFill(Double_t x, Double_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 if (!fBuffer) return -2; Int_t nbentries = (Int_t)fBuffer[0]; if (nbentries < 0) { nbentries = -nbentries; fBuffer[0] = nbentries; if (fEntries > 0) { Double_t *buffer = fBuffer; fBuffer=0; Reset(); fBuffer = buffer; } } if (2*nbentries+2 >= fBufferSize) { BufferEmpty(1); return Fill(x,w); } fBuffer[2*nbentries+1] = w; fBuffer[2*nbentries+2] = x; fBuffer[0] += 1; return -2; } //___________________________________________________________________________ Double_t TH1::Chi2Test(const TH1* h2, Option_t *option, Double_t *res) const { // Begin_Latex #chi^{2} End_Latex test for comparing weighted and unweighted histograms // // Function: Returns p-value. Other return values are specified by the 3rd parameter <br> // // Parameters: // // - h2: the second histogram // - option: // o "UU" = experiment experiment comparison (unweighted-unweighted) // o "UW" = experiment MC comparison (unweighted-weighted). Note that // the first histogram should be unweighted // o "WW" = MC MC comparison (weighted-weighted) // o "NORM" = to be used when one or both of the histograms is scaled // but the histogram originally was unweighted // o by default underflows and overlows are not included: // * "OF" = overflows included // * "UF" = underflows included // o "P" = print chi2, ndf, p_value, igood // o "CHI2" = returns chi2 instead of p-value // o "CHI2/NDF" = returns Begin_Latex #chi^{2}/ndf End_Latex // - res: not empty - computes normalized residuals and returns them in // this array // // The current implementation is based on the papers Begin_Latex #chi^{2} End_Latex test for comparison // of weighted and unweighted histograms" in Proceedings of PHYSTAT05 and // "Comparison weighted and unweighted histograms", arXiv:physics/0605123 // by N.Gagunashvili. This function has been implemented by Daniel Haertl in August 2006. // // Introduction: // // A frequently used technique in data analysis is the comparison of // histograms. First suggested by Pearson [1] the Begin_Latex #chi^{2} End_Latex test of // homogeneity is used widely for comparing usual (unweighted) histograms. // This paper describes the implementation modified Begin_Latex #chi^{2} End_Latex tests // for comparison of weighted and unweighted histograms and two weighted // histograms [2] as well as usual Pearson's Begin_Latex #chi^{2} End_Latex test for // comparison two usual (unweighted) histograms. // // Overview: // // Comparison of two histograms expect hypotheses that two histograms // represent identical distributions. To make a decision p-value should // be calculated. The hypotheses of identity is rejected if the p-value is // lower then some significance level. Traditionally significance levels // 0.1, 0.05 and 0.01 are used. The comparison procedure should include an // analysis of the residuals which is often helpful in identifying the // bins of histograms responsible for a significant overall Begin_Latex #chi^{2} End_Latex value. // Residuals are the difference between bin contents and expected bin // contents. Most convenient for analysis are the normalized residuals. If // hypotheses of identity are valid then normalized residuals are // approximately independent and identically distributed random variables // having N(0,1) distribution. Analysis of residuals expect test of above // mentioned properties of residuals. Notice that indirectly the analysis // of residuals increase the power of Begin_Latex #chi^{2} End_Latex test. // // Methods of comparison: // // Begin_Latex #chi^{2} End_Latex test for comparison two (unweighted) histograms: // Let us consider two histograms with the same binning and the number // of bins equal to r. Let us denote the number of events in the ith bin // in the first histogram as ni and as mi in the second one. The total // number of events in the first histogram is equal to: //Begin_Latex // N = #sum_{i=1}^{r} n_{i} //End_Latex // and //Begin_Latex // M = #sum_{i=1}^{r} m_{i} //End_Latex // in the second histogram. The hypothesis of identity (homogeneity) [3] // is that the two histograms represent random values with identical // distributions. It is equivalent that there exist r constants p1,...,pr, // such that //Begin_Latex // #sum_{i=1}^{r} p_{i}=1 //End_Latex // and the probability of belonging to the ith bin for some measured value // in both experiments is equal to pi. The number of events in the ith // bin is a random variable with a distribution approximated by a Poisson // probability distribution //Begin_Latex // #frac{e^{-Np_{i}}(Np_{i})^{n_{i}}}{n_{i}!} //End_Latex // for the first histogram and with distribution //Begin_Latex // #frac{e^{-Mp_{i}}(Mp_{i})^{m_{i}}}{m_{i}!} //End_Latex // for the second histogram. If the hypothesis of homogeneity is valid, // then the maximum likelihood estimator of pi, i=1,...,r, is //Begin_Latex // #hat{p}_{i}= #frac{n_{i}+m_{i}}{N+M} //End_Latex // and then //Begin_Latex // X^{2} = #sum_{i=1}^{r}#frac{(n_{i}-N#hat{p}_{i})^{2}}{N#hat{p}_{i}} + #sum_{i=1}^{r}#frac{(m_{i}-M#hat{p}_{i})^{2}}{M#hat{p}_{i}} = #frac{1}{MN} #sum_{i=1}^{r}#frac{(Mn_{i}-Nm_{i})^{2}}{n_{i}+m_{i}} //End_Latex // has approximately a Begin_Latex #chi^{2}_{(r-1)} End_Latex distribution [3]. // The comparison procedure can include an analysis of the residuals which // is often helpful in identifying the bins of histograms responsible for // a significant overall Begin_Latex #chi^{2} End_Latexvalue. Most convenient for // analysis are the adjusted (normalized) residuals [4] //Begin_Latex // r_{i} = #frac{n_{i}-N#hat{p}_{i}}{#sqrt{N#hat{p}_{i}}#sqrt{(1-N/(N+M))(1-(n_{i}+m_{i})/(N+M))}} //End_Latex // If hypotheses of homogeneity are valid then residuals ri are // approximately independent and identically distributed random variables // having N(0,1) distribution. The application of the Begin_Latex #chi^{2} End_latex test has // restrictions related to the value of the expected frequencies Npi, // Mpi, i=1,...,r. A conservative rule formulated in [5] is that all the // expectations must be 1 or greater for both histograms. In practical // cases when expected frequencies are not known the estimated expected // frequencies Begin_Latex M#hat{p}_{i}, N#hat{p}_{i}, i=1,...,r End_Latex can be used. // // Unweighted and weighted histograms comparison: // // A simple modification of the ideas described above can be used for the // comparison of the usual (unweighted) and weighted histograms. Let us // denote the number of events in the ith bin in the unweighted // histogram as ni and the common weight of events in the ith bin of the // weighted histogram as wi. The total number of events in the // unweighted histogram is equal to //Begin_Latex // N = #sum_{i=1}^{r} n_{i} //End_Latex // and the total weight of events in the weighted histogram is equal to //Begin_Latex // W = #sum_{i=1}^{r} w_{i} //End_Latex // Let us formulate the hypothesis of identity of an unweighted histogram // to a weighted histogram so that there exist r constants p1,...,pr, such // that //Begin_Latex // #sum_{i=1}^{r} p_{i} = 1 //End_Latex // for the unweighted histogram. The weight wi is a random variable with a // distribution approximated by the normal probability distribution // Begin_Latex N(Wp_{i},#sigma_{i}^{2}) End_Latex where Begin_Latex #sigma_{i}^{2} End_Latex is the variance of the weight wi. // If we replace the variance Begin_Latex #sigma_{i}^{2} End_Latex // with estimate Begin_Latex s_{i}^{2} End_Latex (sum of squares of weights of // events in the ith bin) and the hypothesis of identity is valid, then the // maximum likelihood estimator of pi,i=1,...,r, is //Begin_Latex // #hat{p}_{i} = #frac{Ww_{i}-Ns_{i}^{2}+#sqrt{(Ww_{i}-Ns_{i}^{2})^{2}+4W^{2}s_{i}^{2}n_{i}}}{2W^{2}} //End_Latex // We may then use the test statistic //Begin_Latex // X^{2} = #sum_{i=1}^{r} #frac{(n_{i}-N#hat{p}_{i})^{2}}{N#hat{p}_{i}} + #sum_{i=1}^{r} #frac{(w_{i}-W#hat{p}_{i})^{2}}{s_{i}^{2}} //End_Latex // and it has approximately a Begin_Latex #chi^{2}_{(r-1)} End_Latex distribution [2]. This test, as well // as the original one [3], has a restriction on the expected frequencies. The // expected frequencies recommended for the weighted histogram is more than 25. // The value of the minimal expected frequency can be decreased down to 10 for // the case when the weights of the events are close to constant. In the case // of a weighted histogram if the number of events is unknown, then we can // apply this recommendation for the equivalent number of events as //Begin_Latex // n_{i}^{equiv} = #frac{ w_{i}^{2} }{ s_{i}^{2} } //End_Latex // The minimal expected frequency for an unweighted histogram must be 1. Notice // that any usual (unweighted) histogram can be considered as a weighted // histogram with events that have constant weights equal to 1. // The variance Begin_Latex z_{i}^{2} End_Latex of the difference between the weight wi // and the estimated expectation value of the weight is approximately equal to: //Begin_Latex // z_{i}^{2} = Var(w_{i}-W#hat{p}_{i}) = N#hat{p}_{i}(1-N#hat{p}_{i})#left(#frac{Ws_{i}^{2}}{#sqrt{(Ns_{i}^{2}-w_{i}W)^{2}+4W^{2}s_{i}^{2}n_{i}}}#right)^{2}+#frac{s_{i}^{2}}{4}#left(1+#frac{Ns_{i}^{2}-w_{i}W}{#sqrt{(Ns_{i}^{2}-w_{i}W)^{2}+4W^{2}s_{i}^{2}n_{i}}}#right)^{2} //End_Latex // The residuals //Begin_Latex // r_{i} = #frac{w_{i}-W#hat{p}_{i}}{z_{i}} //End_Latex // have approximately a normal distribution with mean equal to 0 and standard // deviation equal to 1. // // Two weighted histograms comparison: // // Let us denote the common weight of events of the ith bin in the first // histogram as w1i and as w2i in the second one. The total weight of events // in the first histogram is equal to //Begin_Latex // W_{1} = #sum_{i=1}^{r} w_{1i} //End_Latex // and //Begin_Latex // W_{2} = #sum_{i=1}^{r} w_{2i} //End_Latex // in the second histogram. Let us formulate the hypothesis of identity of // weighted histograms so that there exist r constants p1,...,pr, such that //Begin_Latex // #sum_{i=1}^{r} p_{i} = 1 //End_Latex // and also expectation value of weight w1i equal to W1pi and expectation value // of weight w2i equal to W2pi. Weights in both the histograms are random // variables with distributions which can be approximated by a normal // probability distribution Begin_Latex N(W_{1}p_{i},#sigma_{1i}^{2}) End_Latex for the first histogram // and by a distribution Begin_Latex N(W_{2}p_{i},#sigma_{2i}^{2}) End_Latex for the second. // Here Begin_Latex #sigma_{1i}^{2} End_Latex and Begin_Latex #sigma_{2i}^{2} End_Latex are the variances // of w1i and w2i with estimators Begin_Latex s_{1i}^{2} End_Latex and Begin_Latex s_{2i}^{2} End_Latex respectively. // If the hypothesis of identity is valid, then the maximum likelihood and // Least Square Method estimator of pi,i=1,...,r, is //Begin_Latex // #hat{p}_{i} = #frac{w_{1i}W_{1}/s_{1i}^{2}+w_{2i}W_{2} /s_{2i}^{2}}{W_{1}^{2}/s_{1i}^{2}+W_{2}^{2}/s_{2i}^{2}} //End_Latex // We may then use the test statistic //Begin_Latex // X^{2} = #sum_{i=1}^{r} #frac{(w_{1i}-W_{1}#hat{p}_{i})^{2}}{s_{1i}^{2}} + #sum_{i=1}^{r} #frac{(w_{2i}-W_{2}#hat{p}_{i})^{2}}{s_{2i}^{2}} = #sum_{i=1}^{r} #frac{(W_{1}w_{2i}-W_{2}w_{1i})^{2}}{W_{1}^{2}s_{2i}^{2}+W_{2}^{2}s_{1i}^{2}} //End_Latex // and it has approximately a Begin_Latex #chi^{2}_{(r-1)} End_Latex distribution [2]. // The normalized or studentised residuals [6] //Begin_Latex // r_{i} = #frac{w_{1i}-W_{1}#hat{p}_{i}}{s_{1i}#sqrt{1 - #frac{1}{(1+W_{2}^{2}s_{1i}^{2}/W_{1}^{2}s_{2i}^{2})}}} //End_Latex // have approximately a normal distribution with mean equal to 0 and standard // deviation 1. A recommended minimal expected frequency is equal to 10 for // the proposed test. // // Numerical examples: // // The method described herein is now illustrated with an example. // We take a distribution //Begin_Latex // #phi(x) = #frac{2}{(x-10)^{2}+1} + #frac{1}{(x-14)^{2}+1} (1) //End_Latex // defined on the interval [4,16]. Events distributed according to the formula // (1) are simulated to create the unweighted histogram. Uniformly distributed // events are simulated for the weighted histogram with weights calculated by // formula (1). Each histogram has the same number of bins: 20. Fig.1 shows // the result of comparison of the unweighted histogram with 200 events // (minimal expected frequency equal to one) and the weighted histogram with // 500 events (minimal expected frequency equal to 25) //Begin_Macro // ../../../tutorials/math/chi2test.C //End_Macro // Fig 1. An example of comparison of the unweighted histogram with 200 events // and the weighted histogram with 500 events: // a) unweighted histogram; // b) weighted histogram; // c) normalized residuals plot; // d) normal Q-Q plot of residuals. // // The value of the test statistic Begin_Latex #chi^{2} End_Latex is equal to // 21.09 with p-value equal to 0.33, therefore the hypothesis of identity of // the two histograms can be accepted for 0.05 significant level. The behavior // of the normalized residuals plot (see Fig. 1c) and the normal Q-Q plot // (see Fig. 1d) of residuals are regular and we cannot identify the outliers // or bins with a big influence on Begin_Latex #chi^{2} End_Latex. // // The second example presents the same two histograms but 17 events was added // to content of bin number 15 in unweighted histogram. Fig.2 shows the result // of comparison of the unweighted histogram with 217 events (minimal expected // frequency equal to one) and the weighted histogram with 500 events (minimal // expected frequency equal to 25) //Begin_Macro // ../../../tutorials/math/chi2test.C(17) //End_Macro // Fig 2. An example of comparison of the unweighted histogram with 217 events // and the weighted histogram with 500 events: // a) unweighted histogram; // b) weighted histogram; // c) normalized residuals plot; // d) normal Q-Q plot of residuals. // // The value of the test statistic Begin_Latex #chi^{2} End_Latex is equal to // 32.33 with p-value equal to 0.029, therefore the hypothesis of identity of // the two histograms is rejected for 0.05 significant level. The behavior of // the normalized residuals plot (see Fig. 2c) and the normal Q-Q plot (see // Fig. 2d) of residuals are not regular and we can identify the outlier or // bin with a big influence on Begin_Latex #chi^{2} End_Latex. // // References: // // [1] Pearson, K., 1904. On the Theory of Contingency and Its Relation to // Association and Normal Correlation. Drapers' Co. Memoirs, Biometric // Series No. 1, London. // [2] Gagunashvili, N., 2006. Begin_Latex #chi^{2} End_Latex test for comparison // of weighted and unweighted histograms. Statistical Problems in Particle // Physics, Astrophysics and Cosmology, Proceedings of PHYSTAT05, // Oxford, UK, 12-15 September 2005, Imperial College Press, London, 43-44. // Gagunashvili,N., Comparison of weighted and unweighted histograms, // arXiv:physics/0605123, 2006. // [3] Cramer, H., 1946. Mathematical methods of statistics. // Princeton University Press, Princeton. // [4] Haberman, S.J., 1973. The analysis of residuals in cross-classified tables. // Biometrics 29, 205-220. // [5] Lewontin, R.C. and Felsenstein, J., 1965. The robustness of homogeneity // test in 2xN tables. Biometrics 21, 19-33. // [6] Seber, G.A.F., Lee, A.J., 2003, Linear Regression Analysis. // John Wiley & Sons Inc., New York. Double_t chi2 = 0; Int_t ndf = 0, igood = 0; TString opt = option; opt.ToUpper(); Double_t prob = Chi2TestX(h2,chi2,ndf,igood,option,res); if(opt.Contains("P")) { printf("Chi2 = %f, Prob = %g, NDF = %d, igood = %d\n", chi2,prob,ndf,igood); } if(opt.Contains("CHI2/NDF")) { if (ndf == 0) return 0; return chi2/ndf; } if(opt.Contains("CHI2")) { return chi2; } return prob; } //___________________________________________________________________________ Double_t TH1::Chi2TestX(const TH1* h2, Double_t &chi2, Int_t &ndf, Int_t &igood, Option_t *option, Double_t *res) const { // The computation routine of the Chisquare test. For the method description, // see Chi2Test() function. // Returns p-value // parameters: // - h2-second histogram // - option: // "UU" = experiment experiment comparison (unweighted-unweighted) // "UW" = experiment MC comparison (unweighted-weighted). Note that the first // histogram should be unweighted // "WW" = MC MC comparison (weighted-weighted) // // "NORM" = if one or both histograms is scaled // // "OF" = overflows included // "UF" = underflows included // by default underflows and overlows are not included // // - igood: // igood=0 - no problems // For unweighted unweighted comparison // igood=1'There is a bin in the 1st histogram with less than 1 event' // igood=2'There is a bin in the 2nd histogram with less than 1 event' // igood=3'when the conditions for igood=1 and igood=2 are satisfied' // For unweighted weighted comparison // igood=1'There is a bin in the 1st histogram with less then 1 event' // igood=2'There is a bin in the 2nd histogram with less then 10 effective number of events' // igood=3'when the conditions for igood=1 and igood=2 are satisfied' // For weighted weighted comparison // igood=1'There is a bin in the 1st histogram with less then 10 effective // number of events' // igood=2'There is a bin in the 2nd histogram with less then 10 effective // number of events' // igood=3'when the conditions for igood=1 and igood=2 are satisfied' // // - chi2 - chisquare of the test // - ndf - number of degrees of freedom (important, when both histograms have the same // empty bins) // - res - normalized residuals for further analysis Int_t i = 0, j=0, k = 0; Int_t i_start, i_end; Int_t j_start, j_end; Int_t k_start, k_end; Double_t bin1, bin2; Double_t err1,err2; Double_t sum1=0, sum2=0; Double_t sumw1=0, sumw2=0; chi2 = 0; ndf = 0; TString opt = option; opt.ToUpper(); TAxis *xaxis1 = this->GetXaxis(); TAxis *xaxis2 = h2->GetXaxis(); TAxis *yaxis1 = this->GetYaxis(); TAxis *yaxis2 = h2->GetYaxis(); TAxis *zaxis1 = this->GetZaxis(); TAxis *zaxis2 = h2->GetZaxis(); Int_t nbinx1 = xaxis1->GetNbins(); Int_t nbinx2 = xaxis2->GetNbins(); Int_t nbiny1 = yaxis1->GetNbins(); Int_t nbiny2 = yaxis2->GetNbins(); Int_t nbinz1 = zaxis1->GetNbins(); Int_t nbinz2 = zaxis2->GetNbins(); //check dimensions if (this->GetDimension() != h2->GetDimension() ){ Error("ChistatTestX","Histograms have different dimensions."); return 0; } //check number of channels if (nbinx1 != nbinx2) { Error("ChistatTestX","different number of x channels"); } if (nbiny1 != nbiny2) { Error("ChistatTestX","different number of y channels"); } if (nbinz1 != nbinz2) { Error("ChistatTestX","different number of z channels"); } //check for ranges i_start = j_start = k_start = 1; i_end = nbinx1; j_end = nbiny1; k_end = nbinz1; if (xaxis1->TestBit(TAxis::kAxisRange)) { i_start = xaxis1->GetFirst(); i_end = xaxis1->GetLast(); } if (yaxis1->TestBit(TAxis::kAxisRange)) { j_start = yaxis1->GetFirst(); j_end = yaxis1->GetLast(); } if (zaxis1->TestBit(TAxis::kAxisRange)) { k_start = zaxis1->GetFirst(); k_end = zaxis1->GetLast(); } if (opt.Contains("OF")) { if (this->GetDimension() == 3) k_end = ++nbinz1; if (this->GetDimension() >= 2) j_end = ++nbiny1; if (this->GetDimension() >= 1) i_end = ++nbinx1; } if (opt.Contains("UF")) { if (this->GetDimension() == 3) k_start = 0; if (this->GetDimension() >= 2) j_start = 0; if (this->GetDimension() >= 1) i_start = 0; } ndf = (i_end - i_start + 1)*(j_end - j_start + 1)*(k_end - k_start + 1) - 1; Bool_t comparisonUU = opt.Contains("UU"); Bool_t comparisonUW = opt.Contains("UW"); Bool_t comparisonWW = opt.Contains("WW"); Bool_t scaledHistogram = opt.Contains("NORM"); if (scaledHistogram && !comparisonUU) { Info("ChistatTestX","NORM option should be used together with UU option. It is ignored"); } // look at histo global bin content and effective entries Stat_t s[kNstat]; this->GetStats(s);// s[1] sum of squares of weights, s[0] sum of weights double sumBinContent1 = s[0]; double effEntries1 = (s[1] ? s[0]*s[0]/s[1] : 0.); h2->GetStats(s);// s[1] sum of squares of weights, s[0] sum of weights double sumBinContent2 = s[0]; double effEntries2 = (s[1] ? s[0]*s[0]/s[1] : 0.); if (!comparisonUU && !comparisonUW && !comparisonWW ) { // deduce automatically from type of histogram if (TMath::Abs(sumBinContent1 - effEntries1) < 1) { if ( TMath::Abs(sumBinContent2 - effEntries2) < 1) comparisonUU = true; else comparisonUW = true; } else comparisonWW = true; } // check unweighted histogram if (comparisonUW) { if (TMath::Abs(sumBinContent1 - effEntries1) >= 1) { Warning("ChistatTestX","First histogram is not unweighted and option UW has been requested"); } } if ( (!scaledHistogram && comparisonUU) ) { if ( ( TMath::Abs(sumBinContent1 - effEntries1) >= 1) || (TMath::Abs(sumBinContent2 - effEntries2) >= 1) ) { Warning("ChistatTestX","Both histograms are not unweighted and option UU has been requested"); } } //get number of events in histogramm if (comparisonUU && scaledHistogram) { for (i=i_start; i<=i_end; i++) { for (j=j_start; j<=j_end; j++) { for (k=k_start; k<=k_end; k++) { bin1 = this->GetBinContent(i,j,k); bin2 = h2->GetBinContent(i,j,k); err1 = this->GetBinError(i,j,k); err2 = h2->GetBinError(i,j,k); if (err1 > 0 ) { bin1 *= bin1/(err1*err1); //avoid rounding errors bin1 = TMath::Floor(bin1+0.5); } else bin1 = 0; if (err2 > 0) { bin2 *= bin2/(err2*err2); //avoid rounding errors bin2 = TMath::Floor(bin2+0.5); } else bin2 = 0; // sum contents sum1 += bin1; sum2 += bin2; sumw1 += err1*err1; sumw2 += err2*err2; } } } if (sumw1 <= 0 || sumw2 <= 0) { Error("ChistatTestX","Cannot use option NORM when one histogram has all errors zero"); return 0; } } else { for (i=i_start; i<=i_end; i++) { for (j=j_start; j<=j_end; j++) { for (k=k_start; k<=k_end; k++) { sum1 += this->GetBinContent(i,j,k); sum2 += h2->GetBinContent(i,j,k); if ( comparisonWW ) { err1 = this->GetBinError(i,j,k); sumw1 += err1*err1; } if ( comparisonUW || comparisonWW ) { err2 = h2->GetBinError(i,j,k); sumw2 += err2*err2; } } } } } //checks that the histograms are not empty if (sum1 == 0 || sum2 == 0) { Error("ChistatTestX","one histogram is empty"); return 0; } if ( comparisonWW && ( sumw1 <= 0 && sumw2 <=0 ) ){ Error("ChistatTestX","Hist1 and Hist2 have both all errors zero\n"); return 0; } //THE TEST Int_t m=0, n=0; //Experiment - experiment comparison if (comparisonUU) { Double_t sum = sum1 + sum2; for (i=i_start; i<=i_end; i++) { for (j=j_start; j<=j_end; j++) { for (k=k_start; k<=k_end; k++) { bin1 = this->GetBinContent(i,j,k); bin2 = h2->GetBinContent(i,j,k); if ( (bin1 == 0) && (bin2 == 0) ) { --ndf; //no data means one degree of freedom less } else { if (scaledHistogram) { // scale bin value to effective bin entries err1 = this->GetBinError(i,j,k); if (err1 > 0 ) { bin1 *= bin1/(err1*err1); //avoid rounding errors bin1 = TMath::Floor(bin1+0.5); } else bin1 = 0; err2 = h2->GetBinError(i,j,k); if (err2 > 0) { bin2 *= bin2/(err2*err2); //avoid rounding errors bin2 = TMath::Floor(bin2+0.5); } else bin2 = 0; } Double_t binsum = bin1 + bin2; Double_t nexp1 = binsum*sum1/sum; //Double_t nexp2 = binsum*sum2/sum; // if(opt.Contains("P")) printf("bin %d p = %g\t",i,binsum/sum); if (res) res[i-i_start] = (bin1-nexp1)/TMath::Sqrt(nexp1); if (bin1 < 1) { m++; } if (bin2 < 1) { n++; } //Habermann correction for residuals Double_t correc = (1-sum1/sum)*(1-binsum/sum); if (res) { res[i-i_start] /= TMath::Sqrt(correc); } Double_t delta = sum2*bin1-sum1*bin2; chi2 += delta*delta/binsum; } } } } chi2 /= (sum1*sum2); // flag error only when of the two histogram is zero if (m) { igood += 1; Info("Chi2TestX","There is bin in Hist1 with less than 1 number of events.\n"); } if (n) { igood += 2; Info("Chi2TestX","There is bin in Hist2 with less than 1 number of events.\n"); } Double_t prob = TMath::Prob(chi2,ndf); return prob; } //unweighted - weighted comparison if ( comparisonUW ) { for (i=i_start; i<=i_end; i++) { for (j=j_start; j<=j_end; j++) { for (k=k_start; k<=k_end; k++) { Int_t x=0, y=0; bin1 = this->GetBinContent(i,j,k); bin2 = h2->GetBinContent(i,j,k); err2 = h2->GetBinError(i,j,k); err2 *= err2; // case both histogram have zero biin contents if ( (bin1 == 0) && (bin2 == 0) ) { --ndf; //no data means one degree of freedom less continue; } // case weighted histogram has zero bin content and error if (bin2 == 0 && err2 == 0) { if (sumw2 > 0) { // use as approximated error as 1 scaled by a scaling ratio // estimated from the total sum weight and sum weight squared err2 = sumw2/sum2; } else { // return error because infinite discrepancy here: // bin1 != 0 and bin2 =0 in a histogram with all errors zero Error("ChistatTestX","Hist2 has in bin %d,%d,%d zero content and all errors e zero\n", i,j,k); chi2 = 0; return 0; } } // case of err2 = 0 and bin2 not zero is treated without problems // by excluding second chi2 sum if (bin1 < 1) m++; if (err2 > 0 && bin2*bin2/err2 < 10) n++; Double_t var1 = sum2*bin2 - sum1*err2; Double_t var2 = var1*var1 + 4*sum2*sum2*bin1*err2; // if bin1 is zero and bin2=1 and sum1=sum2 var1=0 && var2 ==0 // approximate by adding +1 to bin1 while (var1*var1+bin1 == 0 || var1+var2 == 0) { sum1++; bin1++; x++; y=1; var1 = sum2*bin2 - sum1*err2; var2 = var1*var1 + 4*sum2*sum2*bin1*err2; } var2 = TMath::Sqrt(var2); while (var1+var2 == 0) { sum1++; bin1++; x++; y=1; var1 = sum2*bin2 - sum1*err2; var2 = var1*var1 + 4*sum2*sum2*bin1*err2; while (var1*var1+bin1 == 0 || var1+var2 == 0) { sum1++; bin1++; x++; y=1; var1 = sum2*bin2 - sum1*err2; var2 = var1*var1 + 4*sum2*sum2*bin1*err2; } var2 = TMath::Sqrt(var2); } Double_t probb = (var1+var2)/(2*sum2*sum2); Double_t nexp1 = probb * sum1; Double_t nexp2 = probb * sum2; // if(opt.Contains("P")) printf("bin %d p = %g\t",i,probb); Double_t delta1 = bin1 - nexp1; Double_t delta2 = bin2 - nexp2; chi2 += delta1*delta1/nexp1; if (err2 > 0) { chi2 += delta2*delta2/err2; } if (res) { if (err2 > 0) { Double_t temp1 = sum2*err2/var2; Double_t temp2 = 1 + (sum1*err2 - sum2*bin2)/var2; temp2 = temp1*temp1*sum1*probb*(1-probb) + temp2*temp2*err2/4; // invert sign here res[i-i_start] = - delta2/TMath::Sqrt(temp2); } else res[i-i_start] = delta1/TMath::Sqrt(nexp1); } } } } if (m) { igood += 1; Info("Chi2TestX","There is bin in Hist1 with less than 1 number of events.\n"); } if (n) { igood += 2; Info("Chi2TestX","There is bin in Hist2 with less than 10 effective number of events.\n"); } Double_t prob = TMath::Prob(chi2,ndf); return prob; } // weighted - weighted comparison if (comparisonWW) { for (i=i_start; i<=i_end; i++) { for (j=j_start; j<=j_end; j++) { for (k=k_start; k<=k_end; k++) { bin1 = this->GetBinContent(i,j,k); bin2 = h2->GetBinContent(i,j,k); err1 = this->GetBinError(i,j,k); err2 = h2->GetBinError(i,j,k); err1 *= err1; err2 *= err2; // case both histogram have zero biin contents if ( (bin1 == 0) && (bin2 == 0) ) { --ndf; //no data means one degree of freedom less continue; } if ( (err1 == 0) && (err2 == 0) ) { // case of zero errors but non zero bin content Error("ChistatTestX","Hist1 and Hist2 have both in bin %d,%d,%d errors zero\n", i,j,k); chi2 = 0; return 0; } Double_t sigma = sum1*sum1*err2 + sum2*sum2*err1; Double_t delta = sum2*bin1 - sum1*bin2; chi2 += delta*delta/sigma; // if(opt.Contains("P")) printf("bin %d p = %g\t",i, (bin1*sum1/err1 + bin2*sum2/err2)/(sum1*sum1/err1 + sum2*sum2/err2)); if (res) { Double_t temp = bin1*sum1*err2 + bin2*sum2*err1; Double_t probb = temp/sigma; Double_t z = 0; if (err1 > err2 ) { Double_t d1 = (bin1 - sum1 * probb); Double_t s1 = err1* ( 1. - err2 * sum1 * sum1 / sigma ); z = d1/ TMath::Sqrt(s1); } else { Double_t d2 = (bin2 - sum2 * probb); Double_t s2 = err2* ( 1. - err1 * sum2 * sum2 / sigma ); z = -d2/ TMath::Sqrt(s2); } res[i-i_start] = z; } if (err1 > 0 && bin1*bin1/err1 < 10) m++; if (err2 > 0 && bin2*bin2/err2 < 10) n++; } } } if (m) { igood += 1; Info("Chi2TestX","There is bin in Hist1 with less than 10 effective number of events.\n"); } if (n) { igood += 2; Info("Chi2TestX","There is bin in Hist2 with less than 10 effective number of events.\n"); } Double_t prob = TMath::Prob(chi2,ndf); return prob; } return 0; } //______________________________________________________________________________ Double_t TH1::ComputeIntegral() { // Compute integral (cumulative sum of bins) // The result stored in fIntegral is used by the GetRandom functions. // This function is automatically called by GetRandom when the fIntegral // array does not exist or when the number of entries in the histogram // has changed since the previous call to GetRandom. // The resulting integral is normalized to 1 Int_t bin, binx, biny, binz, ibin; // delete previously computed integral (if any) if (fIntegral) delete [] fIntegral; // - Allocate space to store the integral and compute integral Int_t nbinsx = GetNbinsX(); Int_t nbinsy = GetNbinsY(); Int_t nbinsz = GetNbinsZ(); Int_t nxy = nbinsx*nbinsy; Int_t nbins = nxy*nbinsz; fIntegral = new Double_t[nbins+2]; ibin = 0; fIntegral[ibin] = 0; for (binz=1;binz<=nbinsz;binz++) { for (biny=1;biny<=nbinsy;biny++) { for (binx=1;binx<=nbinsx;binx++) { ibin++; bin = GetBin(binx, biny, binz); fIntegral[ibin] = fIntegral[ibin-1] + GetBinContent(bin); } } } // - Normalize integral to 1 if (fIntegral[nbins] == 0 ) { Error("ComputeIntegral", "Integral = zero"); return 0; } for (bin=1;bin<=nbins;bin++) fIntegral[bin] /= fIntegral[nbins]; fIntegral[nbins+1] = fEntries; return fIntegral[nbins]; } //______________________________________________________________________________ Double_t *TH1::GetIntegral() { // Return a pointer to the array of bins integral. // if the pointer fIntegral is null, TH1::ComputeIntegral is called if (!fIntegral) ComputeIntegral(); return fIntegral; } //______________________________________________________________________________ void TH1::Copy(TObject &obj) const { // -*-*-*-*-*Copy this histogram structure to newth1*-*-*-*-*-*-*-*-*-*-*-* // ======================================= // // Note that this function does not copy the list of associated functions. // Use TObJect::Clone to make a full copy of an histogram. if (((TH1&)obj).fDirectory) { // We are likely to change the hash value of this object // with TNamed::Copy, to keep things correct, we need to // clean up its existing entries. ((TH1&)obj).fDirectory->Remove(&obj); ((TH1&)obj).fDirectory = 0; } TNamed::Copy(obj); ((TH1&)obj).fDimension = fDimension; ((TH1&)obj).fNormFactor= fNormFactor; ((TH1&)obj).fNcells = fNcells; ((TH1&)obj).fBarOffset = fBarOffset; ((TH1&)obj).fBarWidth = fBarWidth; ((TH1&)obj).fOption = fOption; ((TH1&)obj).fBuffer = 0; ((TH1&)obj).fBufferSize= fBufferSize; Int_t i; if (fBuffer) { Double_t *buf = new Double_t[fBufferSize]; for (i=0;i<fBufferSize;i++) buf[i] = fBuffer[i]; ((TH1&)obj).fBuffer = buf; } TArray* a = dynamic_cast<TArray*>(&obj); if (a) a->Set(fNcells); Int_t canRebin = ((TH1&)obj).TestBit(kCanRebin); ((TH1&)obj).ResetBit(kCanRebin); //we want to avoid the call to LabelsInflate for (i=0;i<fNcells;i++) ((TH1&)obj).SetBinContent(i,this->GetBinContent(i)); if (canRebin) ((TH1&)obj).SetBit(kCanRebin); ((TH1&)obj).fEntries = fEntries; ((TH1&)obj).fTsumw = fTsumw; ((TH1&)obj).fTsumw2 = fTsumw2; ((TH1&)obj).fTsumwx = fTsumwx; ((TH1&)obj).fTsumwx2 = fTsumwx2; ((TH1&)obj).fMaximum = fMaximum; ((TH1&)obj).fMinimum = fMinimum; TAttLine::Copy(((TH1&)obj)); TAttFill::Copy(((TH1&)obj)); TAttMarker::Copy(((TH1&)obj)); fXaxis.Copy(((TH1&)obj).fXaxis); fYaxis.Copy(((TH1&)obj).fYaxis); fZaxis.Copy(((TH1&)obj).fZaxis); ((TH1&)obj).fXaxis.SetParent(&obj); ((TH1&)obj).fYaxis.SetParent(&obj); ((TH1&)obj).fZaxis.SetParent(&obj); fContour.Copy(((TH1&)obj).fContour); fSumw2.Copy(((TH1&)obj).fSumw2); // fFunctions->Copy(((TH1&)obj).fFunctions); if (fgAddDirectory && gDirectory) { gDirectory->Append(&obj); ((TH1&)obj).fDirectory = gDirectory; } } //______________________________________________________________________________ void TH1::DirectoryAutoAdd(TDirectory *dir) { // Perform the automatic addition of the histogram to the given directory // // Note this function is called in place when the semantic requires // this object to be added to a directory (I.e. when being read from // a TKey or being Cloned) // Bool_t addStatus = TH1::AddDirectoryStatus(); if (addStatus) { SetDirectory(dir); } } //______________________________________________________________________________ Int_t TH1::DistancetoPrimitive(Int_t px, Int_t py) { // -*-*-*-*-*-*-*-*-*Compute distance from point px,py to a line*-*-*-*-*-* // =========================================== // Compute the closest distance of approach from point px,py to elements // of an histogram. // The distance is computed in pixels units. // // Algorithm: // Currently, this simple model computes the distance from the mouse // to the histogram contour only. // // -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* if (!fPainter) return 9999; return fPainter->DistancetoPrimitive(px,py); } //______________________________________________________________________________ void TH1::Divide(TF1 *f1, Double_t c1) { // Performs the operation: this = this/(c1*f1) // if errors are defined (see TH1::Sumw2), errors are also recalculated. // // Only bins inside the function range are recomputed. // IMPORTANT NOTE: If you intend to use the errors of this histogram later // you should call Sumw2 before making this operation. // This is particularly important if you fit the histogram after TH1::Divide if (!f1) { Error("Add","Attempt to divide by a non-existing function"); return; } Int_t nbinsx = GetNbinsX(); Int_t nbinsy = GetNbinsY(); Int_t nbinsz = GetNbinsZ(); if (fDimension < 2) nbinsy = -1; if (fDimension < 3) nbinsz = -1; SetMinimum(); SetMaximum(); // Reset the kCanRebin option. Otherwise SetBinContent on the overflow bin // would resize the axis limits! ResetBit(kCanRebin); // - Loop on bins (including underflows/overflows) Int_t bin, binx, biny, binz; Double_t cu,w; Double_t xx[3]; Double_t *params = 0; f1->InitArgs(xx,params); for (binz=0;binz<=nbinsz+1;binz++) { xx[2] = fZaxis.GetBinCenter(binz); for (biny=0;biny<=nbinsy+1;biny++) { xx[1] = fYaxis.GetBinCenter(biny); for (binx=0;binx<=nbinsx+1;binx++) { xx[0] = fXaxis.GetBinCenter(binx); if (!f1->IsInside(xx)) continue; TF1::RejectPoint(kFALSE); bin = binx +(nbinsx+2)*(biny + (nbinsy+2)*binz); Double_t error1 = GetBinError(bin); cu = c1*f1->EvalPar(xx); if (TF1::RejectedPoint()) continue; if (cu) w = GetBinContent(bin)/cu; else w = 0; SetBinContent(bin,w); if (fSumw2.fN) { if (cu != 0) fSumw2.fArray[bin] = error1*error1/(cu*cu); else fSumw2.fArray[bin] = 0; } } } } ResetStats(); SetEntries( GetEffectiveEntries() ); } //______________________________________________________________________________ void TH1::Divide(const TH1 *h1) { // -*-*-*-*-*-*-*-*-*Divide this histogram by h1*-*-*-*-*-*-*-*-*-*-*-*-* // =========================== // // this = this/h1 // if errors are defined (see TH1::Sumw2), errors are also recalculated. // Note that if h1 has Sumw2 set, Sumw2 is automatically called for this // if not already set. // The resulting errors are calculated assuming uncorrelated histograms. // See the other TH1::Divide that gives the possibility to optionaly // compute Binomial errors. // // IMPORTANT NOTE: If you intend to use the errors of this histogram later // you should call Sumw2 before making this operation. // This is particularly important if you fit the histogram after TH1::Scale if (!h1) { Error("Divide","Attempt to divide by a non-existing histogram"); return; } Int_t nbinsx = GetNbinsX(); Int_t nbinsy = GetNbinsY(); Int_t nbinsz = GetNbinsZ(); // - Check histogram compatibility if (nbinsx != h1->GetNbinsX() || nbinsy != h1->GetNbinsY() || nbinsz != h1->GetNbinsZ()) { Error("Divide","Attempt to divide histograms with different number of bins"); return; } // - Issue a Warning if histogram limits are different if (fXaxis.GetXmin() != h1->fXaxis.GetXmin() || fXaxis.GetXmax() != h1->fXaxis.GetXmax() || fYaxis.GetXmin() != h1->fYaxis.GetXmin() || fYaxis.GetXmax() != h1->fYaxis.GetXmax() || fZaxis.GetXmin() != h1->fZaxis.GetXmin() || fZaxis.GetXmax() != h1->fZaxis.GetXmax()) { Warning("Divide","Attempt to divide histograms with different axis limits"); } if (fDimension < 2) nbinsy = -1; if (fDimension < 3) nbinsz = -1; if (fDimension < 3) nbinsz = -1; // Create Sumw2 if h1 has Sumw2 set if (fSumw2.fN == 0 && h1->GetSumw2N() != 0) Sumw2(); // Reset the kCanRebin option. Otherwise SetBinContent on the overflow bin // would resize the axis limits! ResetBit(kCanRebin); // - Loop on bins (including underflows/overflows) Int_t bin, binx, biny, binz; Double_t c0,c1,w; for (binz=0;binz<=nbinsz+1;binz++) { for (biny=0;biny<=nbinsy+1;biny++) { for (binx=0;binx<=nbinsx+1;binx++) { bin = GetBin(binx,biny,binz); c0 = GetBinContent(bin); c1 = h1->GetBinContent(bin); if (c1) w = c0/c1; else w = 0; SetBinContent(bin,w); if (fSumw2.fN) { Double_t e0 = GetBinError(bin); Double_t e1 = h1->GetBinError(bin); Double_t c12= c1*c1; if (!c1) { fSumw2.fArray[bin] = 0; continue;} fSumw2.fArray[bin] = (e0*e0*c1*c1 + e1*e1*c0*c0)/(c12*c12); } } } } ResetStats(); SetEntries( GetEffectiveEntries() ); } //______________________________________________________________________________ void TH1::Divide(const TH1 *h1, const TH1 *h2, Double_t c1, Double_t c2, Option_t *option) { // -*-*-*Replace contents of this histogram by the division of h1 by h2*-*-* // ============================================================== // // this = c1*h1/(c2*h2) // // if errors are defined (see TH1::Sumw2), errors are also recalculated // Note that if h1 or h2 have Sumw2 set, Sumw2 is automatically called for this // if not already set. // The resulting errors are calculated assuming uncorrelated histograms. // However, if option ="B" is specified, Binomial errors are computed. // In this case c1 and c2 do not make real sense and they are ignored. // // IMPORTANT NOTE: If you intend to use the errors of this histogram later // you should call Sumw2 before making this operation. // This is particularly important if you fit the histogram after TH1::Divide // // Please note also that in the binomial case errors are calculated using standard // binomial statistics, which means when b1 = b2, the error is zero. // If you prefer to have efficiency errors not going to zero when the efficiency is 1, you must // use the function TGraphAsymmErrors::BayesDivide, which will return an asymmetric and non-zero lower // error for the case b1=b2. TString opt = option; opt.ToLower(); Bool_t binomial = kFALSE; if (opt.Contains("b")) binomial = kTRUE; if (!h1 || !h2) { Error("Divide","Attempt to divide by a non-existing histogram"); return; } Int_t nbinsx = GetNbinsX(); Int_t nbinsy = GetNbinsY(); Int_t nbinsz = GetNbinsZ(); // - Check histogram compatibility if (nbinsx != h1->GetNbinsX() || nbinsy != h1->GetNbinsY() || nbinsz != h1->GetNbinsZ() || nbinsx != h2->GetNbinsX() || nbinsy != h2->GetNbinsY() || nbinsz != h2->GetNbinsZ()) { Error("Divide","Attempt to divide histograms with different number of bins"); return; } if (!c2) { Error("Divide","Coefficient of dividing histogram cannot be zero"); return; } // - Issue a Warning if histogram limits are different if (fXaxis.GetXmin() != h1->fXaxis.GetXmin() || fXaxis.GetXmax() != h1->fXaxis.GetXmax() || fYaxis.GetXmin() != h1->fYaxis.GetXmin() || fYaxis.GetXmax() != h1->fYaxis.GetXmax() || fZaxis.GetXmin() != h1->fZaxis.GetXmin() || fZaxis.GetXmax() != h1->fZaxis.GetXmax()) { Warning("Divide","Attempt to divide histograms with different axis limits"); } if (fXaxis.GetXmin() != h2->fXaxis.GetXmin() || fXaxis.GetXmax() != h2->fXaxis.GetXmax() || fYaxis.GetXmin() != h2->fYaxis.GetXmin() || fYaxis.GetXmax() != h2->fYaxis.GetXmax() || fZaxis.GetXmin() != h2->fZaxis.GetXmin() || fZaxis.GetXmax() != h2->fZaxis.GetXmax()) { Warning("Divide","Attempt to divide histograms with different axis limits"); } if (fDimension < 2) nbinsy = -1; if (fDimension < 3) nbinsz = -1; // Create Sumw2 if h1 or h2 have Sumw2 set if (fSumw2.fN == 0 && (h1->GetSumw2N() != 0 || h2->GetSumw2N() != 0)) Sumw2(); SetMinimum(); SetMaximum(); // Reset the kCanRebin option. Otherwise SetBinContent on the overflow bin // would resize the axis limits! ResetBit(kCanRebin); // - Loop on bins (including underflows/overflows) Int_t bin, binx, biny, binz; Double_t b1,b2,w,d1,d2; d1 = c1*c1; d2 = c2*c2; for (binz=0;binz<=nbinsz+1;binz++) { for (biny=0;biny<=nbinsy+1;biny++) { for (binx=0;binx<=nbinsx+1;binx++) { bin = binx +(nbinsx+2)*(biny + (nbinsy+2)*binz); b1 = h1->GetBinContent(bin); b2 = h2->GetBinContent(bin); if (b2) w = c1*b1/(c2*b2); else w = 0; SetBinContent(bin,w); if (fSumw2.fN) { Double_t e1 = h1->GetBinError(bin); Double_t e2 = h2->GetBinError(bin); Double_t b22= b2*b2*d2; if (!b2) { fSumw2.fArray[bin] = 0; continue;} if (binomial) { if (b1 != b2) { // in the case of binomial statistics c1 and c2 must be 1 otherwise it does not make sense w = b1/b2; // c1 and c2 are ignored //fSumw2.fArray[bin] = TMath::Abs(w*(1-w)/(c2*b2));//this is the formula in Hbook/Hoper1 //fSumw2.fArray[bin] = TMath::Abs(w*(1-w)/b2); // old formula from G. Flucke // formula which works also for weighted histogram (see http://root.cern.ch/phpBB2/viewtopic.php?t=3753 ) fSumw2.fArray[bin] = TMath::Abs( ( (1.-2.*w)*e1*e1 + w*w*e2*e2 )/(b2*b2) ); } else { //in case b1=b2 error is zero //use TGraphAsymmErrors::BayesDivide for getting the asymmetric error not equal to zero fSumw2.fArray[bin] = 0; } } else { fSumw2.fArray[bin] = d1*d2*(e1*e1*b2*b2 + e2*e2*b1*b1)/(b22*b22); } } } } } ResetStats(); if (binomial) // in case of binomial division use denominator for number of entries SetEntries ( h2->GetEntries() ); else SetEntries( GetEffectiveEntries() ); } //______________________________________________________________________________ void TH1::Draw(Option_t *option) { // -*-*-*-*-*-*-*-*-*Draw this histogram with options*-*-*-*-*-*-*-*-*-*-*-* // ================================ // // Histograms are drawn via the THistPainter class. Each histogram has // a pointer to its own painter (to be usable in a multithreaded program). // 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 of the histogram. Once the clone is drawn, the original // histogram may be modified or deleted without affecting the aspect of the // clone. // By default, TH1::Draw clears the current pad. // // 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(); // // See THistPainter::Paint for a description of all the drawing options // ======================= // // -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* TString opt = option; opt.ToLower(); if (gPad) { if (!gPad->IsEditable()) gROOT->MakeDefCanvas(); if (opt.Contains("same")) { if (gPad->GetX1() == 0 && gPad->GetX2() == 1 && gPad->GetY1() == 0 && gPad->GetY2() == 1 && gPad->GetListOfPrimitives()->GetSize()==0) opt.ReplaceAll("same",""); } else { //the following statement is necessary in case one attempts to draw //a temporary histogram already in the current pad if (TestBit(kCanDelete)) gPad->GetListOfPrimitives()->Remove(this); gPad->Clear(); } } else { if (opt.Contains("same")) opt.ReplaceAll("same",""); } AppendPad(option); } //______________________________________________________________________________ TH1 *TH1::DrawCopy(Option_t *) const { // -*-*-*-*-*Copy this histogram and Draw in the current pad*-*-*-*-*-*-*-* // =============================================== // // Once the histogram is drawn into the pad, any further modification // using graphics input will be made on the copy of the histogram, // and not to the original object. // // See Draw for the list of options // // -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* AbstractMethod("DrawCopy"); return 0; } //______________________________________________________________________________ TH1 *TH1::DrawNormalized(Option_t *option, Double_t norm) const { // Draw a normalized copy of this histogram. // // A clone of this histogram is normalized to norm and drawn with option. // A pointer to the normalized histogram is returned. // The contents of the histogram copy are scaled such that the new // sum of weights (excluding under and overflow) is equal to norm. // Note that the returned normalized histogram is not added to the list // of histograms in the current directory in memory. // It is the user's responsability to delete this histogram. // The kCanDelete bit is set for the returned object. If a pad containing // this copy is cleared, the histogram will be automatically deleted. // See also remark about calling Sumw2 before scaling a histogram to get // a correct computation of the error bars. // // See Draw for the list of options // // -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* Double_t sum = GetSumOfWeights(); if (sum == 0) { Error("DrawNormalized","Sum of weights is null. Cannot normalized histogram: %s",GetName()); return 0; } Bool_t addStatus = TH1::AddDirectoryStatus(); TH1::AddDirectory(kFALSE); TH1 *h = (TH1*)Clone(); h->SetBit(kCanDelete); h->Scale(norm/sum); h->Draw(option); TH1::AddDirectory(addStatus); return h; } //______________________________________________________________________________ void TH1::DrawPanel() { // -*-*-*-*-*Display a panel with all histogram drawing options*-*-*-*-*-* // ================================================== // // See class TDrawPanelHist for example if (!fPainter) {Draw(); if (gPad) gPad->Update();} if (fPainter) fPainter->DrawPanel(); } //______________________________________________________________________________ void TH1::Eval(TF1 *f1, Option_t *option) { // -*-*-*Evaluate function f1 at the center of bins of this histogram-*-*-*-* // ============================================================ // // If option "R" is specified, the function is evaluated only // for the bins included in the function range. // If option "A" is specified, the value of the function is added to the // existing bin contents // If option "S" is specified, the value of the function is used to // generate a value, distributed according to the Poisson // distribution, with f1 as the mean. // // -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* Double_t x[3]; Int_t range,stat,add,bin,binx,biny,binz,nbinsx, nbinsy, nbinsz; if (!f1) return; Double_t fu; Double_t e=0; TString opt = option; opt.ToLower(); if (opt.Contains("a")) add = 1; else add = 0; if (opt.Contains("s")) stat = 1; else stat = 0; if (opt.Contains("r")) range = 1; else range = 0; nbinsx = fXaxis.GetNbins(); nbinsy = fYaxis.GetNbins(); nbinsz = fZaxis.GetNbins(); if (!add) Reset(); for (binz=1;binz<=nbinsz;binz++) { x[2] = fZaxis.GetBinCenter(binz); for (biny=1;biny<=nbinsy;biny++) { x[1] = fYaxis.GetBinCenter(biny); for (binx=1;binx<=nbinsx;binx++) { bin = GetBin(binx,biny,binz); x[0] = fXaxis.GetBinCenter(binx); if (range && !f1->IsInside(x)) continue; fu = f1->Eval(x[0],x[1],x[2]); if (stat) fu = gRandom->PoissonD(fu); if (fSumw2.fN) e = fSumw2.fArray[bin]; AddBinContent(bin,fu); if (fSumw2.fN) fSumw2.fArray[bin] = e+ TMath::Abs(fu); } } } } //______________________________________________________________________________ void TH1::ExecuteEvent(Int_t event, Int_t px, Int_t py) { // -*-*-*-*-*-*-*-*-*Execute action corresponding to one event*-*-*-* // ========================================= // This member function is called when a histogram is clicked with the locator // // If Left button clicked on the bin top value, then the content of this bin // is modified according to the new position of the mouse when it is released. // // -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* if (fPainter) fPainter->ExecuteEvent(event, px, py); } //______________________________________________________________________________ TH1* TH1::FFT(TH1* h_output, Option_t *option) { // This function allows to do discrete Fourier transforms of TH1 and TH2. // Available transform types and flags are described below. // // To extract more information about the transform, use the function // TVirtualFFT::GetCurrentTransform() to get a pointer to the current // transform object. // // Parameters: // 1st - histogram for the output. If a null pointer is passed, a new histogram is created // and returned, otherwise, the provided histogram is used and should be big enough // // Options: option parameters consists of 3 parts: // - option on what to return // "RE" - returns a histogram of the real part of the output // "IM" - returns a histogram of the imaginary part of the output // "MAG"- returns a histogram of the magnitude of the output // "PH" - returns a histogram of the phase of the output // // - option of transform type // "R2C" - real to complex transforms - default // "R2HC" - real to halfcomplex (special format of storing output data, // results the same as for R2C) // "DHT" - discrete Hartley transform // real to real transforms (sine and cosine): // "R2R_0", "R2R_1", "R2R_2", "R2R_3" - discrete cosine transforms of types I-IV // "R2R_4", "R2R_5", "R2R_6", "R2R_7" - discrete sine transforms of types I-IV // To specify the type of each dimension of a 2-dimensional real to real // transform, use options of form "R2R_XX", for example, "R2R_02" for a transform, // which is of type "R2R_0" in 1st dimension and "R2R_2" in the 2nd. // // - option of transform flag // "ES" (from "estimate") - no time in preparing the transform, but probably sub-optimal // performance // "M" (from "measure") - some time spend in finding the optimal way to do the transform // "P" (from "patient") - more time spend in finding the optimal way to do the transform // "EX" (from "exhaustive") - the most optimal way is found // This option should be chosen depending on how many transforms of the same size and // type are going to be done. Planning is only done once, for the first transform of this // size and type. Default is "ES". // Examples of valid options: "Mag R2C M" "Re R2R_11" "Im R2C ES" "PH R2HC EX" Int_t ndim[3]; ndim[0] = this->GetNbinsX(); ndim[1] = this->GetNbinsY(); ndim[2] = this->GetNbinsZ(); TVirtualFFT *fft; TString opt = option; opt.ToUpper(); if (!opt.Contains("2R")){ if (!opt.Contains("2C") && !opt.Contains("2HC") && !opt.Contains("DHT")) { //no type specified, "R2C" by default opt.Append("R2C"); } fft = TVirtualFFT::FFT(this->GetDimension(), ndim, opt.Data()); } else { //find the kind of transform Int_t ind = opt.Index("R2R", 3); Int_t *kind = new Int_t[2]; char t; t = opt[ind+4]; kind[0] = atoi(&t); if (h_output->GetDimension()>1) { t = opt[ind+5]; kind[1] = atoi(&t); } fft = TVirtualFFT::SineCosine(this->GetDimension(), ndim, kind, option); delete [] kind; } if (!fft) return 0; Int_t in=0; for (Int_t binx = 1; binx<=ndim[0]; binx++) { for (Int_t biny=1; biny<=ndim[1]; biny++) { for (Int_t binz=1; binz<=ndim[2]; binz++) { fft->SetPoint(in, this->GetBinContent(binx, biny, binz)); in++; } } } fft->Transform(); h_output = TransformHisto(fft, h_output, option); return h_output; } //______________________________________________________________________________ Int_t TH1::Fill(Double_t x) { // -*-*-*-*-*-*-*-*Increment bin with abscissa X by 1*-*-*-*-*-*-*-*-*-*-* // ================================== // // if x is less than the low-edge of the first bin, the Underflow bin is incremented // if x is greater than the upper edge of last bin, the Overflow bin is incremented // // 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 1 in the bin corresponding to x. // // -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* if (fBuffer) return BufferFill(x,1); Int_t bin; fEntries++; bin =fXaxis.FindBin(x); AddBinContent(bin); if (fSumw2.fN) ++fSumw2.fArray[bin]; if (bin == 0 || bin > fXaxis.GetNbins()) { if (!fgStatOverflows) return -1; } ++fTsumw; ++fTsumw2; fTsumwx += x; fTsumwx2 += x*x; return bin; } //______________________________________________________________________________ Int_t TH1::Fill(Double_t x, Double_t w) { // -*-*-*-*-*-*Increment bin with abscissa X with a weight w*-*-*-*-*-*-*-* // ============================================= // // if x is less than the low-edge of the first bin, the Underflow bin is incremented // if x is greater than the upper edge of last bin, the Overflow bin is incremented // // 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 bin corresponding to x. // // -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* if (fBuffer) return BufferFill(x,w); Int_t bin; fEntries++; bin =fXaxis.FindBin(x); AddBinContent(bin, w); if (fSumw2.fN) fSumw2.fArray[bin] += w*w; if (bin == 0 || bin > fXaxis.GetNbins()) { if (!fgStatOverflows) return -1; } Double_t z= (w > 0 ? w : -w); fTsumw += z; fTsumw2 += z*z; fTsumwx += z*x; fTsumwx2 += z*x*x; return bin; } //______________________________________________________________________________ Int_t TH1::Fill(const char *namex, Double_t w) { // Increment bin with namex with a weight w // // if x is less than the low-edge of the first bin, the Underflow bin is incremented // if x is greater than the upper edge of last bin, the Overflow bin is incremented // // 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 bin corresponding to x. // Int_t bin; fEntries++; bin =fXaxis.FindBin(namex); AddBinContent(bin, w); if (fSumw2.fN) fSumw2.fArray[bin] += w*w; if (bin == 0 || bin > fXaxis.GetNbins()) return -1; Double_t x = fXaxis.GetBinCenter(bin); Double_t z= (w > 0 ? w : -w); fTsumw += z; fTsumw2 += z*z; fTsumwx += z*x; fTsumwx2 += z*x*x; return bin; } //______________________________________________________________________________ void TH1::FillN(Int_t ntimes, const Double_t *x, const Double_t *w, Int_t stride) { // -*-*-*-*-*-*Fill this histogram with an array x and weights w*-*-*-*-* // ================================================= // // ntimes: number of entries in arrays x and w (array size must be ntimes*stride) // x: array of values to be histogrammed // w: array of weighs // stride: step size through arrays x and 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[i]^2 in the bin corresponding to x[i]. // if w is NULL each entry is assumed a weight=1 // // -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* Int_t bin,i; //If a buffer is activated, go via standard Fill (sorry) //if (fBuffer) { // for (i=0;i<ntimes;i+=stride) { // if (w) Fill(x[i],w[i]); // else Fill(x[i],0); // } // return; //} fEntries += ntimes; Double_t ww = 1; Int_t nbins = fXaxis.GetNbins(); ntimes *= stride; for (i=0;i<ntimes;i+=stride) { bin =fXaxis.FindBin(x[i]); if (w) ww = w[i]; AddBinContent(bin, ww); if (fSumw2.fN) fSumw2.fArray[bin] += ww*ww; if (bin == 0 || bin > nbins) { if (!fgStatOverflows) continue; } Double_t z= (ww > 0 ? ww : -ww); fTsumw += z; fTsumw2 += z*z; fTsumwx += z*x[i]; fTsumwx2 += z*x[i]*x[i]; } } //______________________________________________________________________________ void TH1::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. // // -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-**-*-*-*-*-*-*-* Int_t bin, binx, ibin, loop; Double_t r1, x; // - Search for fname in the list of ROOT defined functions TF1 *f1 = (TF1*)gROOT->GetFunction(fname); if (!f1) { Error("FillRandom", "Unknown function: %s",fname); return; } // - Allocate temporary space to store the integral and compute integral Int_t nbinsx = GetNbinsX(); Double_t *integral = new Double_t[nbinsx+1]; integral[0] = 0; for (binx=1;binx<=nbinsx;binx++) { Double_t fint = f1->Integral(fXaxis.GetBinLowEdge(binx),fXaxis.GetBinUpEdge(binx)); integral[binx] = integral[binx-1] + fint; } // - Normalize integral to 1 if (integral[nbinsx] == 0 ) { Error("FillRandom", "Integral = zero"); return; } for (bin=1;bin<=nbinsx;bin++) integral[bin] /= integral[nbinsx]; // --------------Start main loop ntimes for (loop=0;loop<ntimes;loop++) { r1 = gRandom->Rndm(loop); ibin = TMath::BinarySearch(nbinsx,&integral[0],r1); //binx = 1 + ibin; //x = fXaxis.GetBinCenter(binx); //this is not OK when SetBuffer is used x = fXaxis.GetBinLowEdge(ibin+1) +fXaxis.GetBinWidth(ibin+1)*(r1-integral[ibin])/(integral[ibin+1] - integral[ibin]); Fill(x, 1.); } delete [] integral; } //______________________________________________________________________________ void TH1::FillRandom(TH1 *h, Int_t ntimes) { // -*-*-*-*-*Fill histogram following distribution in histogram h*-*-*-* // ==================================================== // // The distribution contained in the histogram h (TH1) 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 // // -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-**-*-*-*-*-*-*-* if (!h) { Error("FillRandom", "Null histogram"); return; } if (fDimension != h->GetDimension()) { Error("FillRandom", "Histograms with different dimensions"); return; } if (h->ComputeIntegral() == 0) return; Int_t loop; Double_t x; for (loop=0;loop<ntimes;loop++) { x = h->GetRandom(); Fill(x); } } //______________________________________________________________________________ Int_t TH1::FindBin(Double_t x, Double_t y, Double_t z) { // -*-*-*-*Return Global bin number corresponding to x,y,z*-*-*-*-*-*-* // =============================================== // // 2-D and 3-D histograms are represented with a one dimensional // structure. // This has the advantage that all existing functions, such as // GetBinContent, GetBinError, GetBinFunction work for all dimensions. // See also TH1::GetBin // -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* if (GetDimension() < 2) { return fXaxis.FindBin(x); } if (GetDimension() < 3) { Int_t nx = fXaxis.GetNbins()+2; Int_t binx = fXaxis.FindBin(x); Int_t biny = fYaxis.FindBin(y); return binx + nx*biny; } if (GetDimension() < 4) { Int_t nx = fXaxis.GetNbins()+2; Int_t ny = fYaxis.GetNbins()+2; Int_t binx = fXaxis.FindBin(x); Int_t biny = fYaxis.FindBin(y); Int_t binz = fZaxis.FindBin(z); return binx + nx*(biny +ny*binz); } return -1; } //______________________________________________________________________________ Int_t TH1::FindFirstBinAbove(Double_t threshold, Int_t axis) const { //find first bin with content > threshold for axis (1=x, 2=y, 3=z) //if no bins with content > threshold is found the function returns -1. if (axis != 1) { Warning("FindFirstBinAbove","Invalid axis number : %d, axis x assumed\n",axis); axis = 1; } Int_t nbins = fXaxis.GetNbins(); for (Int_t bin=1;bin<=nbins;bin++) { if (GetBinContent(bin) > threshold) return bin; } return -1; } //______________________________________________________________________________ Int_t TH1::FindLastBinAbove(Double_t threshold, Int_t axis) const { //find last bin with content > threshold for axis (1=x, 2=y, 3=z) //if no bins with content > threshold is found the function returns -1. if (axis != 1) { Warning("FindLastBinAbove","Invalid axis number : %d, axis x assumed\n",axis); axis = 1; } Int_t nbins = fXaxis.GetNbins(); for (Int_t bin=nbins;bin>=1;bin--) { if (GetBinContent(bin) > threshold) return bin; } return -1; } //______________________________________________________________________________ TObject *TH1::FindObject(const char *name) const { // search object named name in the list of functions if (fFunctions) return fFunctions->FindObject(name); return 0; } //______________________________________________________________________________ TObject *TH1::FindObject(const TObject *obj) const { // search object obj in the list of functions if (fFunctions) return fFunctions->FindObject(obj); return 0; } //______________________________________________________________________________ Int_t TH1::Fit(const char *fname ,Option_t *option ,Option_t *goption, Double_t xxmin, Double_t xxmax) { // Fit histogram with function fname // ================================= // fname is the name of an already predefined function created by TF1 or TF2 // Predefined functions such as gaus, expo and poln are automatically // created by ROOT. // fname can also be a formula, accepted by the linear fitter (linear parts divided // by "++" sign), for example "x++sin(x)" for fitting "[0]*x+[1]*sin(x)" // // This function finds a pointer to the TF1 object with name fname // and calls TH1::Fit(TF1 *f1,...) char *linear; linear= (char*)strstr(fname, "++"); TF1 *f1=0; TF2 *f2=0; TF3 *f3=0; Int_t ndim=GetDimension(); if (linear){ if (ndim<2){ f1=new TF1(fname, fname, xxmin, xxmax); return Fit(f1,option,goption,xxmin,xxmax); } else if (ndim<3){ f2=new TF2(fname, fname); return Fit(f2,option,goption,xxmin,xxmax); } else{ f3=new TF3(fname, fname); return Fit(f3,option,goption,xxmin,xxmax); } } else{ f1 = (TF1*)gROOT->GetFunction(fname); if (!f1) { Printf("Unknown function: %s",fname); return -1; } return Fit(f1,option,goption,xxmin,xxmax); } } //______________________________________________________________________________ Int_t TH1::Fit(TF1 *f1 ,Option_t *option ,Option_t *goption, Double_t xxmin, Double_t xxmax) { // Fit histogram with function f1 // ============================== // // Fit this histogram with function f1. // // The list of fit options is given in parameter option. // option = "W" Set all weights to 1 for non empty bins; ignore error bars // = "WW" Set all weights to 1 including empty bins; ignore error bars // = "I" Use integral of function in bin instead of value at bin center // = "L" Use Loglikelihood method (default is chisquare method) // = "LL" Use Loglikelihood method and bin contents are not integers) // = "U" Use a User specified fitting algorithm (via SetFCN) // = "Q" Quiet mode (minimum printing) // = "V" Verbose mode (default is between Q and V) // = "E" Perform better Errors estimation using Minos technique // = "B" Use this option when you want to fix one or more parameters // and the fitting function is like "gaus", "expo", "poln", "landau". // = "M" More. Improve fit results // = "R" Use the Range specified in the function range // = "N" Do not store the graphics function, do not draw // = "0" Do not plot the result of the fit. By default the fitted function // is drawn unless the option"N" above is specified. // = "+" Add this new fitted function to the list of fitted functions // (by default, any previous function is deleted) // = "C" In case of linear fitting, don't calculate the chisquare // (saves time) // = "F" If fitting a polN, switch to minuit fitter // // When the fit is drawn (by default), the parameter goption may be used // to specify a list of graphics options. See TH1::Draw for a complete // list of these options. // // In order to use the Range option, one must first create a function // with the expression to be fitted. For example, if your histogram // has a defined range between -4 and 4 and you want to fit a gaussian // only in the interval 1 to 3, you can do: // TF1 *f1 = new TF1("f1", "gaus", 1, 3); // histo->Fit("f1", "R"); // // Setting initial conditions // ========================== // Parameters must be initialized before invoking the Fit function. // The setting of the parameter initial values is automatic for the // predefined functions : poln, expo, gaus, landau. One can however disable // this automatic computation by specifying the option "B". // Note that if a predefined function is defined with an argument, // eg, gaus(0), expo(1), you must specify the initial values for // the parameters. // You can specify boundary limits for some or all parameters via // f1->SetParLimits(p_number, parmin, parmax); // if parmin>=parmax, the parameter is fixed // Note that you are not forced to fix the limits for all parameters. // For example, if you fit a function with 6 parameters, you can do: // func->SetParameters(0, 3.1, 1.e-6, -8, 0, 100); // func->SetParLimits(3, -10, -4); // func->FixParameter(4, 0); // func->SetParLimits(5, 1, 1); // With this setup, parameters 0->2 can vary freely // Parameter 3 has boundaries [-10,-4] with initial value -8 // Parameter 4 is fixed to 0 // Parameter 5 is fixed to 100. // When the lower limit and upper limit are equal, the parameter is fixed. // However to fix a parameter to 0, one must call the FixParameter function. // // Note that option "I" gives better results but is slower. // // // Changing the fitting objective function // ============================= // By default a chi square function is used for fitting. When option "L" (or "LL") is used // a Poisson likelihood function (see note below) is used. // The functions are defined in the header Fit/Chi2Func.h or Fit/PoissonLikelihoodFCN and they are implemented // using the routines FitUtil::EvaluateChi2 or FitUtil::EvaluatePoissonLogL in the file math/mathcore/src/FitUtil.cxx. // To specify a User defined fitting function, specify option "U" and // call the following functions: // TVirtualFitter::Fitter(myhist)->SetFCN(MyFittingFunction) // where MyFittingFunction is of type: // extern void MyFittingFunction(Int_t &npar, Double_t *gin, Double_t &f, Double_t *u, Int_t flag); // // Likelihood Fits // ================= // When using option "L" a likelihood fit is used instead of the default chi2 square fit. // The likelihood is built assuming a Poisson probability density function for each bin. // This method can then be used only when the bin content represents counts (i.e. errors are = sqrt(N) ). // The likelihood method has the advantage of treating correctly the empty bins and use them in the fit procedure. // In the chi2 method the empty bins are skipped and not considered in the fit. // The likelihood method, although a bit slower, it is the recommended method in case of low bin statistics, where // the chi2 method may give incorrect results. // // Fitting a histogram of dimension N with a function of dimension N-1 // =================================================================== // It is possible to fit a TH2 with a TF1 or a TH3 with a TF2. // In this case the option "Integral" is not allowed and each cell has // equal weight. // // 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"); // // Access to the fit status // ======================== // The function return the status of the fit (fitResult) in the following form // fitResult = migradResult + 10*minosResult + 100*hesseResult + 1000*improveResult // The fitResult is 0 is the fit is OK. // The fitResult is negative in case of an error not connected with the fit. // // Access to the fit results // ========================= // 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 // // Access to the fit covariance matrix // =================================== // Example1: // TH1F h("h", "test", 100, -2, 2); // h.FillRandom("gaus", 1000); // h.Fit("gaus"); // Double_t matrix[3][3]; // gMinuit->mnemat(&matrix[0][0], 3); // Example2: // TH1F h("h", "test", 100, -2, 2); // h.FillRandom("gaus", 1000); // h.Fit("gaus"); // TVirtualFitter *fitter = TVirtualFitter::GetFitter(); // TMatrixD matrix(npar, npar, fitter->GetCovarianceMatrix()); // Double_t errorFirstPar = fitter->GetCovarianceMatrixElement(0, 0); // // // Changing the maximum number of parameters // ========================================= // By default, the fitter TMinuit is initialized with a maximum of 25 parameters. // You can redefine this default value by calling : // TVirtualFitter::Fitter(0, 150); //to get a maximum of 150 parameters // // Excluding points // ================ // Use TF1::RejectPoint inside your fitting function to exclude points // within a certain range from the fit. Example: // Double_t fline(Double_t *x, Double_t *par) // { // if (x[0] > 2.5 && x[0] < 3.5) { // TF1::RejectPoint(); // return 0; // } // return par[0] + par[1]*x[0]; // } // // void exclude() { // TF1 *f1 = new TF1("f1", "[0] +[1]*x +gaus(2)", 0, 5); // f1->SetParameters(6, -1,5, 3, 0.2); // TH1F *h = new TH1F("h", "background + signal", 100, 0, 5); // h->FillRandom("f1", 2000); // TF1 *fline = new TF1("fline", fline, 0, 5, 2); // fline->SetParameters(2, -1); // h->Fit("fline", "l"); // } // // Warning when using the option "0" // ================================= // When selecting the option "0", the fitted function is added to // the list of functions of the histogram, but it is not drawn. // You can undo what you disabled in the following way: // h.Fit("myFunction", "0"); // fit, store function but do not draw // h.Draw(); function is not drawn // const Int_t kNotDraw = 1<<9; // h.GetFunction("myFunction")->ResetBit(kNotDraw); // h.Draw(); // function is visible again // // Access to the Fitter information during fitting // =============================================== // This function calls only the abstract fitter TVirtualFitter. // The default fitter is TFitter (calls TMinuit). // The default fitter can be set in the resource file in etc/system.rootrc // Root.Fitter: Fumili // A different fitter can also be set via TVirtualFitter::SetDefaultFitter. // For example, to call the "Fumili" fitter instead of "Minuit", do // TVirtualFitter::SetDefaultFitter("Fumili"); // During the fitting process, the objective function: // chisquare, likelihood or any user defined algorithm // is called (see eg in the TFitter class, the static functions // H1FitChisquare, H1FitLikelihood). // This objective function, in turn, calls the user theoretical function. // This user function is a static function called from the TF1 *f1 function. // Inside this user defined theoretical function , one can access: // TVirtualFitter *fitter = TVirtualFitter::GetFitter(); //the current fitter // TH1 *hist = (TH1*)fitter->GetObjectFit(); //the histogram being fitted // TF1 +f1 = (TF1*)fitter->GetUserFunction(); //the user theoretical function // // By default, the fitter TMinuit is initialized with a maximum of 25 parameters. // For fitting linear functions (containing the "++" sign" and polN functions, // the linear fitter is initialized. // // -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* // implementation of Fit method is in file hist/src/HFitImpl.cxx return DoFit( f1 , option , goption, xxmin, xxmax); } //______________________________________________________________________________ void TH1::FitPanel() { // -*-*-*-*-*Display a panel with all histogram fit options*-*-*-*-*-* // ============================================== // // See class TFitPanel for example if (!gPad) gROOT->MakeDefCanvas(); if (!gPad) { Error("FitPanel", "Unable to create a default canvas"); return; } // use plugin manager to create instance of TFitEditor TPluginHandler *handler = gROOT->GetPluginManager()->FindHandler("TFitEditor"); if (handler && handler->LoadPlugin() != -1) { if (handler->ExecPlugin(2, gPad, this) == 0) Error("FitPanel", "Unable to crate the FitPanel"); } else Error("FitPanel", "Unable to find the FitPanel plug-in"); } //______________________________________________________________________________ TH1 *TH1::GetAsymmetry(TH1* h2, Double_t c2, Double_t dc2) { // return an histogram containing the asymmetry of this histogram with h2, // where the asymmetry is defined as: // // Asymmetry = (h1 - h2)/(h1 + h2) where h1 = this // // works for 1D, 2D, etc. histograms // c2 is an optional argument that gives a relative weight between the two // histograms, and dc2 is the error on this weight. This is useful, for example, // when forming an asymmetry between two histograms from 2 different data sets that // need to be normalized to each other in some way. The function calculates // the errors asumming Poisson statistics on h1 and h2 (that is, dh = sqrt(h)). // // example: assuming 'h1' and 'h2' are already filled // // h3 = h1->GetAsymmetry(h2) // // then 'h3' is created and filled with the asymmetry between 'h1' and 'h2'; // h1 and h2 are left intact. // // Note that it is the user's responsibility to manage the created histogram. // // code proposed by Jason Seely (seely@mit.edu) and adapted by R.Brun // // clone the histograms so top and bottom will have the // correct dimensions: // Sumw2 just makes sure the errors will be computed properly // when we form sums and ratios below. Bool_t addStatus = TH1::AddDirectoryStatus(); TH1::AddDirectory(kFALSE); TH1 *asym = (TH1*)Clone(); asym->Sumw2(); TH1 *top = (TH1*)asym->Clone(); TH1 *bottom = (TH1*)asym->Clone(); TH1::AddDirectory(addStatus); // form the top and bottom of the asymmetry, and then divide: TH1 *h1 = this; top->Add(h1,h2,1,-c2); bottom->Add(h1,h2,1,c2); asym->Divide(top,bottom); Int_t xmax = asym->GetNbinsX(); Int_t ymax = asym->GetNbinsY(); Int_t zmax = asym->GetNbinsZ(); Double_t bot, error, a, b, da, db; // now loop over bins to calculate the correct errors // the reason this error calculation looks complex is because of c2 for(Int_t i=1; i<= xmax; i++){ for(Int_t j=1; j<= ymax; j++){ for(Int_t k=1; k<= zmax; k++){ // here some bin contents are written into variables to make the error // calculation a little more legible: a = h1->GetBinContent(i,j,k); b = h2->GetBinContent(i,j,k); bot = bottom->GetBinContent(i,j,k); // make sure there are some events, if not, then the errors are set = 0 // automatically. //if(bot < 1){} was changed to the next line from recommendation of Jason Seely (28 Nov 2005) if(bot < 1e-6){} else{ // computation of errors by Christos Leonidopoulos da = h1->GetBinError(i,j,k); db = h2->GetBinError(i,j,k); error = 2*TMath::Sqrt(a*a*c2*c2*db*db + c2*c2*b*b*da*da+a*a*b*b*dc2*dc2)/(bot*bot); asym->SetBinError(i,j,k,error); } } } } delete top; delete bottom; return asym; } //______________________________________________________________________________ Int_t TH1::GetDefaultBufferSize() { // static function // return the default buffer size for automatic histograms // the parameter fgBufferSize may be changed via SetDefaultBufferSize return fgBufferSize; } //______________________________________________________________________________ Bool_t TH1::GetDefaultSumw2() { // static function // return kTRUE if TH1::Sumw2 must be called when creating new histograms. // see TH1::SetDefaultSumw2. return fgDefaultSumw2; } //______________________________________________________________________________ Double_t TH1::GetEntries() const { // return the current number of entries if (fBuffer) ((TH1*)this)->BufferEmpty(); return fEntries; } //______________________________________________________________________________ Double_t TH1::GetEffectiveEntries() const { // number of effective entries of the histogram, // i.e. the number of unweighted entries a histogram would need to // have the same statistical power as this histogram with possibly // weighted entries (i.e. <= TH1::GetEntries()) Stat_t s[kNstat]; this->GetStats(s);// s[1] sum of squares of weights, s[0] sum of weights return (s[1] ? s[0]*s[0]/s[1] : 0.); } //______________________________________________________________________________ char *TH1::GetObjectInfo(Int_t px, Int_t py) const { // Redefines TObject::GetObjectInfo. // Displays the histogram info (bin number, contents, integral up to bin // corresponding to cursor position px,py // return ((TH1*)this)->GetPainter()->GetObjectInfo(px,py); } //______________________________________________________________________________ TVirtualHistPainter *TH1::GetPainter(Option_t *option) { // return pointer to painter // if painter does not exist, it is created if (!fPainter) { TString opt = option; opt.ToLower(); if (opt.Contains("gl") || gStyle->GetCanvasPreferGL()) { //try to create TGLHistPainter TPluginHandler *handler = gROOT->GetPluginManager()->FindHandler("TGLHistPainter"); if (handler && handler->LoadPlugin() != -1) fPainter = reinterpret_cast<TVirtualHistPainter *>(handler->ExecPlugin(1, this)); } } if (!fPainter) fPainter = TVirtualHistPainter::HistPainter(this); return fPainter; } //______________________________________________________________________________ Int_t TH1::GetQuantiles(Int_t nprobSum, Double_t *q, const Double_t *probSum) { // Compute Quantiles for this histogram // Quantile x_q of a probability distribution Function F is defined as // // F(x_q) = q with 0 <= q <= 1. // // For instance the median x_0.5 of a distribution is defined as that value // of the random variable for which the distribution function equals 0.5: // // F(x_0.5) = Probability(x < x_0.5) = 0.5 // // code from Eddy Offermann, Renaissance // // input parameters // - this 1-d histogram (TH1F,D,etc). Could also be a TProfile // - nprobSum maximum size of array q and size of array probSum (if given) // - probSum array of positions where quantiles will be computed. // if probSum is null, probSum will be computed internally and will // have a size = number of bins + 1 in h. it will correspond to the // quantiles calculated at the lowest edge of the histogram (quantile=0) and // all the upper edges of the bins. // if probSum is not null, it is assumed to contain at least nprobSum values. // output // - return value nq (<=nprobSum) with the number of quantiles computed // - array q filled with nq quantiles // // Note that the Integral of the histogram is automatically recomputed // if the number of entries is different of the number of entries when // the integral was computed last time. In case you do not use the Fill // functions to fill your histogram, but SetBinContent, you must call // TH1::ComputeIntegral before calling this function. // // Getting quantiles q from two histograms and storing results in a TGraph, // a so-called QQ-plot // // TGraph *gr = new TGraph(nprob); // h1->GetQuantiles(nprob,gr->GetX()); // h2->GetQuantiles(nprob,gr->GetY()); // gr->Draw("alp"); // // Example: // void quantiles() { // // demo for quantiles // const Int_t nq = 20; // TH1F *h = new TH1F("h","demo quantiles",100,-3,3); // h->FillRandom("gaus",5000); // // Double_t xq[nq]; // position where to compute the quantiles in [0,1] // Double_t yq[nq]; // array to contain the quantiles // for (Int_t i=0;i<nq;i++) xq[i] = Float_t(i+1)/nq; // h->GetQuantiles(nq,yq,xq); // // //show the original histogram in the top pad // TCanvas *c1 = new TCanvas("c1","demo quantiles",10,10,700,900); // c1->Divide(1,2); // c1->cd(1); // h->Draw(); // // // show the quantiles in the bottom pad // c1->cd(2); // gPad->SetGrid(); // TGraph *gr = new TGraph(nq,xq,yq); // gr->SetMarkerStyle(21); // gr->Draw("alp"); // } if (GetDimension() > 1) { Error("GetQuantiles","Only available for 1-d histograms"); return 0; } const Int_t nbins = GetXaxis()->GetNbins(); if (!fIntegral) ComputeIntegral(); if (fIntegral && fIntegral[nbins+1] != fEntries) ComputeIntegral(); Int_t i, ibin; Double_t *prob = (Double_t*)probSum; Int_t nq = nprobSum; if (probSum == 0) { nq = nbins+1; prob = new Double_t[nq]; prob[0] = 0; for (i=1;i<nq;i++) { prob[i] = fIntegral[i]/fIntegral[nbins]; } } for (i = 0; i < nq; i++) { ibin = TMath::BinarySearch(nbins,fIntegral,prob[i]); while (ibin < nbins-1 && fIntegral[ibin+1] == prob[i]) { if (fIntegral[ibin+2] == prob[i]) ibin++; else break; } q[i] = GetBinLowEdge(ibin+1); const Double_t dint = fIntegral[ibin+1]-fIntegral[ibin]; if (dint > 0) q[i] += GetBinWidth(ibin+1)*(prob[i]-fIntegral[ibin])/dint; } if (!probSum) delete [] prob; return nq; } //______________________________________________________________________________ Int_t TH1::FitOptionsMake(Option_t *choptin, Foption_t &fitOption) { // -*-*-*-*-*-*-*Decode string choptin and fill fitOption structure*-*-*-*-*-* // ================================================ Int_t nch = strlen(choptin); if (!nch) return 1; char chopt[32]; strcpy(chopt,choptin); for (Int_t i=0;i<nch;i++) chopt[i] = toupper(choptin[i]); if (strstr(chopt,"Q")) fitOption.Quiet = 1; if (strstr(chopt,"V")) {fitOption.Verbose = 1; fitOption.Quiet = 0;} if (strstr(chopt,"L")) fitOption.Like = 1; if (strstr(chopt,"LL")) fitOption.Like = 2; if (strstr(chopt,"W")) fitOption.W1 = 1; if (strstr(chopt,"WW")) fitOption.W1 = 2; //all bins have weight=1, even empty bins if (strstr(chopt,"E")) fitOption.Errors = 1; if (strstr(chopt,"M")) fitOption.More = 1; if (strstr(chopt,"R")) fitOption.Range = 1; if (strstr(chopt,"G")) fitOption.Gradient= 1; if (strstr(chopt,"N")) fitOption.Nostore = 1; if (strstr(chopt,"0")) fitOption.Nograph = 1; if (strstr(chopt,"+")) fitOption.Plus = 1; if (strstr(chopt,"I")) fitOption.Integral= 1; if (strstr(chopt,"B")) fitOption.Bound = 1; if (strstr(chopt,"U")) {fitOption.User = 1; fitOption.Like = 0;} if (strstr(chopt,"F")) fitOption.Minuit = 1; if (strstr(chopt,"C")) fitOption.Nochisq = 1; return 1; } //______________________________________________________________________________ void H1InitGaus() { // -*-*-*-*Compute Initial values of parameters for a gaussian*-*-*-*-*-*-* // =================================================== Double_t allcha, sumx, sumx2, x, val, rms, mean; Int_t bin; const Double_t sqrtpi = 2.506628; // - Compute mean value and RMS of the histogram in the given range TVirtualFitter *hFitter = TVirtualFitter::GetFitter(); TH1 *curHist = (TH1*)hFitter->GetObjectFit(); Int_t hxfirst = hFitter->GetXfirst(); Int_t hxlast = hFitter->GetXlast(); Double_t valmax = curHist->GetBinContent(hxfirst); Double_t binwidx = curHist->GetBinWidth(hxfirst); allcha = sumx = sumx2 = 0; for (bin=hxfirst;bin<=hxlast;bin++) { x = curHist->GetBinCenter(bin); val = TMath::Abs(curHist->GetBinContent(bin)); if (val > valmax) valmax = val; sumx += val*x; sumx2 += val*x*x; allcha += val; } if (allcha == 0) return; mean = sumx/allcha; rms = sumx2/allcha - mean*mean; if (rms > 0) rms = TMath::Sqrt(rms); else rms = 0; if (rms == 0) rms = binwidx*(hxlast-hxfirst+1)/4; //if the distribution is really gaussian, the best approximation //is binwidx*allcha/(sqrtpi*rms) //However, in case of non-gaussian tails, this underestimates //the normalisation constant. In this case the maximum value //is a better approximation. //We take the average of both quantities Double_t constant = 0.5*(valmax+binwidx*allcha/(sqrtpi*rms)); //In case the mean value is outside the histo limits and //the RMS is bigger than the range, we take // mean = center of bins // rms = half range Double_t xmin = curHist->GetXaxis()->GetXmin(); Double_t xmax = curHist->GetXaxis()->GetXmax(); if ((mean < xmin || mean > xmax) && rms > (xmax-xmin)) { mean = 0.5*(xmax+xmin); rms = 0.5*(xmax-xmin); } TF1 *f1 = (TF1*)hFitter->GetUserFunc(); f1->SetParameter(0,constant); f1->SetParameter(1,mean); f1->SetParameter(2,rms); f1->SetParLimits(2,0,10*rms); } //______________________________________________________________________________ void H1InitExpo() { // -*-*-*-*Compute Initial values of parameters for an exponential*-*-*-*-* // ======================================================= Double_t constant, slope; Int_t ifail; TVirtualFitter *hFitter = TVirtualFitter::GetFitter(); Int_t hxfirst = hFitter->GetXfirst(); Int_t hxlast = hFitter->GetXlast(); Int_t nchanx = hxlast - hxfirst + 1; H1LeastSquareLinearFit(-nchanx, constant, slope, ifail); TF1 *f1 = (TF1*)hFitter->GetUserFunc(); f1->SetParameter(0,constant); f1->SetParameter(1,slope); } //______________________________________________________________________________ void H1InitPolynom() { // -*-*-*-*Compute Initial values of parameters for a polynom*-*-*-*-*-*-* // =================================================== Double_t fitpar[25]; TVirtualFitter *hFitter = TVirtualFitter::GetFitter(); TF1 *f1 = (TF1*)hFitter->GetUserFunc(); Int_t hxfirst = hFitter->GetXfirst(); Int_t hxlast = hFitter->GetXlast(); Int_t nchanx = hxlast - hxfirst + 1; Int_t npar = f1->GetNpar(); if (nchanx <=1 || npar == 1) { TH1 *curHist = (TH1*)hFitter->GetObjectFit(); fitpar[0] = curHist->GetSumOfWeights()/Double_t(nchanx); } else { H1LeastSquareFit( nchanx, npar, fitpar); } for (Int_t i=0;i<npar;i++) f1->SetParameter(i, fitpar[i]); } //______________________________________________________________________________ void H1LeastSquareFit(Int_t n, Int_t m, Double_t *a) { // -*-*-*-*-*-*Least squares lpolynomial fitting without weights*-*-*-*-*-*-* // ================================================= // // n number of points to fit // m number of parameters // a array of parameters // // based on CERNLIB routine LSQ: Translated to C++ by Rene Brun // (E.Keil. revised by B.Schorr, 23.10.1981.) // // -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* const Double_t zero = 0.; const Double_t one = 1.; const Int_t idim = 20; Double_t b[400] /* was [20][20] */; Int_t i, k, l, ifail; Double_t power; Double_t da[20], xk, yk; if (m <= 2) { H1LeastSquareLinearFit(n, a[0], a[1], ifail); return; } if (m > idim || m > n) return; b[0] = Double_t(n); da[0] = zero; for (l = 2; l <= m; ++l) { b[l-1] = zero; b[m + l*20 - 21] = zero; da[l-1] = zero; } TVirtualFitter *hFitter = TVirtualFitter::GetFitter(); TH1 *curHist = (TH1*)hFitter->GetObjectFit(); Int_t hxfirst = hFitter->GetXfirst(); Int_t hxlast = hFitter->GetXlast(); for (k = hxfirst; k <= hxlast; ++k) { xk = curHist->GetBinCenter(k); yk = curHist->GetBinContent(k); power = one; da[0] += yk; for (l = 2; l <= m; ++l) { power *= xk; b[l-1] += power; da[l-1] += power*yk; } for (l = 2; l <= m; ++l) { power *= xk; b[m + l*20 - 21] += power; } } for (i = 3; i <= m; ++i) { for (k = i; k <= m; ++k) { b[k - 1 + (i-1)*20 - 21] = b[k + (i-2)*20 - 21]; } } H1LeastSquareSeqnd(m, b, idim, ifail, 1, da); for (i=0; i<m; ++i) a[i] = da[i]; } //______________________________________________________________________________ void H1LeastSquareLinearFit(Int_t ndata, Double_t &a0, Double_t &a1, Int_t &ifail) { // -*-*-*-*-*-*-*-*Least square linear fit without weights*-*-*-*-*-*-*-*-* // ======================================= // // extracted from CERNLIB LLSQ: Translated to C++ by Rene Brun // (added to LSQ by B. Schorr, 15.02.1982.) // // -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* Double_t xbar, ybar, x2bar; Int_t i, n; Double_t xybar; Double_t fn, xk, yk; Double_t det; n = TMath::Abs(ndata); ifail = -2; xbar = ybar = x2bar = xybar = 0; TVirtualFitter *hFitter = TVirtualFitter::GetFitter(); TH1 *curHist = (TH1*)hFitter->GetObjectFit(); Int_t hxfirst = hFitter->GetXfirst(); Int_t hxlast = hFitter->GetXlast(); for (i = hxfirst; i <= hxlast; ++i) { xk = curHist->GetBinCenter(i); yk = curHist->GetBinContent(i); if (ndata < 0) { if (yk <= 0) yk = 1e-9; yk = TMath::Log(yk); } xbar += xk; ybar += yk; x2bar += xk*xk; xybar += xk*yk; } fn = Double_t(n); det = fn*x2bar - xbar*xbar; ifail = -1; if (det <= 0) { a0 = ybar/fn; a1 = 0; return; } ifail = 0; a0 = (x2bar*ybar - xbar*xybar) / det; a1 = (fn*xybar - xbar*ybar) / det; } //______________________________________________________________________________ void H1LeastSquareSeqnd(Int_t n, Double_t *a, Int_t idim, Int_t &ifail, Int_t k, Double_t *b) { // -*-*-*-*-*-*Extracted from CERN Program library routine DSEQN*-*-*-*-*-* // ================================================= // // : Translated to C++ by Rene Brun // // -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* Int_t a_dim1, a_offset, b_dim1, b_offset; Int_t nmjp1, i, j, l; Int_t im1, jp1, nm1, nmi; Double_t s1, s21, s22; const Double_t one = 1.; /* Parameter adjustments */ b_dim1 = idim; b_offset = b_dim1 + 1; b -= b_offset; a_dim1 = idim; a_offset = a_dim1 + 1; a -= a_offset; if (idim < n) return; ifail = 0; for (j = 1; j <= n; ++j) { if (a[j + j*a_dim1] <= 0) { ifail = -1; return; } a[j + j*a_dim1] = one / a[j + j*a_dim1]; if (j == n) continue; jp1 = j + 1; for (l = jp1; l <= n; ++l) { a[j + l*a_dim1] = a[j + j*a_dim1] * a[l + j*a_dim1]; s1 = -a[l + (j+1)*a_dim1]; for (i = 1; i <= j; ++i) { s1 = a[l + i*a_dim1] * a[i + (j+1)*a_dim1] + s1; } a[l + (j+1)*a_dim1] = -s1; } } if (k <= 0) return; for (l = 1; l <= k; ++l) { b[l*b_dim1 + 1] = a[a_dim1 + 1]*b[l*b_dim1 + 1]; } if (n == 1) return; for (l = 1; l <= k; ++l) { for (i = 2; i <= n; ++i) { im1 = i - 1; s21 = -b[i + l*b_dim1]; for (j = 1; j <= im1; ++j) { s21 = a[i + j*a_dim1]*b[j + l*b_dim1] + s21; } b[i + l*b_dim1] = -a[i + i*a_dim1]*s21; } nm1 = n - 1; for (i = 1; i <= nm1; ++i) { nmi = n - i; s22 = -b[nmi + l*b_dim1]; for (j = 1; j <= i; ++j) { nmjp1 = n - j + 1; s22 = a[nmi + nmjp1*a_dim1]*b[nmjp1 + l*b_dim1] + s22; } b[nmi + l*b_dim1] = -s22; } } } //______________________________________________________________________________ Int_t TH1::GetBin(Int_t binx, Int_t biny, Int_t binz) const { // -*-*-*-*Return Global bin number corresponding to binx,y,z*-*-*-*-*-*-* // ================================================== // // 2-D and 3-D histograms are represented with a one dimensional // structure. // This has the advantage that all existing functions, such as // GetBinContent, GetBinError, GetBinFunction work for all dimensions. // // In case of a TH1x, returns binx directly. // see TH1::GetBinXYZ for the inverse transformation. // // 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. // -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* Int_t nx, ny, nz; if (GetDimension() < 2) { nx = fXaxis.GetNbins()+2; if (binx < 0) binx = 0; if (binx >= nx) binx = nx-1; return binx; } if (GetDimension() < 3) { nx = fXaxis.GetNbins()+2; if (binx < 0) binx = 0; if (binx >= nx) binx = nx-1; ny = fYaxis.GetNbins()+2; if (biny < 0) biny = 0; if (biny >= ny) biny = ny-1; return binx + nx*biny; } if (GetDimension() < 4) { nx = fXaxis.GetNbins()+2; if (binx < 0) binx = 0; if (binx >= nx) binx = nx-1; ny = fYaxis.GetNbins()+2; if (biny < 0) biny = 0; if (biny >= ny) biny = ny-1; nz = fZaxis.GetNbins()+2; if (binz < 0) binz = 0; if (binz >= nz) binz = nz-1; return binx + nx*(biny +ny*binz); } return -1; } //______________________________________________________________________________ void TH1::GetBinXYZ(Int_t binglobal, Int_t &binx, Int_t &biny, Int_t &binz) const { // return binx, biny, binz corresponding to the global bin number globalbin // see TH1::GetBin function above Int_t nx = fXaxis.GetNbins()+2; Int_t ny = fYaxis.GetNbins()+2; if (GetDimension() < 2) { binx = binglobal%nx; } if (GetDimension() < 3) { binx = binglobal%nx; biny = ((binglobal-binx)/nx)%ny; } if (GetDimension() < 4) { binx = binglobal%nx; biny = ((binglobal-binx)/nx)%ny; binz = ((binglobal-binx)/nx -biny)/ny; } } //______________________________________________________________________________ Double_t TH1::GetRandom() const { // return a random number distributed according the histogram bin contents. // This function checks if the bins integral exists. If not, the integral // is evaluated, normalized to one. // The integral is automatically recomputed if the number of entries // is not the same then when the integral was computed. // NB Only valid for 1-d histograms. Use GetRandom2 or 3 otherwise. if (fDimension > 1) { Error("GetRandom","Function only valid for 1-d histograms"); return 0; } Int_t nbinsx = GetNbinsX(); Double_t integral; if (fIntegral) { if (fIntegral[nbinsx+1] != fEntries) integral = ((TH1*)this)->ComputeIntegral(); } else { integral = ((TH1*)this)->ComputeIntegral(); if (integral == 0 || fIntegral == 0) return 0; } Double_t r1 = gRandom->Rndm(); Int_t ibin = TMath::BinarySearch(nbinsx,fIntegral,r1); Double_t x = GetBinLowEdge(ibin+1); if (r1 > fIntegral[ibin]) x += GetBinWidth(ibin+1)*(r1-fIntegral[ibin])/(fIntegral[ibin+1] - fIntegral[ibin]); return x; } //______________________________________________________________________________ Double_t TH1::GetBinContent(Int_t) const { // -*-*-*-*-*Return content of bin number bin // ================================ // Implemented in TH1C,S,F,D // // 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. AbstractMethod("GetBinContent"); return 0; } //______________________________________________________________________________ Double_t TH1::GetBinContent(Int_t binx, Int_t biny) const { // -*-*-*-*-*Return content of bin number binx, biny // ======================================= // NB: Function to be called for 2-D histograms only // see convention for numbering bins in TH1::GetBin Int_t bin = GetBin(binx,biny); return GetBinContent(bin); } //______________________________________________________________________________ Double_t TH1::GetBinContent(Int_t binx, Int_t biny, Int_t binz) const { // -*-*-*-*-*Return content of bin number binx,biny,binz // =========================================== // NB: Function to be called for 3-D histograms only // see convention for numbering bins in TH1::GetBin Int_t bin = GetBin(binx,biny,binz); return GetBinContent(bin); } //______________________________________________________________________________ Double_t TH1::GetBinWithContent(Double_t c, Int_t &binx, Int_t firstx, Int_t lastx,Double_t maxdiff) const { // compute first binx in the range [firstx,lastx] for which // diff = abs(bin_content-c) <= maxdiff // In case several bins in the specified range with diff=0 are found // the first bin found is returned in binx. // In case several bins in the specified range satisfy diff <=maxdiff // the bin with the smallest difference is returned in binx. // 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 // ie if firstx=0 and lastx=0 (default) the search is on all bins. // NOTE2: if maxdiff=0 (default), the first bin with content=c is returned. if (fDimension > 1) { binx = 0; Error("GetBinWithContent","function is only valid for 1-D histograms"); return 0; } if (firstx <= 0) firstx = 1; if (lastx < firstx) lastx = fXaxis.GetNbins(); Int_t binminx = 0; Double_t diff, curmax = 1.e240; for (Int_t i=firstx;i<=lastx;i++) { diff = TMath::Abs(GetBinContent(i)-c); if (diff <= 0) {binx = i; return diff;} if (diff < curmax && diff <= maxdiff) {curmax = diff, binminx=i;} } binx = binminx; return curmax; } //______________________________________________________________________________ TAxis *TH1::GetXaxis() const { // return a pointer to the X axis object return &((TH1*)this)->fXaxis; } //______________________________________________________________________________ TAxis *TH1::GetYaxis() const { // return a pointer to the Y axis object return &((TH1*)this)->fYaxis; } //______________________________________________________________________________ TAxis *TH1::GetZaxis() const { // return a pointer to the Z axis object return &((TH1*)this)->fZaxis; } //______________________________________________________________________________ Double_t TH1::Interpolate(Double_t x) { // Given a point x, approximates the value via linear interpolation // based on the two nearest bin centers // Andy Mastbaum 10/21/08 Int_t xbin = FindBin(x); Double_t x0,x1,y0,y1; if(x<=GetBinCenter(1)) { return GetBinContent(1); } else if(x>=GetBinCenter(GetNbinsX())) { return GetBinContent(GetNbinsX()); } else { if(x<=GetBinCenter(xbin)) { y0 = GetBinContent(xbin-1); x0 = GetBinCenter(xbin-1); y1 = GetBinContent(xbin); x1 = GetBinCenter(xbin); } else { y0 = GetBinContent(xbin); x0 = GetBinCenter(xbin); y1 = GetBinContent(xbin+1); x1 = GetBinCenter(xbin+1); } return y0 + (x-x0)*((y1-y0)/(x1-x0)); } } //______________________________________________________________________________ Double_t TH1::Interpolate(Double_t, Double_t) { //Not yet implemented Error("Interpolate","This function must be called with 1 argument for a TH1"); return 0; } //______________________________________________________________________________ Double_t TH1::Interpolate(Double_t, Double_t, Double_t) { //Not yet implemented Error("Interpolate","This function must be called with 1 argument for a TH1"); return 0; } //______________________________________________________________________________ Bool_t TH1::IsBinOverflow(Int_t bin) const { // Return true if the bin is overflow. Int_t binx, biny, binz; GetBinXYZ(bin, binx, biny, binz); if ( fDimension == 1 ) return binx >= GetNbinsX() + 1; else if ( fDimension == 2 ) return (binx >= GetNbinsX() + 1) || (biny >= GetNbinsY() + 1); else if ( fDimension == 3 ) return (binx >= GetNbinsX() + 1) || (biny >= GetNbinsY() + 1) || (binz >= GetNbinsZ() + 1); else return 0; } //______________________________________________________________________________ Bool_t TH1::IsBinUnderflow(Int_t bin) const { // Return true if the bin is overflow. Int_t binx, biny, binz; GetBinXYZ(bin, binx, biny, binz); if ( fDimension == 1 ) return (binx <= 0); else if ( fDimension == 2 ) return (binx <= 0 || biny <= 0); else if ( fDimension == 3 ) return (binx <= 0 || biny <= 0 || binz <= 0); else return 0; } //___________________________________________________________________________ void TH1::LabelsDeflate(Option_t *ax) { // Reduce the number of bins for this axis to the number of bins having a label. Int_t iaxis = AxisChoice(ax); TAxis *axis = 0; if (iaxis == 1) axis = GetXaxis(); if (iaxis == 2) axis = GetYaxis(); if (iaxis == 3) axis = GetZaxis(); if (!axis) return; if (!axis->GetLabels()) return; TIter next(axis->GetLabels()); TObject *obj; Int_t nbins = 0; while ((obj = next())) { if (obj->GetUniqueID()) nbins++; } if (nbins < 1) nbins = 1; TH1 *hold = (TH1*)Clone(); hold->SetDirectory(0); Bool_t timedisp = axis->GetTimeDisplay(); Double_t xmin = axis->GetXmin(); Double_t xmax = axis->GetBinUpEdge(nbins); if (xmax <= xmin) xmax = xmin +nbins; axis->SetRange(0,0); axis->Set(nbins,xmin,xmax); //Int_t nbinsx = fXaxis.GetNbins(); //Int_t nbinsy = fYaxis.GetNbins(); //Int_t nbinsz = fZaxis.GetNbins(); Int_t nbinsx = hold->GetXaxis()->GetNbins(); Int_t nbinsy = hold->GetYaxis()->GetNbins(); Int_t nbinsz = hold->GetZaxis()->GetNbins(); Int_t ncells = nbinsx+2; if (GetDimension() > 1) ncells *= nbinsy+2; if (GetDimension() > 2) ncells *= nbinsz+2; SetBinsLength(ncells); Int_t errors = fSumw2.fN; if (errors) fSumw2.Set(ncells); axis->SetTimeDisplay(timedisp); //now loop on all bins and refill Double_t err,cu; Int_t bin,ibin,binx,biny,binz; Double_t oldEntries = fEntries; for (binz=1;binz<=nbinsz;binz++) { for (biny=1;biny<=nbinsy;biny++) { for (binx=1;binx<=nbinsx;binx++) { bin = hold->GetBin(binx,biny,binz); ibin= GetBin(binx,biny,binz); cu = hold->GetBinContent(bin); SetBinContent(ibin,cu); if (errors) { err = hold->GetBinError(bin); SetBinError(ibin,err); } } } } fEntries = oldEntries; delete hold; } //______________________________________________________________________________ void TH1::LabelsInflate(Option_t *ax) { // Double the number of bins for axis. // Refill histogram // This function is called by TAxis::FindBin(const char *label) Int_t iaxis = AxisChoice(ax); TAxis *axis = 0; if (iaxis == 1) axis = GetXaxis(); if (iaxis == 2) axis = GetYaxis(); if (iaxis == 3) axis = GetZaxis(); if (!axis) return; TH1 *hold = (TH1*)Clone(); hold->SetDirectory(0); Bool_t timedisp = axis->GetTimeDisplay(); Int_t nbxold = fXaxis.GetNbins(); Int_t nbyold = fYaxis.GetNbins(); Int_t nbzold = fZaxis.GetNbins(); Int_t nbins = axis->GetNbins(); Double_t xmin = axis->GetXmin(); Double_t xmax = axis->GetXmax(); xmax = xmin + 2*(xmax-xmin); axis->SetRange(0,0); axis->Set(2*nbins,xmin,xmax); Int_t nbinsx = fXaxis.GetNbins(); Int_t nbinsy = fYaxis.GetNbins(); Int_t nbinsz = fZaxis.GetNbins(); Int_t ncells = nbinsx+2; if (GetDimension() > 1) ncells *= nbinsy+2; if (GetDimension() > 2) ncells *= nbinsz+2; SetBinsLength(ncells); Int_t errors = fSumw2.fN; if (errors) fSumw2.Set(ncells); axis->SetTimeDisplay(timedisp); //now loop on all bins and refill Double_t err,cu; Double_t oldEntries = fEntries; Int_t bin,ibin,binx,biny,binz; Int_t binxmin = 1; Int_t binxmax = nbinsx; if (fDimension > 1) {binxmin--; binxmax++;} for (binz=1;binz<=nbinsz;binz++) { for (biny=1;biny<=nbinsy;biny++) { for (binx=binxmin;binx<=binxmax;binx++) { bin = hold->GetBin(binx,biny,binz); ibin= GetBin(binx,biny,binz); if (binx > nbxold+1 || biny > nbyold || binz > nbzold) bin = -1; if (bin > 0) cu = hold->GetBinContent(bin); else cu = 0; SetBinContent(ibin,cu); if (errors) { if (bin > 0) err = hold->GetBinError(bin); else err = 0; SetBinError(ibin,err); } } } } fEntries = oldEntries; delete hold; } //______________________________________________________________________________ void TH1::LabelsOption(Option_t *option, Option_t *ax) { // Set option(s) to draw axis with labels // 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) Int_t iaxis = AxisChoice(ax); TAxis *axis = 0; if (iaxis == 1) axis = GetXaxis(); if (iaxis == 2) axis = GetYaxis(); if (iaxis == 3) axis = GetZaxis(); if (!axis) return; THashList *labels = axis->GetLabels(); if (!labels) { Warning("LabelsOption","Cannot sort. No labels"); return; } TString opt = option; opt.ToLower(); if (opt.Contains("h")) { axis->SetBit(TAxis::kLabelsHori); axis->ResetBit(TAxis::kLabelsVert); axis->ResetBit(TAxis::kLabelsDown); axis->ResetBit(TAxis::kLabelsUp); } if (opt.Contains("v")) { axis->SetBit(TAxis::kLabelsVert); axis->ResetBit(TAxis::kLabelsHori); axis->ResetBit(TAxis::kLabelsDown); axis->ResetBit(TAxis::kLabelsUp); } if (opt.Contains("u")) { axis->SetBit(TAxis::kLabelsUp); axis->ResetBit(TAxis::kLabelsVert); axis->ResetBit(TAxis::kLabelsDown); axis->ResetBit(TAxis::kLabelsHori); } if (opt.Contains("d")) { axis->SetBit(TAxis::kLabelsDown); axis->ResetBit(TAxis::kLabelsVert); axis->ResetBit(TAxis::kLabelsHori); axis->ResetBit(TAxis::kLabelsUp); } Int_t sort = -1; if (opt.Contains("a")) sort = 0; if (opt.Contains(">")) sort = 1; if (opt.Contains("<")) sort = 2; if (sort < 0) return; if (sort > 0 && GetDimension() > 2) { Error("LabelsOption","Sorting by value not implemented for 3-D histograms"); return; } Double_t entries = fEntries; Int_t n = TMath::Min(axis->GetNbins(), labels->GetSize()); Int_t *a = new Int_t[n+2]; Int_t i,j,k; Double_t *cont = 0; Double_t *errors = 0; THashList *labold = new THashList(labels->GetSize(),1); TIter nextold(labels); TObject *obj; while ((obj=nextold())) { labold->Add(obj); } labels->Clear(); if (sort > 0) { //---sort by values of bins if (GetDimension() == 1) { cont = new Double_t[n]; if (fSumw2.fN) errors = new Double_t[n]; for (i=1;i<=n;i++) { cont[i-1] = GetBinContent(i); if (errors) errors[i-1] = GetBinError(i); } if (sort ==1) TMath::Sort(n,cont,a,kTRUE); //sort by decreasing values else TMath::Sort(n,cont,a,kFALSE); //sort by increasing values for (i=1;i<=n;i++) { SetBinContent(i,cont[a[i-1]]); if (errors) SetBinError(i,errors[a[i-1]]); } for (i=1;i<=n;i++) { obj = labold->At(a[i-1]); labels->Add(obj); obj->SetUniqueID(i); } } else if (GetDimension()== 2) { Double_t *pcont = new Double_t[n+2]; for (i=0;i<=n;i++) pcont[i] = 0; Int_t nx = fXaxis.GetNbins(); Int_t ny = fYaxis.GetNbins(); cont = new Double_t[(nx+2)*(ny+2)]; if (fSumw2.fN) errors = new Double_t[n]; for (i=1;i<=nx;i++) { for (j=1;j<=ny;j++) { cont[i+nx*j] = GetBinContent(i,j); if (errors) errors[i+nx*j] = GetBinError(i,j); if (axis == GetXaxis()) k = i; else k = j; pcont[k-1] += cont[i+nx*j]; } } if (sort ==1) TMath::Sort(n,pcont,a,kTRUE); //sort by decreasing values else TMath::Sort(n,pcont,a,kFALSE); //sort by increasing values for (i=0;i<n;i++) { obj = labold->At(a[i]); labels->Add(obj); obj->SetUniqueID(i+1); } delete [] pcont; for (i=1;i<=nx;i++) { for (j=1;j<=ny;j++) { if (axis == GetXaxis()) { SetBinContent(i,j,cont[a[i-1]+1+nx*j]); if (errors) SetBinError(i,j,errors[a[i-1]+1+nx*j]); } else { SetBinContent(i,j,cont[i+nx*(a[j-1]+1)]); if (errors) SetBinError(i,j,errors[i+nx*(a[j-1]+1)]); } } } } else { //to be implemented } } else { //---alphabetic sort const UInt_t kUsed = 1<<18; TObject *objk=0; a[0] = 0; a[n+1] = n+1; for (i=1;i<=n;i++) { const char *label = "zzzzzzzzzzzz"; for (j=1;j<=n;j++) { obj = labold->At(j-1); if (!obj) continue; if (obj->TestBit(kUsed)) continue; //use strcasecmp for case non-sensitive sort (may be an option) if (strcmp(label,obj->GetName()) < 0) continue; objk = obj; a[i] = j; label = obj->GetName(); } if (objk) { objk->SetUniqueID(i); labels->Add(objk); objk->SetBit(kUsed); } } for (i=1;i<=n;i++) { obj = labels->At(i-1); if (!obj) continue; obj->ResetBit(kUsed); } if (GetDimension() == 1) { cont = new Double_t[n+2]; if (fSumw2.fN) errors = new Double_t[n+2]; for (i=1;i<=n;i++) { cont[i] = GetBinContent(a[i]); if (errors) errors[i] = GetBinError(a[i]); } for (i=1;i<=n;i++) { SetBinContent(i,cont[i]); if (errors) SetBinError(i,errors[i]); } } else if (GetDimension()== 2) { Int_t nx = fXaxis.GetNbins()+2; Int_t ny = fYaxis.GetNbins()+2; cont = new Double_t[nx*ny]; if (fSumw2.fN) errors = new Double_t[nx*ny]; for (i=0;i<nx;i++) { for (j=0;j<ny;j++) { cont[i+nx*j] = GetBinContent(i,j); if (errors) errors[i+nx*j] = GetBinError(i,j); } } for (i=0;i<nx;i++) { for (j=0;j<ny;j++) { if (axis == GetXaxis()) { SetBinContent(i,j,cont[a[i]+nx*j]); if (errors) SetBinError(i,j,errors[a[i]+nx*j]); } else { SetBinContent(i,j,cont[i+nx*a[j]]); if (errors) SetBinError(i,j,errors[i+nx*a[j]]); } } } } else { Int_t nx = fXaxis.GetNbins()+2; Int_t ny = fYaxis.GetNbins()+2; Int_t nz = fZaxis.GetNbins()+2; cont = new Double_t[nx*ny*nz]; if (fSumw2.fN) errors = new Double_t[nx*ny*nz]; for (i=0;i<nx;i++) { for (j=0;j<ny;j++) { for (k=0;k<nz;k++) { cont[i+nx*(j+ny*k)] = GetBinContent(i,j,k); if (errors) errors[i+nx*(j+ny*k)] = GetBinError(i,j,k); } } } for (i=0;i<nx;i++) { for (j=0;j<ny;j++) { for (k=0;k<nz;k++) { if (axis == GetXaxis()) { SetBinContent(i,j,k,cont[a[i]+nx*(j+ny*k)]); if (errors) SetBinError(i,j,k,errors[a[i]+nx*(j+ny*k)]); } else if (axis == GetYaxis()) { SetBinContent(i,j,k,cont[i+nx*(a[j]+ny*k)]); if (errors) SetBinError(i,j,k,errors[i+nx*(a[j]+ny*k)]); } else { SetBinContent(i,j,k,cont[i+nx*(j+ny*a[k])]); if (errors) SetBinError(i,j,k,errors[i+nx*(j+ny*a[k])]); } } } } } } fEntries = entries; delete labold; if (a) delete [] a; if (cont) delete [] cont; if (errors) delete [] errors; } //______________________________________________________________________________ static Bool_t AlmostEqual(Double_t a, Double_t b, Double_t epsilon = 0.00000001) { return TMath::Abs(a - b) < epsilon; } //______________________________________________________________________________ static Bool_t AlmostInteger(Double_t a, Double_t epsilon = 0.00000001) { return AlmostEqual(a - TMath::Floor(a), 0, epsilon) || AlmostEqual(a - TMath::Floor(a), 1, epsilon); } //______________________________________________________________________________ Bool_t TH1::SameLimitsAndNBins(const TAxis& axis1, const TAxis& axis2) { // Same limits and bins. if ((axis1.GetNbins() == axis2.GetNbins()) && (axis1.GetXmin() == axis2.GetXmin()) && (axis1.GetXmax() == axis2.GetXmax())) return kTRUE; else return kFALSE; } //______________________________________________________________________________ Bool_t TH1::RecomputeAxisLimits(TAxis& destAxis, const TAxis& anAxis) { // Finds new limits for the axis for the Merge function. // returns false if the limits are incompatible if (SameLimitsAndNBins(destAxis, anAxis)) return kTRUE; if (destAxis.GetXbins()->fN || anAxis.GetXbins()->fN) return kFALSE; // user binning not supported Double_t width1 = destAxis.GetBinWidth(0); Double_t width2 = anAxis.GetBinWidth(0); if (width1 == 0 || width2 == 0) return kFALSE; // no binning not supported Double_t xmin = TMath::Min(destAxis.GetXmin(), anAxis.GetXmin()); Double_t xmax = TMath::Max(destAxis.GetXmax(), anAxis.GetXmax()); Double_t width = TMath::Max(width1, width2); // check the bin size if (!AlmostInteger(width/width1) || !AlmostInteger(width/width2)) return kFALSE; // check the limits Double_t delta; delta = (destAxis.GetXmin() - xmin)/width1; if (!AlmostInteger(delta)) xmin -= (TMath::Ceil(delta) - delta)*width1; delta = (anAxis.GetXmin() - xmin)/width2; if (!AlmostInteger(delta)) xmin -= (TMath::Ceil(delta) - delta)*width2; delta = (destAxis.GetXmin() - xmin)/width1; if (!AlmostInteger(delta)) return kFALSE; delta = (xmax - destAxis.GetXmax())/width1; if (!AlmostInteger(delta)) xmax += (TMath::Ceil(delta) - delta)*width1; delta = (xmax - anAxis.GetXmax())/width2; if (!AlmostInteger(delta)) xmax += (TMath::Ceil(delta) - delta)*width2; delta = (xmax - destAxis.GetXmax())/width1; if (!AlmostInteger(delta)) return kFALSE; #ifdef DEBUG if (!AlmostInteger((xmax - xmin) / width)) { // unnecessary check printf("TH1::RecomputeAxisLimits - Impossible\n"); return kFALSE; } #endif destAxis.Set(TMath::Nint((xmax - xmin)/width), xmin, xmax); return kTRUE; } //______________________________________________________________________________ Long64_t TH1::Merge(TCollection *li) { // Add all histograms in the collection to this histogram. // This function computes the min/max for the x axis, // compute a new number of bins, if necessary, // add bin contents, errors and statistics. // If all histograms have bin labels, bins with identical labels // will be merged, no matter what their order is. // 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 axis x 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. // Example: // void atest() { // TH1F *h1 = new TH1F("h1","h1",110,-110,0); // TH1F *h2 = new TH1F("h2","h2",220,0,110); // TH1F *h3 = new TH1F("h3","h3",330,-55,55); // TRandom r; // for (Int_t i=0;i<10000;i++) { // h1->Fill(r.Gaus(-55,10)); // h2->Fill(r.Gaus(55,10)); // h3->Fill(r.Gaus(0,10)); // } // // TList *list = new TList; // list->Add(h1); // list->Add(h2); // list->Add(h3); // TH1F *h = (TH1F*)h1->Clone("h"); // h->Reset(); // h.Merge(list); // h->Draw(); // } if (!li) return 0; if (li->IsEmpty()) return (Int_t) GetEntries(); // We don't want to add the clone to gDirectory, // so remove our kMustCleanup bit temporarily Bool_t mustCleanup = TestBit(kMustCleanup); if (mustCleanup) ResetBit(kMustCleanup); TList inlist; TH1* hclone = (TH1*)Clone("FirstClone"); if (mustCleanup) SetBit(kMustCleanup); R__ASSERT(hclone); BufferEmpty(1); // To remove buffer. Reset(); // BufferEmpty sets limits so we can't use it later. SetEntries(0); inlist.Add(hclone); inlist.AddAll(li); THashList allLabels; THashList* labels=GetXaxis()->GetLabels(); Bool_t haveOneLabel=kFALSE; if (labels) { TIter iL(labels); TObjString* lb; while ((lb=(TObjString*)iL())) { haveOneLabel |= (lb && lb->String().Length()); if (!allLabels.FindObject(lb)) allLabels.Add(lb); } } TAxis newXAxis; Bool_t initialLimitsFound = kFALSE; Bool_t allHaveLabels = haveOneLabel; Bool_t same = kTRUE; Bool_t allHaveLimits = kTRUE; TIter next(&inlist); while (TObject *o = next()) { TH1* h = dynamic_cast<TH1*> (o); if (!h) { Error("Add","Attempt to add object of class: %s to a %s", o->ClassName(),this->ClassName()); return -1; } Bool_t hasLimits = h->GetXaxis()->GetXmin() < h->GetXaxis()->GetXmax(); allHaveLimits = allHaveLimits && hasLimits; if (hasLimits) { h->BufferEmpty(); if (!initialLimitsFound) { initialLimitsFound = kTRUE; newXAxis.Set(h->GetXaxis()->GetNbins(), h->GetXaxis()->GetXmin(), h->GetXaxis()->GetXmax()); } else { if (!RecomputeAxisLimits(newXAxis, *(h->GetXaxis()))) { Error("Merge", "Cannot merge histograms - limits are inconsistent:\n " "first: (%d, %f, %f), second: (%d, %f, %f)", newXAxis.GetNbins(), newXAxis.GetXmin(), newXAxis.GetXmax(), h->GetXaxis()->GetNbins(), h->GetXaxis()->GetXmin(), h->GetXaxis()->GetXmax()); } } } if (allHaveLabels) { THashList* hlabels=h->GetXaxis()->GetLabels(); Bool_t hasOneLabel=kFALSE; if (hlabels) { TIter iL(hlabels); TObjString* lb; while ((lb=(TObjString*)iL())) { hasOneLabel |= (lb && lb->String().Length()); if (!allLabels.FindObject(lb)) { allLabels.Add(lb); same = kFALSE; } } } allHaveLabels&=(labels && hasOneLabel); if (!allHaveLabels) Warning("Merge","Not all histograms have labels. I will ignore labels," " falling back to bin numbering mode."); } } next.Reset(); same = same && SameLimitsAndNBins(newXAxis, *GetXaxis()); if (!same && initialLimitsFound) SetBins(newXAxis.GetNbins(), newXAxis.GetXmin(), newXAxis.GetXmax()); if (!allHaveLimits) { // fill this histogram with all the data from buffers of histograms without limits while (TH1* h = (TH1*)next()) { if (h->GetXaxis()->GetXmin() >= h->GetXaxis()->GetXmax() && h->fBuffer) { // no limits Int_t nbentries = (Int_t)h->fBuffer[0]; for (Int_t i = 0; i < nbentries; i++) Fill(h->fBuffer[2*i + 2], h->fBuffer[2*i + 1]); // Entries from buffers have to be filled one by one // because FillN doesn't resize histograms. } } if (!initialLimitsFound) return (Int_t) GetEntries(); // all histograms have been processed next.Reset(); } //merge bin contents and errors Double_t stats[kNstat], totstats[kNstat]; for (Int_t i=0;i<kNstat;i++) {totstats[i] = stats[i] = 0;} GetStats(totstats); Double_t nentries = GetEntries(); Int_t binx, ix, nx; Double_t cu; Bool_t canRebin=TestBit(kCanRebin); if (!allHaveLabels) ResetBit(kCanRebin); // reset, otherwise setting the under/overflow will rebin while (TH1* h=(TH1*)next()) { // process only if the histogram has limits; otherwise it was processed before if (h->GetXaxis()->GetXmin() < h->GetXaxis()->GetXmax()) { // import statistics h->GetStats(stats); for (Int_t i=0;i<kNstat;i++) totstats[i] += stats[i]; nentries += h->GetEntries(); nx = h->GetXaxis()->GetNbins(); for (binx = 0; binx <= nx + 1; binx++) { cu = h->GetBinContent(binx); if (!allHaveLabels || !binx || binx==nx+1) { if ((!same) && (binx == 0 || binx == nx + 1)) { if (cu != 0) { Error("Merge", "Cannot merge histograms - the histograms have" " different limits and undeflows/overflows are present." " The initial histogram is now broken!"); return -1; } } ix = fXaxis.FindBin(h->GetXaxis()->GetBinCenter(binx)); } else { const char* label=h->GetXaxis()->GetBinLabel(binx); if (!label || label[0]==0) { ix = fXaxis.FindBin(h->GetXaxis()->GetBinCenter(binx)); } else { ix = fXaxis.FindBin(label); if (ix==-1) ix = fXaxis.FindBin(h->GetXaxis()->GetBinCenter(binx)); } } if (ix >= 0) { AddBinContent(ix,cu); if (fSumw2.fN) { Double_t error1 = h->GetBinError(binx); fSumw2.fArray[ix] += error1*error1; } } } } } if (canRebin) SetBit(kCanRebin); //copy merged stats PutStats(totstats); SetEntries(nentries); inlist.Remove(hclone); delete hclone; return (Long64_t)nentries; } //______________________________________________________________________________ void TH1::Multiply(TF1 *f1, Double_t c1) { // Performs the operation: this = this*c1*f1 // if errors are defined (see TH1::Sumw2), errors are also recalculated. // // Only bins inside the function range are recomputed. // IMPORTANT NOTE: If you intend to use the errors of this histogram later // you should call Sumw2 before making this operation. // This is particularly important if you fit the histogram after TH1::Multiply if (!f1) { Error("Add","Attempt to multiply by a non-existing function"); return; } Int_t nbinsx = GetNbinsX(); Int_t nbinsy = GetNbinsY(); Int_t nbinsz = GetNbinsZ(); if (fDimension < 2) nbinsy = -1; if (fDimension < 3) nbinsz = -1; // reset min-maximum SetMinimum(); SetMaximum(); // Reset the kCanRebin option. Otherwise SetBinContent on the overflow bin // would resize the axis limits! ResetBit(kCanRebin); // - Loop on bins (including underflows/overflows) Int_t bin, binx, biny, binz; Double_t cu,w; Double_t xx[3]; Double_t *params = 0; f1->InitArgs(xx,params); for (binz=0;binz<=nbinsz+1;binz++) { xx[2] = fZaxis.GetBinCenter(binz); for (biny=0;biny<=nbinsy+1;biny++) { xx[1] = fYaxis.GetBinCenter(biny); for (binx=0;binx<=nbinsx+1;binx++) { xx[0] = fXaxis.GetBinCenter(binx); if (!f1->IsInside(xx)) continue; TF1::RejectPoint(kFALSE); bin = binx +(nbinsx+2)*(biny + (nbinsy+2)*binz); Double_t error1 = GetBinError(bin); cu = c1*f1->EvalPar(xx); if (TF1::RejectedPoint()) continue; w = GetBinContent(bin)*cu; SetBinContent(bin,w); if (fSumw2.fN) { fSumw2.fArray[bin] = cu*cu*error1*error1; } } } } ResetStats(); SetEntries( GetEffectiveEntries() ); } //______________________________________________________________________________ void TH1::Multiply(const TH1 *h1) { // -*-*-*-*-*-*-*-*-*Multiply this histogram by h1*-*-*-*-*-*-*-*-*-*-*-*-* // ============================= // // this = this*h1 // // If errors of this are available (TH1::Sumw2), errors are recalculated. // Note that if h1 has Sumw2 set, Sumw2 is automatically called for this // if not already set. // // IMPORTANT NOTE: If you intend to use the errors of this histogram later // you should call Sumw2 before making this operation. // This is particularly important if you fit the histogram after TH1::Multiply if (!h1) { Error("Multiply","Attempt to multiply by a non-existing histogram"); return; } Int_t nbinsx = GetNbinsX(); Int_t nbinsy = GetNbinsY(); Int_t nbinsz = GetNbinsZ(); // - Check histogram compatibility if (nbinsx != h1->GetNbinsX() || nbinsy != h1->GetNbinsY() || nbinsz != h1->GetNbinsZ()) { Error("Multiply","Attempt to multiply histograms with different number of bins"); return; } // - Issue a Warning if histogram limits are different if (fXaxis.GetXmin() != h1->fXaxis.GetXmin() || fXaxis.GetXmax() != h1->fXaxis.GetXmax() || fYaxis.GetXmin() != h1->fYaxis.GetXmin() || fYaxis.GetXmax() != h1->fYaxis.GetXmax() || fZaxis.GetXmin() != h1->fZaxis.GetXmin() || fZaxis.GetXmax() != h1->fZaxis.GetXmax()) { Warning("Multiply","Attempt to multiply histograms with different axis limits"); } if (fDimension < 2) nbinsy = -1; if (fDimension < 3) nbinsz = -1; if (fDimension < 3) nbinsz = -1; // Create Sumw2 if h1 has Sumw2 set if (fSumw2.fN == 0 && h1->GetSumw2N() != 0) Sumw2(); // - Reset min- maximum SetMinimum(); SetMaximum(); // Reset the kCanRebin option. Otherwise SetBinContent on the overflow bin // would resize the axis limits! ResetBit(kCanRebin); // - Loop on bins (including underflows/overflows) Int_t bin, binx, biny, binz; Double_t c0,c1,w; for (binz=0;binz<=nbinsz+1;binz++) { for (biny=0;biny<=nbinsy+1;biny++) { for (binx=0;binx<=nbinsx+1;binx++) { bin = GetBin(binx,biny,binz); c0 = GetBinContent(bin); c1 = h1->GetBinContent(bin); w = c0*c1; SetBinContent(bin,w); if (fSumw2.fN) { Double_t e0 = GetBinError(bin); Double_t e1 = h1->GetBinError(bin); fSumw2.fArray[bin] = (e0*e0*c1*c1 + e1*e1*c0*c0); } } } } ResetStats(); SetEntries( GetEffectiveEntries() ); } //______________________________________________________________________________ void TH1::Multiply(const TH1 *h1, const TH1 *h2, Double_t c1, Double_t c2, Option_t *option) { // -*-*-*Replace contents of this histogram by multiplication of h1 by h2*-* // ================================================================ // // this = (c1*h1)*(c2*h2) // // If errors of this are available (TH1::Sumw2), errors are recalculated. // Note that if h1 or h2 have Sumw2 set, Sumw2 is automatically called for this // if not already set. // // IMPORTANT NOTE: If you intend to use the errors of this histogram later // you should call Sumw2 before making this operation. // This is particularly important if you fit the histogram after TH1::Multiply TString opt = option; opt.ToLower(); // Bool_t binomial = kFALSE; // if (opt.Contains("b")) binomial = kTRUE; if (!h1 || !h2) { Error("Multiply","Attempt to multiply by a non-existing histogram"); return; } Int_t nbinsx = GetNbinsX(); Int_t nbinsy = GetNbinsY(); Int_t nbinsz = GetNbinsZ(); // - Check histogram compatibility if (nbinsx != h1->GetNbinsX() || nbinsy != h1->GetNbinsY() || nbinsz != h1->GetNbinsZ() || nbinsx != h2->GetNbinsX() || nbinsy != h2->GetNbinsY() || nbinsz != h2->GetNbinsZ()) { Error("Multiply","Attempt to multiply histograms with different number of bins"); return; } // - Issue a Warning if histogram limits are different if (fXaxis.GetXmin() != h1->fXaxis.GetXmin() || fXaxis.GetXmax() != h1->fXaxis.GetXmax() || fYaxis.GetXmin() != h1->fYaxis.GetXmin() || fYaxis.GetXmax() != h1->fYaxis.GetXmax() || fZaxis.GetXmin() != h1->fZaxis.GetXmin() || fZaxis.GetXmax() != h1->fZaxis.GetXmax()) { Warning("Multiply","Attempt to multiply histograms with different axis limits"); } if (fXaxis.GetXmin() != h2->fXaxis.GetXmin() || fXaxis.GetXmax() != h2->fXaxis.GetXmax() || fYaxis.GetXmin() != h2->fYaxis.GetXmin() || fYaxis.GetXmax() != h2->fYaxis.GetXmax() || fZaxis.GetXmin() != h2->fZaxis.GetXmin() || fZaxis.GetXmax() != h2->fZaxis.GetXmax()) { Warning("Multiply","Attempt to multiply histograms with different axis limits"); } if (fDimension < 2) nbinsy = -1; if (fDimension < 3) nbinsz = -1; // Create Sumw2 if h1 or h2 have Sumw2 set if (fSumw2.fN == 0 && (h1->GetSumw2N() != 0 || h2->GetSumw2N() != 0)) Sumw2(); // - Reset min - maximum SetMinimum(); SetMaximum(); // Reset the kCanRebin option. Otherwise SetBinContent on the overflow bin // would resize the axis limits! ResetBit(kCanRebin); // - Loop on bins (including underflows/overflows) Int_t bin, binx, biny, binz; Double_t b1,b2,w,d1,d2; d1 = c1*c1; d2 = c2*c2; for (binz=0;binz<=nbinsz+1;binz++) { for (biny=0;biny<=nbinsy+1;biny++) { for (binx=0;binx<=nbinsx+1;binx++) { bin = binx +(nbinsx+2)*(biny + (nbinsy+2)*binz); b1 = h1->GetBinContent(bin); b2 = h2->GetBinContent(bin); w = (c1*b1)*(c2*b2); SetBinContent(bin,w); if (fSumw2.fN) { Double_t e1 = h1->GetBinError(bin); Double_t e2 = h2->GetBinError(bin); fSumw2.fArray[bin] = d1*d2*(e1*e1*b2*b2 + e2*e2*b1*b1); } } } } ResetStats(); SetEntries( GetEffectiveEntries() ); } //______________________________________________________________________________ void TH1::Paint(Option_t *option) { // -*-*-*-*-*-*-*Control routine to paint any kind of histograms*-*-*-*-*-*-* // =============================================== // // This function is automatically called by TCanvas::Update. // (see TH1::Draw for the list of options) GetPainter(option); if (fPainter) { if (strlen(option) > 0) fPainter->Paint(option); else fPainter->Paint(fOption.Data()); } } //______________________________________________________________________________ TH1 *TH1::Rebin(Int_t ngroup, const char*newname, const Double_t *xbins) { // Rebin this histogram // // -case 1 xbins=0 // if newname is not blank a new temporary histogram hnew is created. // else the current histogram is modified (default) // The parameter ngroup indicates how many bins of this have to me merged // into one bin of hnew // If the original histogram has errors stored (via Sumw2), the resulting // histograms has new errors correctly calculated. // // examples: if h1 is an existing TH1F histogram with 100 bins // h1->Rebin(); //merges two bins in one in h1: previous contents of h1 are lost // h1->Rebin(5); //merges five bins in one in h1 // TH1F *hnew = h1->Rebin(5,"hnew"); // creates a new histogram hnew // //merging 5 bins of h1 in one bin // // NOTE: If ngroup is not an exact divider of the number of bins, // the top limit of the rebinned histogram is changed // to the upper edge of the bin=newbins*ngroup and the corresponding // bins are added to the overflow bin. // Statistics will be recomputed from the new bin contents. // // -case 2 xbins!=0 // a new histogram is created (you should specify newname). // The parameter is the number of variable size bins in the created histogram. // The array xbins must contain ngroup+1 elements that represent the low-edge // of the bins. // If the original histogram has errors stored (via Sumw2), the resulting // histograms has new errors correctly calculated. // // examples: if h1 is an existing TH1F histogram with 100 bins // Double_t xbins[25] = {...} array of low-edges (xbins[25] is the upper edge of last bin // h1->Rebin(24,"hnew",xbins); //creates a new variable bin size histogram hnew Int_t nbins = fXaxis.GetNbins(); Double_t xmin = fXaxis.GetXmin(); Double_t xmax = fXaxis.GetXmax(); if ((ngroup <= 0) || (ngroup > nbins)) { Error("Rebin", "Illegal value of ngroup=%d",ngroup); return 0; } if (fDimension > 1 || InheritsFrom("TProfile")) { Error("Rebin", "Operation valid on 1-D histograms only"); return 0; } if (!newname && xbins) { Error("Rebin","if xbins is specified, newname must be given"); return 0; } Int_t newbins = nbins/ngroup; if (!xbins) { Int_t nbg = nbins/ngroup; if (nbg*ngroup != nbins) { Warning("Rebin", "ngroup=%d must be an exact divider of nbins=%d",ngroup,nbins); } } else { // in the case of xbins given (rebinning in variable bins) ngroup is the news number of bins. // and number of grouped bins is not constant. // when looping for setting the contents for the new histogram we // need to loop on all bins of original histogram. Set then ngroup=nbins newbins = ngroup; ngroup = nbins; } // Save old bin contents into a new array Double_t entries = fEntries; Double_t *oldBins = new Double_t[nbins+2]; Int_t bin, i; for (bin=0;bin<nbins+2;bin++) oldBins[bin] = GetBinContent(bin); Double_t *oldErrors = 0; if (fSumw2.fN != 0) { oldErrors = new Double_t[nbins+2]; for (bin=0;bin<nbins+2;bin++) oldErrors[bin] = GetBinError(bin); } // create a clone of the old histogram if newname is specified TH1 *hnew = this; if ((newname && strlen(newname) > 0) || xbins) { hnew = (TH1*)Clone(newname); } // save original statistics Double_t stat[kNstat]; GetStats(stat); bool resetStat = false; // change axis specs and rebuild bin contents array::RebinAx if(!xbins && (newbins*ngroup != nbins)) { xmax = fXaxis.GetBinUpEdge(newbins*ngroup); resetStat = true; //stats must be reset because top bins will be moved to overflow bin } // save the TAttAxis members (reset by SetBins) Int_t nDivisions = fXaxis.GetNdivisions(); Color_t axisColor = fXaxis.GetAxisColor(); Color_t labelColor = fXaxis.GetLabelColor(); Style_t labelFont = fXaxis.GetLabelFont(); Float_t labelOffset = fXaxis.GetLabelOffset(); Float_t labelSize = fXaxis.GetLabelSize(); Float_t tickLength = fXaxis.GetTickLength(); Float_t titleOffset = fXaxis.GetTitleOffset(); Float_t titleSize = fXaxis.GetTitleSize(); Color_t titleColor = fXaxis.GetTitleColor(); Style_t titleFont = fXaxis.GetTitleFont(); if(!xbins && (fXaxis.GetXbins()->GetSize() > 0)){ // variable bin sizes Double_t *bins = new Double_t[newbins+1]; for(i = 0; i <= newbins; ++i) bins[i] = fXaxis.GetBinLowEdge(1+i*ngroup); hnew->SetBins(newbins,bins); //this also changes errors array (if any) delete [] bins; } else if (xbins) { hnew->SetBins(newbins,xbins); } else { hnew->SetBins(newbins,xmin,xmax); } // Restore axis attributes fXaxis.SetNdivisions(nDivisions); fXaxis.SetAxisColor(axisColor); fXaxis.SetLabelColor(labelColor); fXaxis.SetLabelFont(labelFont); fXaxis.SetLabelOffset(labelOffset); fXaxis.SetLabelSize(labelSize); fXaxis.SetTickLength(tickLength); fXaxis.SetTitleOffset(titleOffset); fXaxis.SetTitleSize(titleSize); fXaxis.SetTitleColor(titleColor); fXaxis.SetTitleFont(titleFont); // copy merged bin contents (ignore under/overflows) // Start merging only once the new lowest edge is reached Int_t startbin = 1; const Double_t newxmin = hnew->GetXaxis()->GetBinLowEdge(1); while( fXaxis.GetBinCenter(startbin) < newxmin && startbin <= nbins ) { startbin++; } Int_t oldbin = startbin; Double_t binContent, binError; for (bin = 1;bin<=newbins;bin++) { binContent = 0; binError = 0; Int_t imax = ngroup; Double_t xbinmax = hnew->GetXaxis()->GetBinUpEdge(bin); for (i=0;i<ngroup;i++) { if( (hnew == this && (oldbin+i > nbins)) || ( hnew != this && (fXaxis.GetBinCenter(oldbin+i) > xbinmax)) ) { imax = i; break; } binContent += oldBins[oldbin+i]; if (oldErrors) binError += oldErrors[oldbin+i]*oldErrors[oldbin+i]; } hnew->SetBinContent(bin,binContent); if (oldErrors) hnew->SetBinError(bin,TMath::Sqrt(binError)); oldbin += imax; } // sum underfllow and overflow contents until startbin binContent = 0; binError = 0; for (i = 0; i < startbin; ++i) { binContent += oldBins[i]; if (oldErrors) binError += oldErrors[i]*oldErrors[i]; } hnew->SetBinContent(0,binContent); if (oldErrors) hnew->SetBinError(0,TMath::Sqrt(binError)); // sum overflow binContent = 0; binError = 0; for (i = oldbin; i <= nbins+1; ++i) { binContent += oldBins[i]; if (oldErrors) binError += oldErrors[i]*oldErrors[i]; } hnew->SetBinContent(newbins+1,binContent); if (oldErrors) hnew->SetBinError(newbins+1,TMath::Sqrt(binError)); //restore statistics and entries modified by SetBinContent hnew->SetEntries(entries); if (!resetStat) hnew->PutStats(stat); delete [] oldBins; if (oldErrors) delete [] oldErrors; return hnew; } //______________________________________________________________________________ Bool_t TH1::FindNewAxisLimits(const TAxis* axis, const Double_t point, Double_t& newMin, Double_t &newMax) { // finds new limits for the axis so that *point* is within the range and // the limits are compatible with the previous ones (see TH1::Merge). // new limits are put into *newMin* and *newMax* variables. // axis - axis whose limits are to be recomputed // point - point that should fit within the new axis limits // newMin - new minimum will be stored here // newMax - new maximum will be stored here. // false if failed (e.g. if the initial axis limits are wrong // or the new range is more than 2^64 times the old one). Double_t xmin = axis->GetXmin(); Double_t xmax = axis->GetXmax(); if (xmin >= xmax) return kFALSE; Double_t range = xmax-xmin; Double_t binsize = range / axis->GetNbins(); //recompute new axis limits by doubling the current range Int_t ntimes = 0; while (point < xmin) { if (ntimes++ > 64) return kFALSE; xmin = xmin - range; range *= 2; binsize *= 2; // make sure that the merging will be correct if ( xmin / binsize - TMath::Floor(xmin / binsize) >= 0.5) { xmin += 0.5 * binsize; xmax += 0.5 * binsize; // won't work with a histogram with only one bin, but I don't care } } while (point >= xmax) { if (ntimes++ > 64) return kFALSE; xmax = xmax + range; range *= 2; binsize *= 2; // make sure that the merging will be correct if ( xmin / binsize - TMath::Floor(xmin / binsize) >= 0.5) { xmin -= 0.5 * binsize; xmax -= 0.5 * binsize; // won't work with a histogram with only one bin, but I don't care } } newMin = xmin; newMax = xmax; // Info("FindNewAxisLimits", "OldAxis: (%lf, %lf), new: (%lf, %lf), point: %lf", // axis->GetXmin(), axis->GetXmax(), xmin, xmax, point); return kTRUE; } //______________________________________________________________________________ void TH1::RebinAxis(Double_t x, TAxis *axis) { // 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 algorithm works for 1-d, 2-D and 3-D histograms. // The bit kCanRebin must be set before invoking this function. // Ex: h->SetBit(TH1::kCanRebin); if (!TestBit(kCanRebin)) return; if (TMath::IsNaN(x)) { // x may be a NaN ResetBit(kCanRebin); return; } if (axis->GetXmin() >= axis->GetXmax()) return; if (axis->GetNbins() <= 0) return; Double_t xmin, xmax; if (!FindNewAxisLimits(axis, x, xmin, xmax)) return; //save a copy of this histogram TH1 *hold = (TH1*)Clone(); hold->SetDirectory(0); //set new axis limits axis->SetLimits(xmin,xmax); Int_t nbinsx = fXaxis.GetNbins(); Int_t nbinsy = fYaxis.GetNbins(); Int_t nbinsz = fZaxis.GetNbins(); //now loop on all bins and refill Double_t err,cu; Double_t bx,by,bz; Int_t errors = GetSumw2N(); Int_t ix,iy,iz,ibin,binx,biny,binz,bin; Reset("ICE"); //reset only Integral, contents and Errors for (binz=1;binz<=nbinsz;binz++) { bz = hold->GetZaxis()->GetBinCenter(binz); iz = fZaxis.FindFixBin(bz); for (biny=1;biny<=nbinsy;biny++) { by = hold->GetYaxis()->GetBinCenter(biny); iy = fYaxis.FindFixBin(by); for (binx=1;binx<=nbinsx;binx++) { bx = hold->GetXaxis()->GetBinCenter(binx); ix = fXaxis.FindFixBin(bx); bin = hold->GetBin(binx,biny,binz); ibin= GetBin(ix,iy,iz); cu = hold->GetBinContent(bin); AddBinContent(ibin,cu); if (errors) { err = hold->GetBinError(bin); fSumw2.fArray[ibin] += err*err; } } } } delete hold; } //______________________________________________________________________________ void TH1::RecursiveRemove(TObject *obj) { // Recursively remove object from the list of functions if (fFunctions) { if (!fFunctions->TestBit(kInvalidObject)) fFunctions->RecursiveRemove(obj); } } //______________________________________________________________________________ void TH1::Scale(Double_t c1, Option_t *option) { // -*-*-*Multiply this histogram by a constant c1*-*-*-*-*-*-*-*-* // ======================================== // // this = c1*this // // Note that both contents and errors(if any) are scaled. // This function uses the services of TH1::Add // // IMPORTANT NOTE: If you intend to use the errors of this histogram later // you should call Sumw2 before making this operation. // This is particularly important if you fit the histogram after TH1::Scale // // 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. // // If option contains "width" the bin contents and errors are divided // by the bin width. TString opt = option; opt.ToLower(); Double_t ent = fEntries; if (opt.Contains("width")) Add(this,this,c1,-1); else Add(this,this,c1,0); fEntries = ent; //if contours set, must also scale contours Int_t ncontours = GetContour(); if (ncontours == 0) return; Double_t *levels = fContour.GetArray(); for (Int_t i=0;i<ncontours;i++) { levels[i] *= c1; } } //______________________________________________________________________________ void TH1::SetDefaultBufferSize(Int_t buffersize) { // static function to set the default buffer size for automatic histograms. // When an histogram is created with one of its axis lower limit greater // or equal to its upper limit, the function SetBuffer is automatically // called with the default buffer size. if (buffersize < 0) buffersize = 0; fgBufferSize = buffersize; } //______________________________________________________________________________ void TH1::SetDefaultSumw2(Bool_t sumw2) { // static function. // When this static function is called with sumw2=kTRUE, all new // histograms will automatically activate the storage // of the sum of squares of errors, ie TH1::Sumw2 is automatically called. fgDefaultSumw2 = sumw2; } //______________________________________________________________________________ void TH1::SetTitle(const char *title) { // Change (i.e. set) the title // // if title is in the form "stringt;stringx;stringy;stringz" // the histogram title is set to stringt, the x axis title to stringx, // the y axis title to stringy, and the z axis title to stringz. // To insert the character ";" in one of the titles, one should use "#;" // or "#semicolon". fTitle = title; fTitle.ReplaceAll("#;",2,"#semicolon",10); // Decode fTitle. It may contain X, Y and Z titles TString str1 = fTitle, str2; Int_t isc = str1.Index(";"); Int_t lns = str1.Length(); if (isc >=0 ) { fTitle = str1(0,isc); str1 = str1(isc+1, lns); isc = str1.Index(";"); if (isc >=0 ) { str2 = str1(0,isc); str2.ReplaceAll("#semicolon",10,";",1); fXaxis.SetTitle(str2.Data()); lns = str1.Length(); str1 = str1(isc+1, lns); isc = str1.Index(";"); if (isc >=0 ) { str2 = str1(0,isc); str2.ReplaceAll("#semicolon",10,";",1); fYaxis.SetTitle(str2.Data()); lns = str1.Length(); str1 = str1(isc+1, lns); str1.ReplaceAll("#semicolon",10,";",1); fZaxis.SetTitle(str1.Data()); } else { str1.ReplaceAll("#semicolon",10,";",1); fYaxis.SetTitle(str1.Data()); } } else { str1.ReplaceAll("#semicolon",10,";",1); fXaxis.SetTitle(str1.Data()); } } fTitle.ReplaceAll("#semicolon",10,";",1); if (gPad && TestBit(kMustCleanup)) gPad->Modified(); } // ------------------------------------------------------------------------- void TH1::SmoothArray(Int_t nn, Double_t *xx, Int_t ntimes) { // smooth array xx, translation of Hbook routine hsmoof.F // based on algorithm 353QH twice presented by J. Friedman // in Proc.of the 1974 CERN School of Computing, Norway, 11-24 August, 1974. Int_t ii, jj, ik, jk, kk, nn2; Double_t hh[6] = {0,0,0,0,0,0}; Double_t *yy = new Double_t[nn]; Double_t *zz = new Double_t[nn]; Double_t *rr = new Double_t[nn]; for (Int_t pass=0;pass<ntimes;pass++) { // first copy original data into temp array for (ii = 0; ii < nn; ii++) { yy[ii] = xx[ii]; } // do 353 i.e. running median 3, 5, and 3 in a single loop for (kk = 1; kk <= 3; kk++) { ik = 0; if (kk == 2) ik = 1; nn2 = nn - ik - 1; // do all elements beside the first and last point for median 3 // and first two and last 2 for median 5 for (ii = ik + 1; ii < nn2; ii++) { for (jj = 0; jj < 3; jj++) { hh[jj] = yy[ii + jj - 1]; } zz[ii] = TMath::Median(3 + 2*ik, hh); } if (kk == 1) { // first median 3 // first point hh[0] = 3*yy[1] - 2*yy[2]; hh[1] = yy[0]; hh[2] = yy[1]; zz[0] = TMath::Median(3, hh); // last point hh[0] = yy[nn - 2]; hh[1] = yy[nn - 1]; hh[2] = 3*yy[nn - 2] - 2*yy[nn - 3]; zz[nn - 1] = TMath::Median(3, hh); } if (kk == 2) { // median 5 // first point remains the same zz[0] = yy[0]; for (ii = 0; ii < 3; ii++) { hh[ii] = yy[ii]; } zz[1] = TMath::Median(3, hh); // last two points for (ii = 0; ii < 3; ii++) { hh[ii] = yy[nn - 3 + ii]; } zz[nn - 2] = TMath::Median(3, hh); zz[nn - 1] = yy[nn - 1]; } } // quadratic interpolation for flat segments for (ii = 2; ii < (nn - 2); ii++) { if (zz[ii - 1] != zz[ii]) continue; if (zz[ii] != zz[ii + 1]) continue; hh[0] = zz[ii - 2] - zz[ii]; hh[1] = zz[ii + 2] - zz[ii]; if (hh[0] * hh[1] < 0) continue; jk = 1; if ( TMath::Abs(hh[1]) > TMath::Abs(hh[0]) ) jk = -1; yy[ii] = -0.5*zz[ii - 2*jk] + zz[ii]/0.75 + zz[ii + 2*jk] /6.; yy[ii + jk] = 0.5*(zz[ii + 2*jk] - zz[ii - 2*jk]) + zz[ii]; } // running means for (ii = 1; ii < nn - 1; ii++) { rr[ii] = 0.25*yy[ii - 1] + 0.5*yy[ii] + 0.25*yy[ii + 1]; } rr[0] = yy[0]; rr[nn - 1] = yy[nn - 1]; // now do the same for residuals for (ii = 0; ii < nn; ii++) { yy[ii] = xx[ii] - rr[ii]; } // do 353 i.e. running median 3, 5, and 3 in a single loop for (kk = 1; kk <= 3; kk++) { ik = 0; if (kk == 2) ik = 1; nn2 = nn - ik - 1; // do all elements beside the first and last point for median 3 // and first two and last 2 for median 5 for (ii = ik + 1; ii < nn2; ii++) { for (jj = 0; jj < 3; jj++) { hh[jj] = yy[ii + jj - 1]; } zz[ii] = TMath::Median(3 + 2*ik, hh); } if (kk == 1) { // first median 3 // first point hh[0] = 3*yy[1] - 2*yy[2]; hh[1] = yy[0]; hh[2] = yy[1]; zz[0] = TMath::Median(3, hh); // last point hh[0] = yy[nn - 2]; hh[1] = yy[nn - 1]; hh[2] = 3*yy[nn - 2] - 2*yy[nn - 3]; zz[nn - 1] = TMath::Median(3, hh); } if (kk == 2) { // median 5 // first point remains the same zz[0] = yy[0]; for (ii = 0; ii < 3; ii++) { hh[ii] = yy[ii]; } zz[1] = TMath::Median(3, hh); // last two points for (ii = 0; ii < 3; ii++) { hh[ii] = yy[nn - 3 + ii]; } zz[nn - 2] = TMath::Median(3, hh); zz[nn - 1] = yy[nn - 1]; } } // quadratic interpolation for flat segments for (ii = 2; ii < (nn - 2); ii++) { if (zz[ii - 1] != zz[ii]) continue; if (zz[ii] != zz[ii + 1]) continue; hh[0] = zz[ii - 2] - zz[ii]; hh[1] = zz[ii + 2] - zz[ii]; if (hh[0] * hh[1] < 0) continue; jk = 1; if ( TMath::Abs(hh[1]) > TMath::Abs(hh[0]) ) jk = -1; yy[ii] = -0.5*zz[ii - 2*jk] + zz[ii]/0.75 + zz[ii + 2*jk]/6.; yy[ii + jk] = 0.5*(zz[ii + 2*jk] - zz[ii - 2*jk]) + zz[ii]; } // running means for (ii = 1; ii < (nn - 1); ii++) { zz[ii] = 0.25*yy[ii - 1] + 0.5*yy[ii] + 0.25*yy[ii + 1]; } zz[0] = yy[0]; zz[nn - 1] = yy[nn - 1]; // add smoothed xx and smoothed residuals for (ii = 0; ii < nn; ii++) { if (xx[ii] < 0) xx[ii] = rr[ii] + zz[ii]; else xx[ii] = TMath::Abs(rr[ii] + zz[ii]); } } delete [] yy; delete [] zz; delete [] rr; } // ------------------------------------------------------------------------ void TH1::Smooth(Int_t ntimes, Option_t *option) { // Smooth bin contents of this histogram. // if option contains "R" smoothing is applied only to the bins // defined in the X axis range (default is to smooth all bins) // Bin contents are replaced by their smooth values. // Errors (if any) are not modified. // the smoothing procedure is repeated ntimes (default=1) if (fDimension != 1) { Error("Smooth","Smooth only supported for 1-d histograms"); return; } Int_t nbins = fXaxis.GetNbins(); Int_t firstbin = 1, lastbin = nbins; TString opt = option; opt.ToLower(); if (opt.Contains("r")) { firstbin= fXaxis.GetFirst(); lastbin = fXaxis.GetLast(); } nbins = lastbin - firstbin + 1; Double_t *xx = new Double_t[nbins]; Double_t nent = fEntries; Int_t i; for (i=0;i<nbins;i++) { xx[i] = GetBinContent(i+firstbin); } TH1::SmoothArray(nbins,xx,ntimes); for (i=0;i<nbins;i++) { SetBinContent(i+firstbin,xx[i]); } fEntries = nent; delete [] xx; if (gPad) gPad->Modified(); } // ------------------------------------------------------------------------ void TH1::StatOverflows(Bool_t flag) { // if flag=kTRUE, underflows and overflows are used by the Fill functions // in the computation of statistics (mean value, RMS). // By default, underflows or overflows are not used. fgStatOverflows = flag; } //_______________________________________________________________________ void TH1::Streamer(TBuffer &b) { // -*-*-*-*-*-*-*Stream a class object*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* // ===================== if (b.IsReading()) { UInt_t R__s, R__c; Version_t R__v = b.ReadVersion(&R__s, &R__c); fDirectory = 0; if (R__v > 2) { b.ReadClassBuffer(TH1::Class(), this, R__v, R__s, R__c); fXaxis.SetParent(this); fYaxis.SetParent(this); fZaxis.SetParent(this); ResetBit(kCanDelete); ResetBit(kMustCleanup); return; } //process old versions before automatic schema evolution TNamed::Streamer(b); TAttLine::Streamer(b); TAttFill::Streamer(b); TAttMarker::Streamer(b); b >> fNcells; fXaxis.Streamer(b); fYaxis.Streamer(b); fZaxis.Streamer(b); fXaxis.SetParent(this); fYaxis.SetParent(this); fZaxis.SetParent(this); b >> fBarOffset; b >> fBarWidth; b >> fEntries; b >> fTsumw; b >> fTsumw2; b >> fTsumwx; b >> fTsumwx2; if (R__v < 2) { Float_t maximum, minimum, norm; Float_t *contour=0; b >> maximum; fMaximum = maximum; b >> minimum; fMinimum = minimum; b >> norm; fNormFactor = norm; Int_t n = b.ReadArray(contour); fContour.Set(n); for (Int_t i=0;i<n;i++) fContour.fArray[i] = contour[i]; delete [] contour; } else { b >> fMaximum; b >> fMinimum; b >> fNormFactor; fContour.Streamer(b); } fSumw2.Streamer(b); fOption.Streamer(b); fFunctions->Delete(); fFunctions->Streamer(b); b.CheckByteCount(R__s, R__c, TH1::IsA()); } else { b.WriteClassBuffer(TH1::Class(),this); } } //______________________________________________________________________________ void TH1::Print(Option_t *option) const { // -*-*-*-*-*Print some global quantities for this histogram*-*-*-*-*-*-*-* // =============================================== // // If option "base" is given, number of bins and ranges are also printed // If option "range" is given, bin contents and errors are also printed // for all bins in the current range (default 1-->nbins) // If option "all" is given, bin contents and errors are also printed // for all bins including under and overflows. // printf( "TH1.Print Name = %s, Entries= %d, Total sum= %g\n",GetName(),Int_t(fEntries),GetSumOfWeights()); TString opt = option; opt.ToLower(); Int_t all; if (opt.Contains("all")) all = 0; else if (opt.Contains("range")) all = 1; else if (opt.Contains("base")) all = 2; else return; Int_t bin, binx, biny, binz; Int_t firstx=0,lastx=0,firsty=0,lasty=0,firstz=0,lastz=0; if (all == 0) { lastx = fXaxis.GetNbins()+1; if (fDimension > 1) lasty = fYaxis.GetNbins()+1; if (fDimension > 2) lastz = fZaxis.GetNbins()+1; } else { firstx = fXaxis.GetFirst(); lastx = fXaxis.GetLast(); if (fDimension > 1) {firsty = fYaxis.GetFirst(); lasty = fYaxis.GetLast();} if (fDimension > 2) {firstz = fZaxis.GetFirst(); lastz = fZaxis.GetLast();} } if (all== 2) { printf(" Title = %s\n", GetTitle()); printf(" NbinsX= %d, xmin= %g, xmax=%g", fXaxis.GetNbins(), fXaxis.GetXmin(), fXaxis.GetXmax()); if( fDimension > 1) printf(", NbinsY= %d, ymin= %g, ymax=%g", fYaxis.GetNbins(), fYaxis.GetXmin(), fYaxis.GetXmax()); if( fDimension > 2) printf(", NbinsZ= %d, zmin= %g, zmax=%g", fZaxis.GetNbins(), fZaxis.GetXmin(), fZaxis.GetXmax()); printf("\n"); return; } Double_t w,e; Double_t x,y,z; if (fDimension == 1) { for (binx=firstx;binx<=lastx;binx++) { x = fXaxis.GetBinCenter(binx); w = GetBinContent(binx); e = GetBinError(binx); if(fSumw2.fN) printf(" fSumw[%d]=%g, x=%g, error=%g\n",binx,w,x,e); else printf(" fSumw[%d]=%g, x=%g\n",binx,w,x); } } if (fDimension == 2) { for (biny=firsty;biny<=lasty;biny++) { y = fYaxis.GetBinCenter(biny); for (binx=firstx;binx<=lastx;binx++) { bin = GetBin(binx,biny); x = fXaxis.GetBinCenter(binx); w = GetBinContent(bin); e = GetBinError(bin); if(fSumw2.fN) printf(" fSumw[%d][%d]=%g, x=%g, y=%g, error=%g\n",binx,biny,w,x,y,e); else printf(" fSumw[%d][%d]=%g, x=%g, y=%g\n",binx,biny,w,x,y); } } } if (fDimension == 3) { for (binz=firstz;binz<=lastz;binz++) { z = fZaxis.GetBinCenter(binz); for (biny=firsty;biny<=lasty;biny++) { y = fYaxis.GetBinCenter(biny); for (binx=firstx;binx<=lastx;binx++) { bin = GetBin(binx,biny,binz); x = fXaxis.GetBinCenter(binx); w = GetBinContent(bin); e = GetBinError(bin); if(fSumw2.fN) printf(" fSumw[%d][%d][%d]=%g, x=%g, y=%g, z=%g, error=%g\n",binx,biny,binz,w,x,y,z,e); else printf(" fSumw[%d][%d][%d]=%g, x=%g, y=%g, z=%g\n",binx,biny,binz,w,x,y,z); } } } } } //______________________________________________________________________________ void TH1::Rebuild(Option_t *) { // Using the current bin info, recompute the arrays for contents and errors SetBinsLength(); if (fSumw2.fN) { fSumw2.Set(fNcells); } } //______________________________________________________________________________ void TH1::Reset(Option_t *option) { // -*-*-*-*-*-*Reset this histogram: contents, errors, etc*-*-*-*-*-*-*-* // =========================================== // // if option "ICE" is specified, resets only Integral, Contents and Errors. // if option "M" is specified, resets also Minimum and Maximum TString opt = option; opt.ToUpper(); fSumw2.Reset(); if (fIntegral) {delete [] fIntegral; fIntegral = 0;} if (opt.Contains("M")) { SetMinimum(); SetMaximum(); } if (opt.Contains("ICE")) return; if (fBuffer) {BufferEmpty(); fBuffer[0] = 0;} fTsumw = 0; fTsumw2 = 0; fTsumwx = 0; fTsumwx2 = 0; fEntries = 0; TObject *stats = fFunctions->FindObject("stats"); fFunctions->Remove(stats); //special logic to support the case where the same object is //added multiple times in fFunctions. //This case happens when the same object is added with different //drawing modes TObject *obj; while ((obj = fFunctions->First())) { while(fFunctions->Remove(obj)) { } delete obj; } if(stats) fFunctions->Add(stats); fContour.Set(0); } //______________________________________________________________________________ void TH1::SavePrimitive(ostream &out, Option_t *option /*= ""*/) { // Save primitive as a C++ statement(s) on output stream out Bool_t nonEqiX = kFALSE; Bool_t nonEqiY = kFALSE; Bool_t nonEqiZ = kFALSE; Int_t i; static Int_t nxaxis = 0; static Int_t nyaxis = 0; static Int_t nzaxis = 0; TString sxaxis="xAxis",syaxis="yAxis",szaxis="zAxis"; // Check if the histogram has equidistant X bins or not. If not, we // create an array holding the bins. if (GetXaxis()->GetXbins()->fN && GetXaxis()->GetXbins()->fArray) { nonEqiX = kTRUE; nxaxis++; sxaxis += nxaxis; out << " Double_t "<<sxaxis<<"[" << GetXaxis()->GetXbins()->fN << "] = {"; for (i = 0; i < GetXaxis()->GetXbins()->fN; i++) { if (i != 0) out << ", "; out << GetXaxis()->GetXbins()->fArray[i]; } out << "}; " << endl; } // If the histogram is 2 or 3 dimensional, check if the histogram // has equidistant Y bins or not. If not, we create an array // holding the bins. if (fDimension > 1 && GetYaxis()->GetXbins()->fN && GetYaxis()->GetXbins()->fArray) { nonEqiY = kTRUE; nyaxis++; syaxis += nyaxis; out << " Double_t "<<syaxis<<"[" << GetYaxis()->GetXbins()->fN << "] = {"; for (i = 0; i < GetYaxis()->GetXbins()->fN; i++) { if (i != 0) out << ", "; out << GetYaxis()->GetXbins()->fArray[i]; } out << "}; " << endl; } // IF the histogram is 3 dimensional, check if the histogram // has equidistant Z bins or not. If not, we create an array // holding the bins. if (fDimension > 2 && GetZaxis()->GetXbins()->fN && GetZaxis()->GetXbins()->fArray) { nonEqiZ = kTRUE; nzaxis++; szaxis += nzaxis; out << " Double_t "<<szaxis<<"[" << GetZaxis()->GetXbins()->fN << "] = {"; for (i = 0; i < GetZaxis()->GetXbins()->fN; i++) { if (i != 0) out << ", "; out << GetZaxis()->GetXbins()->fArray[i]; } out << "}; " << endl; } char quote = '"'; out <<" "<<endl; out <<" "<<"TH1"<<" *"; out << GetName() << " = new " << ClassName() << "(" << quote << GetName() << quote << "," << quote<< GetTitle() << quote << "," << GetXaxis()->GetNbins(); if (nonEqiX) out << ", "<<sxaxis; else out << "," << GetXaxis()->GetXmin() << "," << GetXaxis()->GetXmax(); if (fDimension > 1) { out << "," << GetYaxis()->GetNbins(); if (nonEqiY) out << ", "<<syaxis; else out << "," << GetYaxis()->GetXmin() << "," << GetYaxis()->GetXmax(); } if (fDimension > 2) { out << "," << GetZaxis()->GetNbins(); if (nonEqiZ) out << ", "<<szaxis; else out << "," << GetZaxis()->GetXmin() << "," << GetZaxis()->GetXmax(); } out << ");" << endl; // save bin contents Int_t bin; for (bin=0;bin<fNcells;bin++) { Double_t bc = GetBinContent(bin); if (bc) { out<<" "<<GetName()<<"->SetBinContent("<<bin<<","<<bc<<");"<<endl; } } // save bin errors if (fSumw2.fN) { for (bin=0;bin<fNcells;bin++) { Double_t be = GetBinError(bin); if (be) { out<<" "<<GetName()<<"->SetBinError("<<bin<<","<<be<<");"<<endl; } } } TH1::SavePrimitiveHelp(out, option); } //______________________________________________________________________________ void TH1::SavePrimitiveHelp(ostream &out, Option_t *option /*= ""*/) { // helper function for the SavePrimitive functions from TH1 // or classes derived from TH1, eg TProfile, TProfile2D. char quote = '"'; if (TMath::Abs(GetBarOffset()) > 1e-5) { out<<" "<<GetName()<<"->SetBarOffset("<<GetBarOffset()<<");"<<endl; } if (TMath::Abs(GetBarWidth()-1) > 1e-5) { out<<" "<<GetName()<<"->SetBarWidth("<<GetBarWidth()<<");"<<endl; } if (fMinimum != -1111) { out<<" "<<GetName()<<"->SetMinimum("<<fMinimum<<");"<<endl; } if (fMaximum != -1111) { out<<" "<<GetName()<<"->SetMaximum("<<fMaximum<<");"<<endl; } if (fNormFactor != 0) { out<<" "<<GetName()<<"->SetNormFactor("<<fNormFactor<<");"<<endl; } if (fEntries != 0) { out<<" "<<GetName()<<"->SetEntries("<<fEntries<<");"<<endl; } if (fDirectory == 0) { out<<" "<<GetName()<<"->SetDirectory(0);"<<endl; } if (TestBit(kNoStats)) { out<<" "<<GetName()<<"->SetStats(0);"<<endl; } if (fOption.Length() != 0) { out<<" "<<GetName()<<"->SetOption("<<quote<<fOption.Data()<<quote<<");"<<endl; } // save contour levels Int_t ncontours = GetContour(); if (ncontours > 0) { out<<" "<<GetName()<<"->SetContour("<<ncontours<<");"<<endl; Double_t zlevel; for (Int_t bin=0;bin<ncontours;bin++) { if (gPad->GetLogz()) { zlevel = TMath::Power(10,GetContourLevel(bin)); } else { zlevel = GetContourLevel(bin); } out<<" "<<GetName()<<"->SetContourLevel("<<bin<<","<<zlevel<<");"<<endl; } } // save list of functions TObjOptLink *lnk = (TObjOptLink*)fFunctions->FirstLink(); TObject *obj; while (lnk) { obj = lnk->GetObject(); obj->SavePrimitive(out,"nodraw"); if (obj->InheritsFrom("TF1")) { out<<" "<<GetName()<<"->GetListOfFunctions()->Add("<<obj->GetName()<<");"<<endl; } else if (obj->InheritsFrom("TPaveStats")) { out<<" "<<GetName()<<"->GetListOfFunctions()->Add(ptstats);"<<endl; out<<" ptstats->SetParent("<<GetName()<<"->GetListOfFunctions());"<<endl; } else { out<<" "<<GetName()<<"->GetListOfFunctions()->Add("<<obj->GetName()<<","<<quote<<lnk->GetOption()<<quote<<");"<<endl; } lnk = (TObjOptLink*)lnk->Next(); } // save attributes SaveFillAttributes(out,GetName(),0,1001); SaveLineAttributes(out,GetName(),1,1,1); SaveMarkerAttributes(out,GetName(),1,1,1); fXaxis.SaveAttributes(out,GetName(),"->GetXaxis()"); fYaxis.SaveAttributes(out,GetName(),"->GetYaxis()"); fZaxis.SaveAttributes(out,GetName(),"->GetZaxis()"); TString opt = option; opt.ToLower(); if (!opt.Contains("nodraw")) { out<<" "<<GetName()<<"->Draw(" <<quote<<option<<quote<<");"<<endl; } } //______________________________________________________________________________ void TH1::UseCurrentStyle() { // Copy current attributes from/to current style if (!gStyle) return; if (gStyle->IsReading()) { fXaxis.ResetAttAxis("X"); fYaxis.ResetAttAxis("Y"); fZaxis.ResetAttAxis("Z"); SetBarOffset(gStyle->GetBarOffset()); SetBarWidth(gStyle->GetBarWidth()); SetFillColor(gStyle->GetHistFillColor()); SetFillStyle(gStyle->GetHistFillStyle()); SetLineColor(gStyle->GetHistLineColor()); SetLineStyle(gStyle->GetHistLineStyle()); SetLineWidth(gStyle->GetHistLineWidth()); SetMarkerColor(gStyle->GetMarkerColor()); SetMarkerStyle(gStyle->GetMarkerStyle()); SetMarkerSize(gStyle->GetMarkerSize()); Int_t dostat = gStyle->GetOptStat(); if (gStyle->GetOptFit() && !dostat) dostat = 1000000001; SetStats(dostat); } else { gStyle->SetBarOffset(fBarOffset); gStyle->SetBarWidth(fBarWidth); gStyle->SetHistFillColor(GetFillColor()); gStyle->SetHistFillStyle(GetFillStyle()); gStyle->SetHistLineColor(GetLineColor()); gStyle->SetHistLineStyle(GetLineStyle()); gStyle->SetHistLineWidth(GetLineWidth()); gStyle->SetMarkerColor(GetMarkerColor()); gStyle->SetMarkerStyle(GetMarkerStyle()); gStyle->SetMarkerSize(GetMarkerSize()); gStyle->SetOptStat(TestBit(kNoStats)); } TIter next(GetListOfFunctions()); TObject *obj; while ((obj = next())) { obj->UseCurrentStyle(); } } //______________________________________________________________________________ Double_t TH1::GetMean(Int_t axis) const { // For axis = 1,2 or 3 returns the mean value of the histogram along // X,Y or Z axis. // For axis = 11, 12, 13 returns the standard error of the mean value // of the histogram along X, Y or Z axis // // Note that the mean value/RMS is computed using the bins in the currently // defined range (see TAxis::SetRange). By default the range includes // all bins from 1 to nbins included, excluding underflows and overflows. // To force the underflows and overflows in the computation, one must // call the static function TH1::StatOverflows(kTRUE) before filling // the histogram. // -*-*-*-*-*-*Return mean value of this histogram along the X axis*-*-*-*-* // ==================================================== // Note that the mean value/RMS is computed using the bins in the currently // defined range (see TAxis::SetRange). By default the range includes // all bins from 1 to nbins included, excluding underflows and overflows. // To force the underflows and overflows in the computation, one must // call the static function TH1::StatOverflows(kTRUE) before filling // the histogram. if (axis<1 || (axis>3 && axis<11) || axis>13) return 0; Double_t stats[kNstat]; for (Int_t i=4;i<kNstat;i++) stats[i] = 0; GetStats(stats); if (stats[0] == 0) return 0; if (axis<10){ Int_t ax[3] = {2,4,7}; return stats[ax[axis-1]]/stats[0]; } else { // mean error = RMS / sqrt( Neff ) Double_t rms = GetRMS(axis-10); Double_t neff = GetEffectiveEntries(); return ( neff > 0 ? rms/TMath::Sqrt(neff) : 0. ); } } //______________________________________________________________________________ Double_t TH1::GetMeanError(Int_t axis) const { // -*-*-*-*-*-*Return standard error of mean of this histogram along the X axis*-*-*-*-* // ==================================================== // Note that the mean value/RMS is computed using the bins in the currently // defined range (see TAxis::SetRange). By default the range includes // all bins from 1 to nbins included, excluding underflows and overflows. // To force the underflows and overflows in the computation, one must // call the static function TH1::StatOverflows(kTRUE) before filling // the histogram. // Also note, that although the definition of standard error doesn't include the // assumption of normality, many uses of this feature implicitly assume it. return GetMean(axis+10); } //______________________________________________________________________________ Double_t TH1::GetRMS(Int_t axis) const { // For axis = 1,2 or 3 returns the Sigma value of the histogram along // X, Y or Z axis // For axis = 11, 12 or 13 returns the error of RMS estimation along // X, Y or Z axis for Normal distribution // // Note that the mean value/sigma is computed using the bins in the currently // defined range (see TAxis::SetRange). By default the range includes // all bins from 1 to nbins included, excluding underflows and overflows. // To force the underflows and overflows in the computation, one must // call the static function TH1::StatOverflows(kTRUE) before filling // the histogram. // Note that this function returns the Standard Deviation (Sigma) // of the distribution (not RMS). // The Sigma estimate is computed as Sqrt((1/N)*(Sum(x_i-x_mean)^2)) // The name "RMS" was introduced many years ago (Hbook/PAW times). // We kept the name for continuity. if (axis<1 || (axis>3 && axis<11) || axis>13) return 0; Double_t x, rms2, stats[kNstat]; for (Int_t i=4;i<kNstat;i++) stats[i] = 0; GetStats(stats); if (stats[0] == 0) return 0; Int_t ax[3] = {2,4,7}; Int_t axm = ax[axis%10 - 1]; x = stats[axm]/stats[0]; rms2 = TMath::Abs(stats[axm+1]/stats[0] -x*x); if (axis<10) return TMath::Sqrt(rms2); else { // The right formula for RMS error depends on 4th momentum (see Kendall-Stuart Vol 1 pag 243) // formula valid for only gaussian distribution ( 4-th momentum = 3 * sigma^4 ) Double_t neff = GetEffectiveEntries(); return ( neff > 0 ? TMath::Sqrt(rms2/(2*neff) ) : 0. ); } } //______________________________________________________________________________ Double_t TH1::GetRMSError(Int_t axis) const { // Return error of RMS estimation for Normal distribution // // Note that the mean value/RMS is computed using the bins in the currently // defined range (see TAxis::SetRange). By default the range includes // all bins from 1 to nbins included, excluding underflows and overflows. // To force the underflows and overflows in the computation, one must // call the static function TH1::StatOverflows(kTRUE) before filling // the histogram. // Value returned is standard deviation of sample standard deviation. // Note that it is an approximated value which is valid only in the case that the // original data distribution is Normal. The correct one would require // the 4-th momentum value, which cannot be accuratly estimated from an histogram since // the x-information for all entries is not kept. return GetRMS(axis+10); } //______________________________________________________________________________ Double_t TH1::GetSkewness(Int_t axis) const { //For axis = 1, 2 or 3 returns skewness of the histogram along x, y or z axis. //For axis = 11, 12 or 13 returns the approximate standard error of skewness //of the histogram along x, y or z axis //Note, that since third and fourth moment are not calculated //at the fill time, skewness and its standard error are computed bin by bin if (axis > 0 && axis <= 3){ Double_t mean = GetMean(axis); Double_t rms = GetRMS(axis); Double_t rms3 = rms*rms*rms; Int_t firstBinX = fXaxis.GetFirst(); Int_t lastBinX = fXaxis.GetLast(); Int_t firstBinY = fYaxis.GetFirst(); Int_t lastBinY = fYaxis.GetLast(); Int_t firstBinZ = fZaxis.GetFirst(); Int_t lastBinZ = fZaxis.GetLast(); // include underflow/overflow if TH1::StatOverflows(kTRUE) in case no range is set on the axis if (fgStatOverflows) { if ( !fXaxis.TestBit(TAxis::kAxisRange) ) { if (firstBinX == 1) firstBinX = 0; if (lastBinX == fXaxis.GetNbins() ) lastBinX += 1; } if ( !fYaxis.TestBit(TAxis::kAxisRange) ) { if (firstBinY == 1) firstBinY = 0; if (lastBinY == fYaxis.GetNbins() ) lastBinY += 1; } if ( !fZaxis.TestBit(TAxis::kAxisRange) ) { if (firstBinZ == 1) firstBinZ = 0; if (lastBinZ == fZaxis.GetNbins() ) lastBinZ += 1; } } Double_t x = 0; Double_t sum=0; Double_t np=0; for (Int_t binx = firstBinX; binx <= lastBinX; binx++) { for (Int_t biny = firstBinY; biny <= lastBinY; biny++) { for (Int_t binz = firstBinZ; binz <= lastBinZ; binz++) { if (axis==1 ) x = fXaxis.GetBinCenter(binx); else if (axis==2 ) x = fYaxis.GetBinCenter(biny); else if (axis==3 ) x = fZaxis.GetBinCenter(binz); Double_t w = GetBinContent(binx,biny,binz); np+=w; sum+=w*(x-mean)*(x-mean)*(x-mean); } } } sum/=np*rms3; return sum; } else if (axis > 10 && axis <= 13) { //compute standard error of skewness // assume parent normal distribution use formula from Kendall-Stuart, Vol 1 pag 243, second edition Double_t neff = GetEffectiveEntries(); return ( neff > 0 ? TMath::Sqrt(6./neff ) : 0. ); } else { Error("GetSkewness", "illegal value of parameter"); return 0; } } //______________________________________________________________________________ Double_t TH1::GetKurtosis(Int_t axis) const { //For axis =1, 2 or 3 returns kurtosis of the histogram along x, y or z axis. //Kurtosis(gaussian(0, 1)) = 0. //For axis =11, 12 or 13 returns the approximate standard error of kurtosis //of the histogram along x, y or z axis //Note, that since third and fourth moment are not calculated //at the fill time, kurtosis and its standard error are computed bin by bin if (axis > 0 && axis <= 3){ Double_t mean = GetMean(axis); Double_t rms = GetRMS(axis); Double_t rms4 = rms*rms*rms*rms; Int_t firstBinX = fXaxis.GetFirst(); Int_t lastBinX = fXaxis.GetLast(); Int_t firstBinY = fYaxis.GetFirst(); Int_t lastBinY = fYaxis.GetLast(); Int_t firstBinZ = fZaxis.GetFirst(); Int_t lastBinZ = fZaxis.GetLast(); // include underflow/overflow if TH1::StatOverflows(kTRUE) in case no range is set on the axis if (fgStatOverflows) { if ( !fXaxis.TestBit(TAxis::kAxisRange) ) { if (firstBinX == 1) firstBinX = 0; if (lastBinX == fXaxis.GetNbins() ) lastBinX += 1; } if ( !fYaxis.TestBit(TAxis::kAxisRange) ) { if (firstBinY == 1) firstBinY = 0; if (lastBinY == fYaxis.GetNbins() ) lastBinY += 1; } if ( !fZaxis.TestBit(TAxis::kAxisRange) ) { if (firstBinZ == 1) firstBinZ = 0; if (lastBinZ == fZaxis.GetNbins() ) lastBinZ += 1; } } Double_t x = 0; Double_t sum=0; Double_t np=0; for (Int_t binx = firstBinX; binx <= lastBinX; binx++) { for (Int_t biny = firstBinY; biny <= lastBinY; biny++) { for (Int_t binz = firstBinZ; binz <= lastBinZ; binz++) { if (axis==1 ) x = fXaxis.GetBinCenter(binx); else if (axis==2 ) x = fYaxis.GetBinCenter(biny); else if (axis==3 ) x = fZaxis.GetBinCenter(binz); Double_t w = GetBinContent(binx,biny,binz); np+=w; sum+=w*(x-mean)*(x-mean)*(x-mean)*(x-mean); } } } sum/=(np*rms4); return sum-3; } else if (axis > 10 && axis <= 13) { //compute standard error of skewness // assume parent normal distribution use formula from Kendall-Stuart, Vol 1 pag 243, second edition Double_t neff = GetEffectiveEntries(); return ( neff > 0 ? TMath::Sqrt(24./neff ) : 0. ); } else { Error("GetKurtosis", "illegal value of parameter"); return 0; } } //______________________________________________________________________________ void TH1::GetStats(Double_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 // // 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. // // Note that the mean value/RMS is computed using the bins in the currently // defined range (see TAxis::SetRange). By default the range includes // all bins from 1 to nbins included, excluding underflows and overflows. // To force the underflows and overflows in the computation, one must // call the static function TH1::StatOverflows(kTRUE) before filling // the histogram. if (fBuffer) ((TH1*)this)->BufferEmpty(); // Loop on bins (possibly including underflows/overflows) Int_t bin, binx; Double_t w,err; Double_t x; if ((fTsumw == 0 && fEntries > 0) || fXaxis.TestBit(TAxis::kAxisRange)) { for (bin=0;bin<4;bin++) stats[bin] = 0; Int_t firstBinX = fXaxis.GetFirst(); Int_t lastBinX = fXaxis.GetLast(); // include underflow/overflow if TH1::StatOverflows(kTRUE) in case no range is set on the axis if (fgStatOverflows && !fXaxis.TestBit(TAxis::kAxisRange)) { if (firstBinX == 1) firstBinX = 0; if (lastBinX == fXaxis.GetNbins() ) lastBinX += 1; } for (binx = firstBinX; binx <= lastBinX; binx++) { x = fXaxis.GetBinCenter(binx); w = TMath::Abs(GetBinContent(binx)); err = TMath::Abs(GetBinError(binx)); stats[0] += w; stats[1] += err*err; stats[2] += w*x; stats[3] += w*x*x; } } else { stats[0] = fTsumw; stats[1] = fTsumw2; stats[2] = fTsumwx; stats[3] = fTsumwx2; } } //______________________________________________________________________________ void TH1::PutStats(Double_t *stats) { // Replace current statistics with the values in array stats fTsumw = stats[0]; fTsumw2 = stats[1]; fTsumwx = stats[2]; fTsumwx2 = stats[3]; } //______________________________________________________________________________ Double_t TH1::GetSumOfWeights() const { // -*-*-*-*-*-*Return the sum of weights excluding under/overflows*-*-*-*-* // =================================================== Int_t bin,binx,biny,binz; Double_t sum =0; for(binz=1; binz<=fZaxis.GetNbins(); binz++) { for(biny=1; biny<=fYaxis.GetNbins(); biny++) { for(binx=1; binx<=fXaxis.GetNbins(); binx++) { bin = GetBin(binx,biny,binz); sum += GetBinContent(bin); } } } return sum; } //______________________________________________________________________________ Double_t TH1::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. return Integral(fXaxis.GetFirst(),fXaxis.GetLast(),option); } //______________________________________________________________________________ Double_t TH1::Integral(Int_t binx1, Int_t binx2, Option_t *option) const { //Return integral of bin contents between binx1 and binx2 for a 1-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. Int_t nbinsx = GetNbinsX(); if (binx1 < 0) binx1 = 0; if (binx2 > nbinsx+1) binx2 = nbinsx+1; if (binx2 < binx1) binx2 = nbinsx; Double_t integral = 0; // - Loop on bins in specified range TString opt = option; opt.ToLower(); Bool_t width = kFALSE; if (opt.Contains("width")) width = kTRUE; Int_t binx; for (binx=binx1;binx<=binx2;binx++) { if (width) integral += GetBinContent(binx)*fXaxis.GetBinWidth(binx); else integral += GetBinContent(binx); } return integral; } //______________________________________________________________________________ Double_t TH1::KolmogorovTest(const 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 (also for 2-dim) // "O" include Overflows (also valid for 2-dim) // "N" include comparison of normalizations // "D" Put out a line of "Debug" printout // "M" Return the Maximum Kolmogorov distance instead of prob // "X" Run the pseudo experiments post-processor with the following procedure: // make pseudoexperiments based on random values from the parent // distribution and compare the KS distance of the pseudoexperiment // to the parent distribution. Bin the KS distances in a histogram, // and then take the integral of all the KS values above the value // obtained from the original data to Monte Carlo distribution. // The number of pseudo-experiments nEXPT is currently fixed at 1000. // The function returns the integral. // (thanks to Ben Kilminster to submit this procedure). Note that // this option "X" is much slower. // // The returned function value is the probability of test // (much less than one means NOT compatible) // // Code adapted by Rene Brun from original HBOOK routine HDIFF // // NOTE1 // A good description of the Kolmogorov test can be seen at: // http://www.itl.nist.gov/div898/handbook/eda/section3/eda35g.htm // // NOTE2 // see also alternative function TH1::Chi2Test // The Kolmogorov test is assumed to give better results than Chi2Test // in case of histograms with low statistics. // // NOTE3 (Jan Conrad, Fred James) // "The returned value PROB is calculated such that it will be // uniformly distributed between zero and one for compatible histograms, // provided the data are not binned (or the number of bins is very large // compared with the number of events). Users who have access to unbinned // data and wish exact confidence levels should therefore not put their data // into histograms, but should call directly TMath::KolmogorovTest. On // the other hand, since TH1 is a convenient way of collecting data and // saving space, this function has been provided. However, the values of // PROB for binned data will be shifted slightly higher than expected, // depending on the effects of the binning. For example, when comparing two // uniform distributions of 500 events in 100 bins, the values of PROB, // instead of being exactly uniformly distributed between zero and one, have // a mean value of about 0.56. We can apply a useful // rule: As long as the bin width is small compared with any significant // physical effect (for example the experimental resolution) then the binning // cannot have an important effect. Therefore, we believe that for all // practical purposes, the probability value PROB is calculated correctly // provided the user is aware that: // 1. The value of PROB should not be expected to have exactly the correct // distribution for binned data. // 2. The user is responsible for seeing to it that the bin widths are // small compared with any physical phenomena of interest. // 3. The effect of binning (if any) is always to make the value of PROB // slightly too big. That is, setting an acceptance criterion of (PROB>0.05 // will assure that at most 5% of truly compatible histograms are rejected, // and usually somewhat less." TString opt = option; opt.ToUpper(); Double_t prob = 0; TH1 *h1 = (TH1*)this; if (h2 == 0) return 0; TAxis *axis1 = h1->GetXaxis(); TAxis *axis2 = h2->GetXaxis(); Int_t ncx1 = axis1->GetNbins(); Int_t ncx2 = axis2->GetNbins(); // Check consistency of dimensions if (h1->GetDimension() != 1 || h2->GetDimension() != 1) { Error("KolmogorovTest","Histograms must be 1-D\n"); return 0; } // Check consistency in number of channels if (ncx1 != ncx2) { Error("KolmogorovTest","Number of channels is different, %d and %d\n",ncx1,ncx2); return 0; } // Check consistency in channel edges Double_t difprec = 1e-5; Double_t diff1 = TMath::Abs(axis1->GetXmin() - axis2->GetXmin()); Double_t diff2 = TMath::Abs(axis1->GetXmax() - axis2->GetXmax()); if (diff1 > difprec || diff2 > difprec) { Error("KolmogorovTest","histograms with different binning"); return 0; } Bool_t afunc1 = kFALSE; Bool_t afunc2 = kFALSE; Double_t sum1 = 0, sum2 = 0; Double_t ew1, ew2, w1 = 0, w2 = 0; Int_t bin; Int_t ifirst = 1; Int_t ilast = ncx1; // integral of all bins (use underflow/overflow if option) if (opt.Contains("U")) ifirst = 0; if (opt.Contains("O")) ilast = ncx1 +1; for (bin = ifirst; bin <= ilast; bin++) { sum1 += h1->GetBinContent(bin); sum2 += h2->GetBinContent(bin); ew1 = h1->GetBinError(bin); ew2 = h2->GetBinError(bin); w1 += ew1*ew1; w2 += ew2*ew2; } if (sum1 == 0) { Error("KolmogorovTest","Histogram1 %s integral is zero\n",h1->GetName()); return 0; } if (sum2 == 0) { Error("KolmogorovTest","Histogram2 %s integral is zero\n",h2->GetName()); return 0; } // calculate the effective entries. // the case when errors are zero (w1 == 0 or w2 ==0) are equivalent to // compare to a function. In that case the rescaling is done only on sqrt(esum2) or sqrt(esum1) Double_t esum1 = 0, esum2 = 0; if (w1 > 0) esum1 = sum1 * sum1 / w1; else afunc1 = kTRUE; // use later for calculating z if (w2 > 0) esum2 = sum2 * sum2 / w2; else afunc2 = kTRUE; // use later for calculating z if (afunc2 && afunc1) { Error("KolmogorovTest","Errors are zero for both histograms\n"); return 0; } Double_t s1 = 1/sum1; Double_t s2 = 1/sum2; // Find largest difference for Kolmogorov Test Double_t dfmax =0, rsum1 = 0, rsum2 = 0; for (bin=ifirst;bin<=ilast;bin++) { rsum1 += s1*h1->GetBinContent(bin); rsum2 += s2*h2->GetBinContent(bin); dfmax = TMath::Max(dfmax,TMath::Abs(rsum1-rsum2)); } // Get Kolmogorov probability Double_t z, prb1=0, prb2=0, prb3=0; // case h1 is exact (has zero errors) if (afunc1) z = dfmax*TMath::Sqrt(esum2); // case h2 has zero errors else if (afunc2) z = dfmax*TMath::Sqrt(esum1); else // for comparison between two data sets z = dfmax*TMath::Sqrt(esum1*esum2/(esum1+esum2)); prob = TMath::KolmogorovProb(z); // option N to combine normalization makes sense if both afunc1 and afunc2 are false if (opt.Contains("N") && !(afunc1 || afunc2 ) ) { // Combine probabilities for shape and normalization, prb1 = prob; Double_t d12 = esum1-esum2; Double_t chi2 = d12*d12/(esum1+esum2); prb2 = TMath::Prob(chi2,1); // see Eadie et al., section 11.6.2 if (prob > 0 && prb2 > 0) prob *= prb2*(1-TMath::Log(prob*prb2)); else prob = 0; } // X option. Pseudo-experiments post-processor to determine KS probability const Int_t nEXPT = 1000; if (opt.Contains("X") && !(afunc1 || afunc2 ) ) { Double_t dSEXPT; TH1 *hExpt = (TH1*)(gDirectory ? gDirectory->CloneObject(this,kFALSE) : gROOT->CloneObject(this,kFALSE)); // make nEXPT experiments (this should be a parameter) prb3 = 0; for (Int_t i=0; i < nEXPT; i++) { hExpt->Reset(); hExpt->FillRandom(h1,(Int_t)esum2); dSEXPT = KolmogorovTest(hExpt,"M"); if (dSEXPT>dfmax) prb3 += 1.0; } prb3 /= (Double_t)nEXPT; delete hExpt; } // debug printout if (opt.Contains("D")) { printf(" Kolmo Prob h1 = %s, sum bin content =%g effective entries =%g\n",h1->GetName(),sum1,esum1); printf(" Kolmo Prob h2 = %s, sum bin content =%g effective entries =%g\n",h2->GetName(),sum2,esum2); printf(" Kolmo Prob = %g, Max Dist = %g\n",prob,dfmax); if (opt.Contains("N")) printf(" Kolmo Prob = %f for shape alone, =%f for normalisation alone\n",prb1,prb2); if (opt.Contains("X")) printf(" Kolmo Prob = %f with %d pseudo-experiments\n",prb3,nEXPT); } // This numerical error condition should never occur: if (TMath::Abs(rsum1-1) > 0.002) Warning("KolmogorovTest","Numerical problems with h1=%s\n",h1->GetName()); if (TMath::Abs(rsum2-1) > 0.002) Warning("KolmogorovTest","Numerical problems with h2=%s\n",h2->GetName()); if(opt.Contains("M")) return dfmax; else if(opt.Contains("X")) return prb3; else return prob; } //______________________________________________________________________________ void TH1::SetContent(const Double_t *content) { // -*-*-*-*-*-*Replace bin contents by the contents of array content*-*-*-* // ===================================================== Int_t bin; Double_t bincontent; for (bin=0; bin<fNcells; bin++) { bincontent = *(content + bin); SetBinContent(bin, bincontent); } } //______________________________________________________________________________ Int_t TH1::GetContour(Double_t *levels) { // Return contour values into array levels if pointer levels is non zero // // The function returns the number of contour levels. // see GetContourLevel to return one contour only // Int_t nlevels = fContour.fN; if (levels) { if (nlevels == 0) { nlevels = 20; SetContour(nlevels); } else { if (TestBit(kUserContour) == 0) SetContour(nlevels); } for (Int_t level=0; level<nlevels; level++) levels[level] = fContour.fArray[level]; } return nlevels; } //______________________________________________________________________________ Double_t TH1::GetContourLevel(Int_t level) const { // Return value of contour number level // see GetContour to return the array of all contour levels if (level <0 || level >= fContour.fN) return 0; Double_t zlevel = fContour.fArray[level]; return zlevel; } //______________________________________________________________________________ Double_t TH1::GetContourLevelPad(Int_t level) const { // Return the value of contour number "level" in Pad coordinates ie: if the Pad // is in log scale along Z it returns le log of the contour level value. // see GetContour to return the array of all contour levels if (level <0 || level >= fContour.fN) return 0; Double_t zlevel = fContour.fArray[level]; // In case of user defined contours and Pad in log scale along Z, // fContour.fArray doesn't contain the log of the contour whereas it does // in case of equidistant contours. if (gPad && gPad->GetLogz() && TestBit(kUserContour)) { if (zlevel <= 0) return 0; zlevel = TMath::Log10(zlevel); } return zlevel; } //______________________________________________________________________________ void TH1::SetBuffer(Int_t buffersize, Option_t * /*option*/) { // set the maximum number of entries to be kept in the buffer if (fBuffer) { BufferEmpty(); delete [] fBuffer; fBuffer = 0; } if (buffersize <= 0) { fBufferSize = 0; return; } if (buffersize < 100) buffersize = 100; fBufferSize = 1 + buffersize*(fDimension+1); fBuffer = new Double_t[fBufferSize]; memset(fBuffer,0,8*fBufferSize); } //______________________________________________________________________________ void TH1::SetContour(Int_t nlevels, const Double_t *levels) { // -*-*-*-*-*-*Set the number and values of contour levels*-*-*-*-*-*-*-*-* // =========================================== // // By default the number of contour levels is set to 20. // // if argument levels = 0 or missing, equidistant contours are computed // Int_t level; ResetBit(kUserContour); if (nlevels <=0 ) { fContour.Set(0); return; } fContour.Set(nlevels); // - Contour levels are specified if (levels) { SetBit(kUserContour); for (level=0; level<nlevels; level++) fContour.fArray[level] = levels[level]; } else { // - contour levels are computed automatically as equidistant contours Double_t zmin = GetMinimum(); Double_t zmax = GetMaximum(); if ((zmin == zmax) && (zmin != 0)) { zmax += 0.01*TMath::Abs(zmax); zmin -= 0.01*TMath::Abs(zmin); } Double_t dz = (zmax-zmin)/Double_t(nlevels); if (gPad && gPad->GetLogz()) { if (zmax <= 0) return; if (zmin <= 0) zmin = 0.001*zmax; zmin = TMath::Log10(zmin); zmax = TMath::Log10(zmax); dz = (zmax-zmin)/Double_t(nlevels); } for (level=0; level<nlevels; level++) { fContour.fArray[level] = zmin + dz*Double_t(level); } } } //______________________________________________________________________________ void TH1::SetContourLevel(Int_t level, Double_t value) { // -*-*-*-*-*-*-*-*-*Set value for one contour level*-*-*-*-*-*-*-*-*-*-*-* // =============================== if (level <0 || level >= fContour.fN) return; SetBit(kUserContour); fContour.fArray[level] = value; } //______________________________________________________________________________ Double_t TH1::GetMaximum(Double_t maxval) const { // Return maximum value smaller than maxval of bins in the range*-*-*-*-*-* if (fMaximum != -1111) return fMaximum; Int_t bin, binx, biny, binz; Int_t xfirst = fXaxis.GetFirst(); Int_t xlast = fXaxis.GetLast(); Int_t yfirst = fYaxis.GetFirst(); Int_t ylast = fYaxis.GetLast(); Int_t zfirst = fZaxis.GetFirst(); Int_t zlast = fZaxis.GetLast(); Double_t maximum = -FLT_MAX, value; for (binz=zfirst;binz<=zlast;binz++) { for (biny=yfirst;biny<=ylast;biny++) { for (binx=xfirst;binx<=xlast;binx++) { bin = GetBin(binx,biny,binz); value = GetBinContent(bin); if (value > maximum && value < maxval) maximum = value; } } } return maximum; } //______________________________________________________________________________ Int_t TH1::GetMaximumBin() const { // -*-*-*-*-*Return location of bin with maximum value in the range*-* // ====================================================== Int_t locmax, locmay, locmaz; return GetMaximumBin(locmax, locmay, locmaz); } //______________________________________________________________________________ Int_t TH1::GetMaximumBin(Int_t &locmax, Int_t &locmay, Int_t &locmaz) const { // -*-*-*-*-*Return location of bin with maximum value in the range*-* // ====================================================== Int_t bin, binx, biny, binz; Int_t locm; Int_t xfirst = fXaxis.GetFirst(); Int_t xlast = fXaxis.GetLast(); Int_t yfirst = fYaxis.GetFirst(); Int_t ylast = fYaxis.GetLast(); Int_t zfirst = fZaxis.GetFirst(); Int_t zlast = fZaxis.GetLast(); Double_t maximum = -FLT_MAX, value; locm = locmax = locmay = locmaz = 0; for (binz=zfirst;binz<=zlast;binz++) { for (biny=yfirst;biny<=ylast;biny++) { for (binx=xfirst;binx<=xlast;binx++) { bin = GetBin(binx,biny,binz); value = GetBinContent(bin); if (value > maximum) { maximum = value; locm = bin; locmax = binx; locmay = biny; locmaz = binz; } } } } return locm; } //______________________________________________________________________________ Double_t TH1::GetMinimum(Double_t minval) const { // Return minimum value greater than minval of bins in the range if (fMinimum != -1111) return fMinimum; Int_t bin, binx, biny, binz; Int_t xfirst = fXaxis.GetFirst(); Int_t xlast = fXaxis.GetLast(); Int_t yfirst = fYaxis.GetFirst(); Int_t ylast = fYaxis.GetLast(); Int_t zfirst = fZaxis.GetFirst(); Int_t zlast = fZaxis.GetLast(); Double_t minimum=FLT_MAX, value; for (binz=zfirst;binz<=zlast;binz++) { for (biny=yfirst;biny<=ylast;biny++) { for (binx=xfirst;binx<=xlast;binx++) { bin = GetBin(binx,biny,binz); value = GetBinContent(bin); if (value < minimum && value > minval) minimum = value; } } } return minimum; } //______________________________________________________________________________ Int_t TH1::GetMinimumBin() const { // -*-*-*-*-*Return location of bin with minimum value in the range*-* // ====================================================== Int_t locmix, locmiy, locmiz; return GetMinimumBin(locmix, locmiy, locmiz); } //______________________________________________________________________________ Int_t TH1::GetMinimumBin(Int_t &locmix, Int_t &locmiy, Int_t &locmiz) const { // -*-*-*-*-*Return location of bin with minimum value in the range*-* // ====================================================== Int_t bin, binx, biny, binz; Int_t locm; Int_t xfirst = fXaxis.GetFirst(); Int_t xlast = fXaxis.GetLast(); Int_t yfirst = fYaxis.GetFirst(); Int_t ylast = fYaxis.GetLast(); Int_t zfirst = fZaxis.GetFirst(); Int_t zlast = fZaxis.GetLast(); Double_t minimum = FLT_MAX, value; locm = locmix = locmiy = locmiz = 0; for (binz=zfirst;binz<=zlast;binz++) { for (biny=yfirst;biny<=ylast;biny++) { for (binx=xfirst;binx<=xlast;binx++) { bin = GetBin(binx,biny,binz); value = GetBinContent(bin); if (value < minimum) { minimum = value; locm = bin; locmix = binx; locmiy = biny; locmiz = binz; } } } } return locm; } //______________________________________________________________________________ void TH1::SetBins(Int_t nx, Double_t xmin, Double_t xmax) { // -*-*-*-*-*-*-*Redefine x axis parameters*-*-*-*-*-*-*-*-*-*-*-* // =========================== // The X axis parameters are modified. // The bins content array is resized // if errors (Sumw2) the errors array is resized // The previous bin contents are lost // To change only the axis limits, see TAxis::SetRange if (GetDimension() != 1) { Error("SetBins","Operation only valid for 1-d histograms"); return; } fXaxis.SetRange(0,0); fXaxis.Set(nx,xmin,xmax); fYaxis.Set(1,0,1); fZaxis.Set(1,0,1); fNcells = nx+2; SetBinsLength(fNcells); if (fSumw2.fN) { fSumw2.Set(fNcells); } } //______________________________________________________________________________ void TH1::SetBins(Int_t nx, const Double_t *xBins) { // -*-*-*-*-*-*-*Redefine x axis parameters with variable bin sizes *-*-*-*-*-*-*-*-*-* // =================================================== // The X axis parameters are modified. // The bins content array is resized // if errors (Sumw2) the errors array is resized // The previous bin contents are lost // To change only the axis limits, see TAxis::SetRange // xBins is supposed to be of length nx+1 if (GetDimension() != 1) { Error("SetBins","Operation only valid for 1-d histograms"); return; } fXaxis.SetRange(0,0); fXaxis.Set(nx,xBins); fYaxis.Set(1,0,1); fZaxis.Set(1,0,1); fNcells = nx+2; SetBinsLength(fNcells); if (fSumw2.fN) { fSumw2.Set(fNcells); } } //______________________________________________________________________________ void TH1::SetBins(Int_t nx, Double_t xmin, Double_t xmax, Int_t ny, Double_t ymin, Double_t ymax) { // -*-*-*-*-*-*-*Redefine x and y axis parameters*-*-*-*-*-*-*-*-*-*-*-* // ================================= // The X and Y axis parameters are modified. // The bins content array is resized // if errors (Sumw2) the errors array is resized // The previous bin contents are lost // To change only the axis limits, see TAxis::SetRange if (GetDimension() != 2) { Error("SetBins","Operation only valid for 2-D histograms"); return; } fXaxis.SetRange(0,0); fYaxis.SetRange(0,0); fXaxis.Set(nx,xmin,xmax); fYaxis.Set(ny,ymin,ymax); fZaxis.Set(1,0,1); fNcells = (nx+2)*(ny+2); SetBinsLength(fNcells); if (fSumw2.fN) { fSumw2.Set(fNcells); } } //______________________________________________________________________________ void TH1::SetBins(Int_t nx, const Double_t *xBins, Int_t ny, const Double_t *yBins) { // -*-*-*-*-*-*-*Redefine x and y axis parameters with variable bin sizes *-*-*-*-*-*-*-*-* // ========================================================= // The X and Y axis parameters are modified. // The bins content array is resized // if errors (Sumw2) the errors array is resized // The previous bin contents are lost // To change only the axis limits, see TAxis::SetRange // xBins is supposed to be of length nx+1, yBins is supposed to be of length ny+1 if (GetDimension() != 2) { Error("SetBins","Operation only valid for 2-D histograms"); return; } fXaxis.SetRange(0,0); fYaxis.SetRange(0,0); fXaxis.Set(nx,xBins); fYaxis.Set(ny,yBins); fZaxis.Set(1,0,1); fNcells = (nx+2)*(ny+2); SetBinsLength(fNcells); if (fSumw2.fN) { fSumw2.Set(fNcells); } } //______________________________________________________________________________ void TH1::SetBins(Int_t nx, Double_t xmin, Double_t xmax, Int_t ny, Double_t ymin, Double_t ymax, Int_t nz, Double_t zmin, Double_t zmax) { // -*-*-*-*-*-*-*Redefine x, y and z axis parameters*-*-*-*-*-*-*-*-*-*-*-* // ==================================== // The X, Y and Z axis parameters are modified. // The bins content array is resized // if errors (Sumw2) the errors array is resized // The previous bin contents are lost // To change only the axis limits, see TAxis::SetRange if (GetDimension() != 3) { Error("SetBins","Operation only valid for 3-D histograms"); return; } fXaxis.SetRange(0,0); fYaxis.SetRange(0,0); fZaxis.SetRange(0,0); fXaxis.Set(nx,xmin,xmax); fYaxis.Set(ny,ymin,ymax); fZaxis.Set(nz,zmin,zmax); fNcells = (nx+2)*(ny+2)*(nz+2); SetBinsLength(fNcells); if (fSumw2.fN) { fSumw2.Set(fNcells); } } //______________________________________________________________________________ void TH1::SetMaximum(Double_t maximum) { // -*-*-*-*-*-*-*Set the maximum value for the Y axis*-*-*-*-*-*-*-*-*-*-*-* // ==================================== // By default the maximum value is automatically set to the maximum // bin content plus a margin of 10 per cent. // Use TH1::GetMaximum to find the maximum value of an histogram // Use TH1::GetMaximumBin to find the bin with the maximum value of an histogram // fMaximum = maximum; } //______________________________________________________________________________ void TH1::SetMinimum(Double_t minimum) { // -*-*-*-*-*-*-*Set the minimum value for the Y axis*-*-*-*-*-*-*-*-*-*-*-* // ==================================== // By default the minimum value is automatically set to zero if all bin contents // are positive or the minimum - 10 per cent otherwise. // Use TH1::GetMinimum to find the minimum value of an histogram // Use TH1::GetMinimumBin to find the bin with the minimum value of an histogram // fMinimum = minimum; } //______________________________________________________________________________ void TH1::SetDirectory(TDirectory *dir) { // By default when an histogram is created, it is added to the list // of histogram objects in the current directory in memory. // Remove reference to this histogram from current directory and add // reference to new directory dir. dir can be 0 in which case the // histogram does not belong to any directory. if (fDirectory == dir) return; if (fDirectory) fDirectory->Remove(this); fDirectory = dir; if (fDirectory) fDirectory->Append(this); } //______________________________________________________________________________ void TH1::SetError(const Double_t *error) { // -*-*-*-*-*-*-*Replace bin errors by values in array error*-*-*-*-*-*-*-*-* // =========================================== Int_t bin; Double_t binerror; for (bin=0; bin<fNcells; bin++) { binerror = error[bin]; SetBinError(bin, binerror); } } //______________________________________________________________________________ void TH1::SetName(const char *name) { // Change the name of this histogram // // Histograms are named objects in a THashList. // We must update the hashlist if we change the name if (fDirectory) fDirectory->Remove(this); fName = name; if (fDirectory) fDirectory->Append(this); } //______________________________________________________________________________ void TH1::SetNameTitle(const char *name, const char *title) { // Change the name and title of this histogram // // Histograms are named objects in a THashList. // We must update the hashlist if we change the name if (fDirectory) fDirectory->Remove(this); fName = name; SetTitle(title); if (fDirectory) fDirectory->Append(this); } //______________________________________________________________________________ void TH1::SetStats(Bool_t stats) { // -*-*-*-*-*-*-*Set statistics option on/off // ============================ // By default, the statistics box is drawn. // The paint options can be selected via gStyle->SetOptStats. // This function sets/resets the kNoStats bin in the histogram object. // It has priority over the Style option. ResetBit(kNoStats); if (!stats) { SetBit(kNoStats); //remove the "stats" object from the list of functions if (fFunctions) { TObject *obj = fFunctions->FindObject("stats"); if (obj) { fFunctions->Remove(obj); delete obj; } } } } //______________________________________________________________________________ void TH1::Sumw2() { // Create structure to store sum of squares of weights*-*-*-*-*-*-*-* // // if histogram is already filled, the sum of squares of weights // is filled with the existing bin contents // // The error per bin will be computed as sqrt(sum of squares of weight) // for each bin. // // This function is automatically called when the histogram is created // if the static function TH1::SetDefaultSumw2 has been called before. if (fSumw2.fN == fNcells) { if (!fgDefaultSumw2 ) Warning("Sumw2","Sum of squares of weights structure already created"); return; } fSumw2.Set(fNcells); if ( fEntries > 0 ) for (Int_t bin=0; bin<fNcells; bin++) { fSumw2.fArray[bin] = GetBinContent(bin); } } //______________________________________________________________________________ TF1 *TH1::GetFunction(const char *name) const { // -*-*-*Return pointer to function with name*-*-*-*-*-*-*-*-*-*-*-*-* // =================================== // // Functions such as TH1::Fit store the fitted function in the list of // functions of this histogram. return (TF1*)fFunctions->FindObject(name); } //______________________________________________________________________________ Double_t TH1::GetBinError(Int_t bin) const { // -*-*-*-*-*Return value of error associated to bin number bin*-*-*-*-* // ================================================== // // if the sum of squares of weights has been defined (via Sumw2), // this function returns the sqrt(sum of w2). // otherwise it returns the sqrt(contents) for this bin. // // -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* if (bin < 0) bin = 0; if (bin >= fNcells) bin = fNcells-1; if (fBuffer) ((TH1*)this)->BufferEmpty(); if (fSumw2.fN) { Double_t err2 = fSumw2.fArray[bin]; return TMath::Sqrt(err2); } Double_t error2 = TMath::Abs(GetBinContent(bin)); return TMath::Sqrt(error2); } //______________________________________________________________________________ Double_t TH1::GetBinError(Int_t binx, Int_t biny) const { // -*-*-*-*-*Return error of bin number binx, biny // ===================================== // NB: Function to be called for 2-D histograms only Int_t bin = GetBin(binx,biny); return GetBinError(bin); } //______________________________________________________________________________ Double_t TH1::GetBinError(Int_t binx, Int_t biny, Int_t binz) const { // -*-*-*-*-*Return error of bin number binx,biny,binz // ========================================= // NB: Function to be called for 3-D histograms only Int_t bin = GetBin(binx,biny,binz); return GetBinError(bin); } //______________________________________________________________________________ Double_t TH1::GetCellContent(Int_t binx, Int_t biny) const { // -*-*-*-*-*Return content of bin number binx, biny // ===================================== // NB: Function to be called for 2-D histograms only Int_t bin = GetBin(binx,biny); return GetBinContent(bin); } //______________________________________________________________________________ Double_t TH1::GetCellError(Int_t binx, Int_t biny) const { // -*-*-*-*-*Return error of bin number binx, biny // ===================================== // NB: Function to be called for 2-D histograms only Int_t bin = GetBin(binx,biny); return GetBinError(bin); } //______________________________________________________________________________ void TH1::SetBinError(Int_t bin, Double_t error) { // see convention for numbering bins in TH1::GetBin if (!fSumw2.fN) Sumw2(); if (bin <0 || bin>= fSumw2.fN) return; fSumw2.fArray[bin] = error*error; } //______________________________________________________________________________ void TH1::SetBinContent(Int_t binx, Int_t biny, Double_t content) { // see convention for numbering bins in TH1::GetBin if (binx <0 || binx>fXaxis.GetNbins()+1) return; if (biny <0 || biny>fYaxis.GetNbins()+1) return; Int_t bin = GetBin(binx,biny); SetBinContent(bin,content); } //______________________________________________________________________________ void TH1::SetBinContent(Int_t binx, Int_t biny, Int_t binz, Double_t content) { // see convention for numbering bins in TH1::GetBin if (binx <0 || binx>fXaxis.GetNbins()+1) return; if (biny <0 || biny>fYaxis.GetNbins()+1) return; if (binz <0 || binz>fZaxis.GetNbins()+1) return; Int_t bin = GetBin(binx,biny,binz); SetBinContent(bin,content); } //______________________________________________________________________________ void TH1::SetCellContent(Int_t binx, Int_t biny, Double_t content) { // Set cell content. if (binx <0 || binx>fXaxis.GetNbins()+1) return; if (biny <0 || biny>fYaxis.GetNbins()+1) return; Int_t bin = GetBin(binx,biny); SetBinContent(bin,content); } //______________________________________________________________________________ void TH1::SetBinError(Int_t binx, Int_t biny, Double_t error) { // see convention for numbering bins in TH1::GetBin if (binx <0 || binx>fXaxis.GetNbins()+1) return; if (biny <0 || biny>fYaxis.GetNbins()+1) return; Int_t bin = GetBin(binx,biny); SetBinError(bin,error); } //______________________________________________________________________________ void TH1::SetBinError(Int_t binx, Int_t biny, Int_t binz, Double_t error) { // see convention for numbering bins in TH1::GetBin if (binx <0 || binx>fXaxis.GetNbins()+1) return; if (biny <0 || biny>fYaxis.GetNbins()+1) return; if (binz <0 || binz>fZaxis.GetNbins()+1) return; Int_t bin = GetBin(binx,biny,binz); SetBinError(bin,error); } //______________________________________________________________________________ void TH1::SetCellError(Int_t binx, Int_t biny, Double_t error) { // see convention for numbering bins in TH1::GetBin if (binx <0 || binx>fXaxis.GetNbins()+1) return; if (biny <0 || biny>fYaxis.GetNbins()+1) return; if (!fSumw2.fN) Sumw2(); Int_t bin = biny*(fXaxis.GetNbins()+2) + binx; fSumw2.fArray[bin] = error*error; } //______________________________________________________________________________ void TH1::SetBinContent(Int_t, Double_t) { // see convention for numbering bins in TH1::GetBin AbstractMethod("SetBinContent"); } //______________________________________________________________________________ TH1 *TH1::ShowBackground(Int_t niter, Option_t *option) { // This function calculates the background spectrum in this histogram. // The background is returned as a histogram. // // Function parameters: // -niter, number of iterations (default value = 2) // Increasing niter make the result smoother and lower. // -option: may contain one of the following options // - to set the direction parameter // "BackDecreasingWindow". By default the direction is BackIncreasingWindow // - filterOrder-order of clipping filter, (default "BackOrder2" // -possible values= "BackOrder4" // "BackOrder6" // "BackOrder8" // - "nosmoothing"- if selected, the background is not smoothed // By default the background is smoothed. // - smoothWindow-width of smoothing window, (default is "BackSmoothing3") // -possible values= "BackSmoothing5" // "BackSmoothing7" // "BackSmoothing9" // "BackSmoothing11" // "BackSmoothing13" // "BackSmoothing15" // - "nocompton"- if selected the estimation of Compton edge // will be not be included (by default the compton estimation is set) // - "same" : if this option is specified, the resulting background // histogram is superimposed on the picture in the current pad. // This option is given by default. // // NOTE that the background is only evaluated in the current range of this histogram. // i.e., if this has a bin range (set via h->GetXaxis()->SetRange(binmin, binmax), // the returned histogram will be created with the same number of bins // as this input histogram, but only bins from binmin to binmax will be filled // with the estimated background. // return (TH1*)gROOT->ProcessLineFast(Form("TSpectrum::StaticBackground((TH1*)0x%lx,%d,\"%s\")",this,niter,option)); } //______________________________________________________________________________ Int_t TH1::ShowPeaks(Double_t sigma, Option_t *option, Double_t threshold) { //Interface to TSpectrum::Search //the function finds peaks in this histogram where the width is > sigma //and the peak maximum greater than threshold*maximum bin content of this. //for more detauils see TSpectrum::Search. //note the difference in the default value for option compared to TSpectrum::Search //option="" by default (instead of "goff") return (Int_t)gROOT->ProcessLineFast(Form("TSpectrum::StaticSearch((TH1*)0x%lx,%g,\"%s\",%g)",this,sigma,option,threshold)); } //______________________________________________________________________________ TH1* TH1::TransformHisto(TVirtualFFT *fft, TH1* h_output, Option_t *option) { //For a given transform (first parameter), fills the histogram (second parameter) //with the transform output data, specified in the third parameter //If the 2nd parameter h_output is empty, a new histogram (TH1D or TH2D) is created //and the user is responsible for deleting it. // Available options: // "RE" - real part of the output // "IM" - imaginary part of the output // "MAG" - magnitude of the output // "PH" - phase of the output if (fft->GetNdim()>2){ printf("Only 1d and 2d\n"); return 0; } Int_t binx,biny; TString opt = option; opt.ToUpper(); Int_t *n = fft->GetN(); TH1 *hout=0; if (h_output) hout = h_output; else { char name[10]; sprintf(name, "out_%s", opt.Data()); if (fft->GetNdim()==1) hout = new TH1D(name, name,n[0], 0, n[0]); else if (fft->GetNdim()==2) hout = new TH2D(name, name, n[0], 0, n[0], n[1], 0, n[1]); } TString type=fft->GetType(); Int_t ind[2]; if (opt.Contains("RE")){ if (type.Contains("2C") || type.Contains("2HC")) { Double_t re, im; for (binx = 1; binx<=hout->GetNbinsX(); binx++) { for (biny=1; biny<=hout->GetNbinsY(); biny++) { ind[0] = binx-1; ind[1] = biny-1; fft->GetPointComplex(ind, re, im); hout->SetBinContent(binx, biny, re); } } } else { for (binx = 1; binx<=hout->GetNbinsX(); binx++) { for (biny=1; biny<=hout->GetNbinsY(); biny++) { ind[0] = binx-1; ind[1] = biny-1; hout->SetBinContent(binx, biny, fft->GetPointReal(ind)); } } } } if (opt.Contains("IM")) { if (type.Contains("2C") || type.Contains("2HC")) { Double_t re, im; for (binx = 1; binx<=hout->GetNbinsX(); binx++) { for (biny=1; biny<=hout->GetNbinsY(); biny++) { ind[0] = binx-1; ind[1] = biny-1; fft->GetPointComplex(ind, re, im); hout->SetBinContent(binx, biny, im); } } } else { printf("No complex numbers in the output"); return 0; } } if (opt.Contains("MA")) { if (type.Contains("2C") || type.Contains("2HC")) { Double_t re, im; for (binx = 1; binx<=hout->GetNbinsX(); binx++) { for (biny=1; biny<=hout->GetNbinsY(); biny++) { ind[0] = binx-1; ind[1] = biny-1; fft->GetPointComplex(ind, re, im); hout->SetBinContent(binx, biny, TMath::Sqrt(re*re + im*im)); } } } else { for (binx = 1; binx<=hout->GetNbinsX(); binx++) { for (biny=1; biny<=hout->GetNbinsY(); biny++) { ind[0] = binx-1; ind[1] = biny-1; hout->SetBinContent(binx, biny, TMath::Abs(fft->GetPointReal(ind))); } } } } if (opt.Contains("PH")) { if (type.Contains("2C") || type.Contains("2HC")){ Double_t re, im, ph; for (binx = 1; binx<=hout->GetNbinsX(); binx++){ for (biny=1; biny<=hout->GetNbinsY(); biny++){ ind[0] = binx-1; ind[1] = biny-1; fft->GetPointComplex(ind, re, im); if (TMath::Abs(re) > 1e-13){ ph = TMath::ATan(im/re); //find the correct quadrant if (re<0 && im<0) ph -= TMath::Pi(); if (re<0 && im>=0) ph += TMath::Pi(); } else { if (TMath::Abs(im) < 1e-13) ph = 0; else if (im>0) ph = TMath::Pi()*0.5; else ph = -TMath::Pi()*0.5; } hout->SetBinContent(binx, biny, ph); } } } else { printf("Pure real output, no phase"); return 0; } } return hout; } //______________________________________________________________________________ // TH1C methods // TH1C : histograms with one byte per channel. Maximum bin content = 127 //______________________________________________________________________________ ClassImp(TH1C) //______________________________________________________________________________ TH1C::TH1C(): TH1(), TArrayC() { // Constructor. fDimension = 1; SetBinsLength(3); if (fgDefaultSumw2) Sumw2(); } //______________________________________________________________________________ TH1C::TH1C(const char *name,const char *title,Int_t nbins,Double_t xlow,Double_t xup) : TH1(name,title,nbins,xlow,xup) { // // Create a 1-Dim histogram with fix bins of type char (one byte per channel) // ========================================================================== // (see TH1::TH1 for explanation of parameters) // fDimension = 1; TArrayC::Set(fNcells); if (xlow >= xup) SetBuffer(fgBufferSize); if (fgDefaultSumw2) Sumw2(); } //______________________________________________________________________________ TH1C::TH1C(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 char (one byte per channel) // ========================================================================== // (see TH1::TH1 for explanation of parameters) // fDimension = 1; TArrayC::Set(fNcells); if (fgDefaultSumw2) Sumw2(); } //______________________________________________________________________________ TH1C::TH1C(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 char (one byte per channel) // ========================================================================== // (see TH1::TH1 for explanation of parameters) // fDimension = 1; TArrayC::Set(fNcells); if (fgDefaultSumw2) Sumw2(); } //______________________________________________________________________________ TH1C::~TH1C() { // Destructor. } //______________________________________________________________________________ TH1C::TH1C(const TH1C &h1c) : TH1(), TArrayC() { // Copy constructor. ((TH1C&)h1c).Copy(*this); } //______________________________________________________________________________ void TH1C::AddBinContent(Int_t bin) { // -*-*-*-*-*-*-*-*Increment bin content by 1*-*-*-*-*-*-*-*-*-*-*-*-*-* // ========================== if (fArray[bin] < 127) fArray[bin]++; } //______________________________________________________________________________ void TH1C::AddBinContent(Int_t bin, Double_t w) { // -*-*-*-*-*-*-*-*Increment bin content by w*-*-*-*-*-*-*-*-*-*-*-*-*-* // ========================== Int_t newval = fArray[bin] + Int_t(w); if (newval > -128 && newval < 128) {fArray[bin] = Char_t(newval); return;} if (newval < -127) fArray[bin] = -127; if (newval > 127) fArray[bin] = 127; } //______________________________________________________________________________ void TH1C::Copy(TObject &newth1) const { // Copy this to newth1 TH1::Copy(newth1); } //______________________________________________________________________________ TH1 *TH1C::DrawCopy(Option_t *option) const { // Draw copy. TString opt = option; opt.ToLower(); if (gPad && !opt.Contains("same")) gPad->Clear(); TH1C *newth1 = (TH1C*)Clone(); newth1->SetDirectory(0); newth1->SetBit(kCanDelete); newth1->AppendPad(option); return newth1; } //______________________________________________________________________________ Double_t TH1C::GetBinContent(Int_t bin) const { // see convention for numbering bins in TH1::GetBin if (fBuffer) ((TH1C*)this)->BufferEmpty(); if (bin < 0) bin = 0; if (bin >= fNcells) bin = fNcells-1; if (!fArray) return 0; return Double_t (fArray[bin]); } //______________________________________________________________________________ void TH1C::Reset(Option_t *option) { // Reset. TH1::Reset(option); TArrayC::Reset(); } //______________________________________________________________________________ void TH1C::SetBinContent(Int_t bin, Double_t content) { // Set bin content // see convention for numbering bins in TH1::GetBin // 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 if (bin < 0) return; if (bin >= fNcells-1) { if (fXaxis.GetTimeDisplay()) { while (bin >= fNcells-1) LabelsInflate(); } else { if (!TestBit(kCanRebin)) { if (bin == fNcells-1) fArray[bin] = Char_t (content); return; } while (bin >= fNcells-1) LabelsInflate(); } } fArray[bin] = Char_t (content); fEntries++; fTsumw = 0; } //______________________________________________________________________________ void TH1C::SetBinsLength(Int_t n) { // Set total number of bins including under/overflow // Reallocate bin contents array if (n < 0) n = fXaxis.GetNbins() + 2; fNcells = n; TArrayC::Set(n); } //______________________________________________________________________________ TH1C& TH1C::operator=(const TH1C &h1) { // Operator = if (this != &h1) ((TH1C&)h1).Copy(*this); return *this; } //______________________________________________________________________________ TH1C operator*(Double_t c1, const TH1C &h1) { // Operator * TH1C hnew = h1; hnew.Scale(c1); hnew.SetDirectory(0); return hnew; } //______________________________________________________________________________ TH1C operator+(const TH1C &h1, const TH1C &h2) { // Operator + TH1C hnew = h1; hnew.Add(&h2,1); hnew.SetDirectory(0); return hnew; } //______________________________________________________________________________ TH1C operator-(const TH1C &h1, const TH1C &h2) { // Operator - TH1C hnew = h1; hnew.Add(&h2,-1); hnew.SetDirectory(0); return hnew; } //______________________________________________________________________________ TH1C operator*(const TH1C &h1, const TH1C &h2) { // Operator * TH1C hnew = h1; hnew.Multiply(&h2); hnew.SetDirectory(0); return hnew; } //______________________________________________________________________________ TH1C operator/(const TH1C &h1, const TH1C &h2) { // Operator / TH1C hnew = h1; hnew.Divide(&h2); hnew.SetDirectory(0); return hnew; } //______________________________________________________________________________ // TH1S methods // TH1S : histograms with one short per channel. Maximum bin content = 32767 //______________________________________________________________________________ ClassImp(TH1S) //______________________________________________________________________________ TH1S::TH1S(): TH1(), TArrayS() { // Constructor. fDimension = 1; SetBinsLength(3); if (fgDefaultSumw2) Sumw2(); } //______________________________________________________________________________ TH1S::TH1S(const char *name,const char *title,Int_t nbins,Double_t xlow,Double_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) // fDimension = 1; TArrayS::Set(fNcells); if (xlow >= xup) SetBuffer(fgBufferSize); if (fgDefaultSumw2) Sumw2(); } //______________________________________________________________________________ TH1S::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) // fDimension = 1; TArrayS::Set(fNcells); if (fgDefaultSumw2) Sumw2(); } //______________________________________________________________________________ TH1S::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) // fDimension = 1; TArrayS::Set(fNcells); if (fgDefaultSumw2) Sumw2(); } //______________________________________________________________________________ TH1S::~TH1S() { // Destructor. } //______________________________________________________________________________ TH1S::TH1S(const TH1S &h1s) : TH1(), TArrayS() { // Copy constructor. ((TH1S&)h1s).Copy(*this); } //______________________________________________________________________________ void TH1S::AddBinContent(Int_t bin) { // -*-*-*-*-*-*-*-*Increment bin content by 1*-*-*-*-*-*-*-*-*-*-*-*-*-* // ========================== if (fArray[bin] < 32767) fArray[bin]++; } //______________________________________________________________________________ void TH1S::AddBinContent(Int_t bin, Double_t w) { // Increment bin content by w // ========================== Int_t newval = fArray[bin] + Int_t(w); if (newval > -32768 && newval < 32768) {fArray[bin] = Short_t(newval); return;} if (newval < -32767) fArray[bin] = -32767; if (newval > 32767) fArray[bin] = 32767; } //______________________________________________________________________________ void TH1S::Copy(TObject &newth1) const { // Copy this to newth1 TH1::Copy(newth1); } //______________________________________________________________________________ TH1 *TH1S::DrawCopy(Option_t *option) const { // Draw copy. TString opt = option; opt.ToLower(); if (gPad && !opt.Contains("same")) gPad->Clear(); TH1S *newth1 = (TH1S*)Clone(); newth1->SetDirectory(0); newth1->SetBit(kCanDelete); newth1->AppendPad(option); return newth1; } //______________________________________________________________________________ Double_t TH1S::GetBinContent(Int_t bin) const { // see convention for numbering bins in TH1::GetBin if (fBuffer) ((TH1S*)this)->BufferEmpty(); if (bin < 0) bin = 0; if (bin >= fNcells) bin = fNcells-1; if (!fArray) return 0; return Double_t (fArray[bin]); } //______________________________________________________________________________ void TH1S::Reset(Option_t *option) { // Reset. TH1::Reset(option); TArrayS::Reset(); } //______________________________________________________________________________ void TH1S::SetBinContent(Int_t bin, Double_t content) { // Set bin content // see convention for numbering bins in TH1::GetBin // 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 if (bin < 0) return; if (bin >= fNcells-1) { if (fXaxis.GetTimeDisplay()) { while (bin >= fNcells-1) LabelsInflate(); } else { if (!TestBit(kCanRebin)) { if (bin == fNcells-1) fArray[bin] = Short_t (content); return; } while (bin >= fNcells-1) LabelsInflate(); } } fArray[bin] = Short_t (content); fEntries++; fTsumw = 0; } //______________________________________________________________________________ void TH1S::SetBinsLength(Int_t n) { // Set total number of bins including under/overflow // Reallocate bin contents array if (n < 0) n = fXaxis.GetNbins() + 2; fNcells = n; TArrayS::Set(n); } //______________________________________________________________________________ TH1S& TH1S::operator=(const TH1S &h1) { // Operator = if (this != &h1) ((TH1S&)h1).Copy(*this); return *this; } //______________________________________________________________________________ TH1S operator*(Double_t c1, const TH1S &h1) { // Operator * TH1S hnew = h1; hnew.Scale(c1); hnew.SetDirectory(0); return hnew; } //______________________________________________________________________________ TH1S operator+(const TH1S &h1, const TH1S &h2) { // Operator + TH1S hnew = h1; hnew.Add(&h2,1); hnew.SetDirectory(0); return hnew; } //______________________________________________________________________________ TH1S operator-(const TH1S &h1, const TH1S &h2) { // Operator - TH1S hnew = h1; hnew.Add(&h2,-1); hnew.SetDirectory(0); return hnew; } //______________________________________________________________________________ TH1S operator*(const TH1S &h1, const TH1S &h2) { // Operator * TH1S hnew = h1; hnew.Multiply(&h2); hnew.SetDirectory(0); return hnew; } //______________________________________________________________________________ TH1S operator/(const TH1S &h1, const TH1S &h2) { // Operator / TH1S hnew = h1; hnew.Divide(&h2); hnew.SetDirectory(0); return hnew; } //______________________________________________________________________________ // TH1I methods // TH1I : histograms with one int per channel. Maximum bin content = 2147483647 //______________________________________________________________________________ ClassImp(TH1I) //______________________________________________________________________________ TH1I::TH1I(): TH1(), TArrayI() { // Constructor. fDimension = 1; SetBinsLength(3); if (fgDefaultSumw2) Sumw2(); } //______________________________________________________________________________ TH1I::TH1I(const char *name,const char *title,Int_t nbins,Double_t xlow,Double_t xup) : TH1(name,title,nbins,xlow,xup) { // // Create a 1-Dim histogram with fix bins of type integer // ==================================================== // (see TH1::TH1 for explanation of parameters) // fDimension = 1; TArrayI::Set(fNcells); if (xlow >= xup) SetBuffer(fgBufferSize); if (fgDefaultSumw2) Sumw2(); } //______________________________________________________________________________ TH1I::TH1I(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 integer // ========================================================= // (see TH1::TH1 for explanation of parameters) // fDimension = 1; TArrayI::Set(fNcells); if (fgDefaultSumw2) Sumw2(); } //______________________________________________________________________________ TH1I::TH1I(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 integer // ========================================================= // (see TH1::TH1 for explanation of parameters) // fDimension = 1; TArrayI::Set(fNcells); } //______________________________________________________________________________ TH1I::~TH1I() { // Destructor. } //______________________________________________________________________________ TH1I::TH1I(const TH1I &h1i) : TH1(), TArrayI() { // Copy constructor. ((TH1I&)h1i).Copy(*this); } //______________________________________________________________________________ void TH1I::AddBinContent(Int_t bin) { // -*-*-*-*-*-*-*-*Increment bin content by 1*-*-*-*-*-*-*-*-*-*-*-*-*-* // ========================== if (fArray[bin] < 2147483647) fArray[bin]++; } //______________________________________________________________________________ void TH1I::AddBinContent(Int_t bin, Double_t w) { // Increment bin content by w // ========================== Int_t newval = fArray[bin] + Int_t(w); if (newval > -2147483647 && newval < 2147483647) {fArray[bin] = Int_t(newval); return;} if (newval < -2147483647) fArray[bin] = -2147483647; if (newval > 2147483647) fArray[bin] = 2147483647; } //______________________________________________________________________________ void TH1I::Copy(TObject &newth1) const { // Copy this to newth1 TH1::Copy(newth1); } //______________________________________________________________________________ TH1 *TH1I::DrawCopy(Option_t *option) const { // Draw copy. TString opt = option; opt.ToLower(); if (gPad && !opt.Contains("same")) gPad->Clear(); TH1I *newth1 = (TH1I*)Clone(); newth1->SetDirectory(0); newth1->SetBit(kCanDelete); newth1->AppendPad(option); return newth1; } //______________________________________________________________________________ Double_t TH1I::GetBinContent(Int_t bin) const { // see convention for numbering bins in TH1::GetBin if (fBuffer) ((TH1I*)this)->BufferEmpty(); if (bin < 0) bin = 0; if (bin >= fNcells) bin = fNcells-1; if (!fArray) return 0; return Double_t (fArray[bin]); } //______________________________________________________________________________ void TH1I::Reset(Option_t *option) { // Reset. TH1::Reset(option); TArrayI::Reset(); } //______________________________________________________________________________ void TH1I::SetBinContent(Int_t bin, Double_t content) { // Set bin content // see convention for numbering bins in TH1::GetBin // 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 if (bin < 0) return; if (bin >= fNcells-1) { if (fXaxis.GetTimeDisplay()) { while (bin >= fNcells-1) LabelsInflate(); } else { if (!TestBit(kCanRebin)) { if (bin == fNcells-1) fArray[bin] = Int_t (content); return; } while (bin >= fNcells-1) LabelsInflate(); } } fArray[bin] = Int_t (content); fEntries++; fTsumw = 0; } //______________________________________________________________________________ void TH1I::SetBinsLength(Int_t n) { // Set total number of bins including under/overflow // Reallocate bin contents array if (n < 0) n = fXaxis.GetNbins() + 2; fNcells = n; TArrayI::Set(n); } //______________________________________________________________________________ TH1I& TH1I::operator=(const TH1I &h1) { // Operator = if (this != &h1) ((TH1I&)h1).Copy(*this); return *this; } //______________________________________________________________________________ TH1I operator*(Double_t c1, const TH1I &h1) { // Operator * TH1I hnew = h1; hnew.Scale(c1); hnew.SetDirectory(0); return hnew; } //______________________________________________________________________________ TH1I operator+(const TH1I &h1, const TH1I &h2) { // Operator + TH1I hnew = h1; hnew.Add(&h2,1); hnew.SetDirectory(0); return hnew; } //______________________________________________________________________________ TH1I operator-(const TH1I &h1, const TH1I &h2) { // Operator - TH1I hnew = h1; hnew.Add(&h2,-1); hnew.SetDirectory(0); return hnew; } //______________________________________________________________________________ TH1I operator*(const TH1I &h1, const TH1I &h2) { // Operator * TH1I hnew = h1; hnew.Multiply(&h2); hnew.SetDirectory(0); return hnew; } //______________________________________________________________________________ TH1I operator/(const TH1I &h1, const TH1I &h2) { // Operator / TH1I hnew = h1; hnew.Divide(&h2); hnew.SetDirectory(0); return hnew; } //______________________________________________________________________________ // TH1F methods // TH1F : histograms with one float per channel. Maximum precision 7 digits //______________________________________________________________________________ ClassImp(TH1F) //______________________________________________________________________________ TH1F::TH1F(): TH1(), TArrayF() { // Constructor. fDimension = 1; SetBinsLength(3); if (fgDefaultSumw2) Sumw2(); } //______________________________________________________________________________ TH1F::TH1F(const char *name,const char *title,Int_t nbins,Double_t xlow,Double_t xup) : TH1(name,title,nbins,xlow,xup) { // // Create a 1-Dim histogram with fix bins of type float // ==================================================== // (see TH1::TH1 for explanation of parameters) // fDimension = 1; TArrayF::Set(fNcells); if (xlow >= xup) SetBuffer(fgBufferSize); if (fgDefaultSumw2) Sumw2(); } //______________________________________________________________________________ TH1F::TH1F(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 float // ========================================================= // (see TH1::TH1 for explanation of parameters) // fDimension = 1; TArrayF::Set(fNcells); if (fgDefaultSumw2) Sumw2(); } //______________________________________________________________________________ TH1F::TH1F(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 float // ========================================================= // (see TH1::TH1 for explanation of parameters) // fDimension = 1; TArrayF::Set(fNcells); if (fgDefaultSumw2) Sumw2(); } //______________________________________________________________________________ TH1F::TH1F(const TVectorF &v) : TH1("TVectorF","",v.GetNrows(),0,v.GetNrows()) { // Create a histogram from a TVectorF // by default the histogram name is "TVectorF" and title = "" TArrayF::Set(fNcells); fDimension = 1; Int_t ivlow = v.GetLwb(); for (Int_t i=0;i<fNcells-2;i++) { SetBinContent(i+1,v(i+ivlow)); } TArrayF::Set(fNcells); if (fgDefaultSumw2) Sumw2(); } //______________________________________________________________________________ TH1F::TH1F(const TH1F &h) : TH1(), TArrayF() { // Copy Constructor. ((TH1F&)h).Copy(*this); } //______________________________________________________________________________ TH1F::~TH1F() { // Destructor. } //______________________________________________________________________________ void TH1F::Copy(TObject &newth1) const { // Copy this to newth1. TH1::Copy(newth1); } //______________________________________________________________________________ TH1 *TH1F::DrawCopy(Option_t *option) const { // Draw copy. TString opt = option; opt.ToLower(); if (gPad && !opt.Contains("same")) gPad->Clear(); TH1F *newth1 = (TH1F*)Clone(); newth1->SetDirectory(0); newth1->SetBit(kCanDelete); newth1->AppendPad(option); return newth1; } //______________________________________________________________________________ Double_t TH1F::GetBinContent(Int_t bin) const { // see convention for numbering bins in TH1::GetBin if (fBuffer) ((TH1F*)this)->BufferEmpty(); if (bin < 0) bin = 0; if (bin >= fNcells) bin = fNcells-1; if (!fArray) return 0; return Double_t (fArray[bin]); } //______________________________________________________________________________ void TH1F::Reset(Option_t *option) { // Reset. TH1::Reset(option); TArrayF::Reset(); } //______________________________________________________________________________ void TH1F::SetBinContent(Int_t bin, Double_t content) { // Set bin content // see convention for numbering bins in TH1::GetBin // 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 if (bin < 0) return; if (bin >= fNcells-1) { if (fXaxis.GetTimeDisplay()) { while (bin >= fNcells-1) LabelsInflate(); } else { if (!TestBit(kCanRebin)) { if (bin == fNcells-1) fArray[bin] = Float_t (content); return; } while (bin >= fNcells-1) LabelsInflate(); } } fArray[bin] = Float_t (content); fEntries++; fTsumw = 0; } //______________________________________________________________________________ void TH1F::SetBinsLength(Int_t n) { // Set total number of bins including under/overflow // Reallocate bin contents array if (n < 0) n = fXaxis.GetNbins() + 2; fNcells = n; TArrayF::Set(n); } //______________________________________________________________________________ TH1F& TH1F::operator=(const TH1F &h1) { // Operator = if (this != &h1) ((TH1F&)h1).Copy(*this); return *this; } //______________________________________________________________________________ TH1F operator*(Double_t c1, const TH1F &h1) { // Operator * TH1F hnew = h1; hnew.Scale(c1); hnew.SetDirectory(0); return hnew; } //______________________________________________________________________________ TH1F operator+(const TH1F &h1, const TH1F &h2) { // Operator + TH1F hnew = h1; hnew.Add(&h2,1); hnew.SetDirectory(0); return hnew; } //______________________________________________________________________________ TH1F operator-(const TH1F &h1, const TH1F &h2) { // Operator - TH1F hnew = h1; hnew.Add(&h2,-1); hnew.SetDirectory(0); return hnew; } //______________________________________________________________________________ TH1F operator*(const TH1F &h1, const TH1F &h2) { // Operator * TH1F hnew = h1; hnew.Multiply(&h2); hnew.SetDirectory(0); return hnew; } //______________________________________________________________________________ TH1F operator/(const TH1F &h1, const TH1F &h2) { // Operator / TH1F hnew = h1; hnew.Divide(&h2); hnew.SetDirectory(0); return hnew; } //______________________________________________________________________________ // TH1D methods // TH1D : histograms with one double per channel. Maximum precision 14 digits //______________________________________________________________________________ ClassImp(TH1D) //______________________________________________________________________________ TH1D::TH1D(): TH1(), TArrayD() { // Constructor. fDimension = 1; SetBinsLength(3); if (fgDefaultSumw2) Sumw2(); } //______________________________________________________________________________ TH1D::TH1D(const char *name,const char *title,Int_t nbins,Double_t xlow,Double_t xup) : TH1(name,title,nbins,xlow,xup) { // // Create a 1-Dim histogram with fix bins of type double // ===================================================== // (see TH1::TH1 for explanation of parameters) // fDimension = 1; TArrayD::Set(fNcells); if (xlow >= xup) SetBuffer(fgBufferSize); if (fgDefaultSumw2) Sumw2(); } //______________________________________________________________________________ TH1D::TH1D(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 double // ===================================================== // (see TH1::TH1 for explanation of parameters) // fDimension = 1; TArrayD::Set(fNcells); if (fgDefaultSumw2) Sumw2(); } //______________________________________________________________________________ TH1D::TH1D(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 double // ===================================================== // (see TH1::TH1 for explanation of parameters) // fDimension = 1; TArrayD::Set(fNcells); if (fgDefaultSumw2) Sumw2(); } //______________________________________________________________________________ TH1D::TH1D(const TVectorD &v) : TH1("TVectorD","",v.GetNrows(),0,v.GetNrows()) { // Create a histogram from a TVectorD // by default the histogram name is "TVectorD" and title = "" TArrayD::Set(fNcells); fDimension = 1; Int_t ivlow = v.GetLwb(); for (Int_t i=0;i<fNcells-2;i++) { SetBinContent(i+1,v(i+ivlow)); } TArrayD::Set(fNcells); if (fgDefaultSumw2) Sumw2(); } //______________________________________________________________________________ TH1D::~TH1D() { // Destructor. } //______________________________________________________________________________ TH1D::TH1D(const TH1D &h1d) : TH1(), TArrayD() { // Constructor. ((TH1D&)h1d).Copy(*this); } //______________________________________________________________________________ void TH1D::Copy(TObject &newth1) const { // Copy this to newth1 TH1::Copy(newth1); } //______________________________________________________________________________ TH1 *TH1D::DrawCopy(Option_t *option) const { // Draw copy. TString opt = option; opt.ToLower(); if (gPad && !opt.Contains("same")) gPad->Clear(); TH1D *newth1 = (TH1D*)Clone(); newth1->SetDirectory(0); newth1->SetBit(kCanDelete); newth1->AppendPad(option); return newth1; } //______________________________________________________________________________ Double_t TH1D::GetBinContent(Int_t bin) const { // see convention for numbering bins in TH1::GetBin if (fBuffer) ((TH1D*)this)->BufferEmpty(); if (bin < 0) bin = 0; if (bin >= fNcells) bin = fNcells-1; if (!fArray) return 0; return Double_t (fArray[bin]); } //______________________________________________________________________________ void TH1D::Reset(Option_t *option) { // Reset. TH1::Reset(option); TArrayD::Reset(); } //______________________________________________________________________________ void TH1D::SetBinContent(Int_t bin, Double_t content) { // Set bin content // see convention for numbering bins in TH1::GetBin // 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 if (bin < 0) return; if (bin >= fNcells-1) { if (fXaxis.GetTimeDisplay()) { while (bin >= fNcells-1) LabelsInflate(); } else { if (!TestBit(kCanRebin)) { if (bin == fNcells-1) fArray[bin] = content; return; } while (bin >= fNcells-1) LabelsInflate(); } } fArray[bin] = content; fEntries++; fTsumw = 0; } //______________________________________________________________________________ void TH1D::SetBinsLength(Int_t n) { // Set total number of bins including under/overflow // Reallocate bin contents array if (n < 0) n = fXaxis.GetNbins() + 2; fNcells = n; TArrayD::Set(n); } //______________________________________________________________________________ TH1D& TH1D::operator=(const TH1D &h1) { // Operator = if (this != &h1) ((TH1D&)h1).Copy(*this); return *this; } //______________________________________________________________________________ TH1D operator*(Double_t c1, const TH1D &h1) { // Operator * TH1D hnew = h1; hnew.Scale(c1); hnew.SetDirectory(0); return hnew; } //______________________________________________________________________________ TH1D operator+(const TH1D &h1, const TH1D &h2) { // Operator + TH1D hnew = h1; hnew.Add(&h2,1); hnew.SetDirectory(0); return hnew; } //______________________________________________________________________________ TH1D operator-(const TH1D &h1, const TH1D &h2) { // Operator - TH1D hnew = h1; hnew.Add(&h2,-1); hnew.SetDirectory(0); return hnew; } //______________________________________________________________________________ TH1D operator*(const TH1D &h1, const TH1D &h2) { // Operator * TH1D hnew = h1; hnew.Multiply(&h2); hnew.SetDirectory(0); return hnew; } //______________________________________________________________________________ TH1D operator/(const TH1D &h1, const TH1D &h2) { // Operator / TH1D hnew = h1; hnew.Divide(&h2); hnew.SetDirectory(0); return hnew; } //______________________________________________________________________________ TH1 *R__H(Int_t hid) { //return pointer to histogram with name // hid if id >=0 // h_id if id <0 char hname[20]; if(hid >= 0) sprintf(hname,"h%d",hid); else sprintf(hname,"h_%d",hid); return (TH1*)gDirectory->Get(hname); } //______________________________________________________________________________ TH1 *R__H(const char * hname) { //return pointer to histogram with name hname return (TH1*)gDirectory->Get(hname); }
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