/* ======================================================================== *\ ! ! * ! * This file is part of MARS, the MAGIC Analysis and Reconstruction ! * Software. It is distributed to you in the hope that it can be a useful ! * and timesaving tool in analysing Data of imaging Cerenkov telescopes. ! * It is distributed WITHOUT ANY WARRANTY. ! * ! * Permission to use, copy, modify and distribute this software and its ! * documentation for any purpose is hereby granted without fee, ! * provided that the above copyright notice appear in all copies and ! * that both that copyright notice and this permission notice appear ! * in supporting documentation. It is provided "as is" without express ! * or implied warranty. ! * ! ! ! Author(s): Markus Gaug 02/2004 ! ! Copyright: MAGIC Software Development, 2000-2004 ! ! \* ======================================================================== */ ////////////////////////////////////////////////////////////////////////////// // // MHGausEvents // // A base class for events which are believed to follow a Gaussian distribution // with time, e.g. calibration events, observables containing white noise, ... // // MHGausEvents derives from MH, thus all features of MH can be used by a class // deriving from MHGausEvents, especially the filling functions. // // The central objects are: // // 1) The TH1F fHGausHist: // ==================== // // It is created with a default name and title and resides in directory NULL. // - Any class deriving from MHGausEvents needs to apply a binning to fHGausHist // (e.g. by setting the variables fNbins, fFirst, fLast and calling the function // InitBins() or by directly calling fHGausHist.SetBins(..) ) // - The histogram is filled with the functions FillHist() or FillHistAndArray(). // - The histogram can be fitted with the function FitGaus(). This involves stripping // of all zeros at the lower and upper end of the histogram and re-binning to // a new number of bins, specified in the variable fBinsAfterStripping. // - The fit result's probability is compared to a reference probability fProbLimit // The NDF is compared to fNDFLimit and a check is made whether results are NaNs. // Accordingly, a flag IsGausFitOK() is set. // - One can repeat the fit within a given amount of sigmas from the previous mean // (specified by the variables fPickupLimit and fBlackoutLimit) with the function RepeatFit() // // 2) The TArrayF fEvents: // ========================== // // It is created with 0 entries and not expanded unless FillArray() or FillHistAndArray() // are called. // - A first call to FillArray() or FillHistAndArray() initializes fEvents by default // to 512 entries. // - Any later call to FillArray() or FillHistAndArray() fills up the array. // Reaching the limit, the array is expanded by a factor 2. // - The array can be fourier-transformed into the array fPowerSpectrum. // Note that any FFT accepts only number of events which are a power of 2. // Thus, fEvents is cut to the next power of 2 smaller than its actual number of entries. // Be aware that you might lose information at the end of your analysis. // - Calling the function CreateFourierSpectrum() creates the array fPowerSpectrum // and its projection fHPowerProbability which in turn is fit to an exponential. // - The fit result's probability is compared to a referenc probability fProbLimit // and accordingly the flag IsExpFitOK() is set. // - The flag IsFourierSpectrumOK() is set accordingly to IsExpFitOK(). // Later, a closer check will be installed. // - You can display all arrays by calls to: CreateGraphEvents() and // CreateGraphPowerSpectrum() and successive calls to the corresponding Getters. // // To see an example, have a look at: Draw() // ////////////////////////////////////////////////////////////////////////////// #include "MHGausEvents.h" #include #include #include #include #include #include #include #include #include "MFFT.h" #include "MArrayF.h" #include "MH.h" #include "MLog.h" #include "MLogManip.h" ClassImp(MHGausEvents); using namespace std; const Int_t MHGausEvents::fgNDFLimit = 2; const Float_t MHGausEvents::fgProbLimit = 0.001; const Int_t MHGausEvents::fgPowerProbabilityBins = 30; // -------------------------------------------------------------------------- // // Default Constructor. // Sets: // - the default Probability Bins for fPowerProbabilityBins (fgPowerProbabilityBins) // - the default Probability Limit for fProbLimit (fgProbLimit) // - the default NDF Limit for fNDFLimit (fgNDFLimit) // - the default number of bins after stripping for fBinsAfterStipping (fgBinsAfterStipping) // - the default name of the fHGausHist ("HGausHist") // - the default title of the fHGausHist ("Histogram of Events with Gaussian Distribution") // - the default directory of the fHGausHist (NULL) // - the default for fNbins (100) // - the default for fFirst (0.) // - the default for fLast (100.) // // Initializes: // - fEvents to 0 entries // - fHGausHist() // - all other pointers to NULL // - all variables to 0. // - all flags to kFALSE // MHGausEvents::MHGausEvents(const char *name, const char *title) : fEventFrequency(0), fFlags(0), fHPowerProbability(NULL), fPowerSpectrum(NULL), fFExpFit(NULL), fGraphEvents(NULL), fGraphPowerSpectrum(NULL), fFirst(0.), fLast(100.), fNbins(100), fFGausFit(NULL) { fName = name ? name : "MHGausEvents"; fTitle = title ? title : "Events with expected Gaussian distributions"; Clear(); SetBinsAfterStripping(); SetNDFLimit(); SetPowerProbabilityBins(); SetProbLimit(); fHGausHist.SetName("HGausHist"); fHGausHist.SetTitle("Histogram of Events with Gaussian Distribution"); // important, other ROOT will not draw the axes: fHGausHist.UseCurrentStyle(); fHGausHist.SetDirectory(NULL); TAxis *yaxe = fHGausHist.GetYaxis(); yaxe->CenterTitle(); } // -------------------------------------------------------------------------- // // Default Destructor. // // Deletes (if Pointer is not NULL): // // - fHPowerProbability // - fPowerSpectrum // - fGraphEvents // - fGraphPowerSpectrum // // - fFGausFit // - fFExpFit // MHGausEvents::~MHGausEvents() { // // The next two lines are important for the case that // the class has been stored to a file and is read again. // In this case, the next two lines prevent a segm. violation // in the destructor // gROOT->GetListOfFunctions()->Remove(fFGausFit); gROOT->GetListOfFunctions()->Remove(fFExpFit); // delete fits if (fFGausFit) delete fFGausFit; if (fFExpFit) delete fFExpFit; // delete histograms if (fHPowerProbability) delete fHPowerProbability; // delete arrays if (fPowerSpectrum) delete fPowerSpectrum; // delete graphs if (fGraphEvents) delete fGraphEvents; if (fGraphPowerSpectrum) delete fGraphPowerSpectrum; } // -------------------------------------------------------------------------- // // Default Clear(), can be overloaded. // // Sets: // - all other pointers to NULL // - all variables to 0. and keep fEventFrequency // - all flags to kFALSE // // Deletes (if not NULL): // - all pointers // void MHGausEvents::Clear(Option_t *o) { SetGausFitOK ( kFALSE ); SetExpFitOK ( kFALSE ); SetFourierSpectrumOK( kFALSE ); SetExcluded ( kFALSE ); fMean = 0.; fSigma = 0.; fMeanErr = 0.; fSigmaErr = 0.; fProb = 0.; fCurrentSize = 0; if (fHPowerProbability) { delete fHPowerProbability; fHPowerProbability = NULL; } // delete fits if (fFGausFit) { delete fFGausFit; fFGausFit = NULL; } if (fFExpFit) { delete fFExpFit; fFExpFit = NULL; } // delete arrays if (fPowerSpectrum) { delete fPowerSpectrum; fPowerSpectrum = NULL; } // delete graphs if (fGraphEvents) { delete fGraphEvents; fGraphEvents = NULL; } if (fGraphPowerSpectrum) { delete fGraphPowerSpectrum; fGraphPowerSpectrum = NULL; } } // ------------------------------------------------------------------- // // Create the fourier spectrum using the class MFFT. // The result is projected into a histogram and fitted by an exponential // void MHGausEvents::CreateFourierSpectrum() { if (fFExpFit) return; if (fEvents.GetSize() < 8) { *fLog << warn << "Cannot create Fourier spectrum in: " << fName << ". Number of events smaller than 8 " << endl; return; } // // The number of entries HAS to be a potence of 2, // so we can only cut out from the last potence of 2 to the rest. // Another possibility would be to fill everything with // zeros, but that gives a low frequency peak, which we would // have to cut out later again. // // So, we have to live with the possibility that at the end // of the calibration run, something has happened without noticing // it... // // This cuts only the non-used zero's, but MFFT will later cut the rest fEvents.StripZeros(); if (fEvents.GetSize() < 8) { /* *fLog << warn << "Cannot create Fourier spectrum. " << endl; *fLog << warn << "Number of events (after stripping of zeros) is smaller than 8 " << "in pixel: " << fPixId << endl; */ return; } MFFT fourier; fPowerSpectrum = fourier.PowerSpectrumDensity(&fEvents); fHPowerProbability = ProjectArray(*fPowerSpectrum, fPowerProbabilityBins, Form("%s%s","PowerProb",GetName()), "Probability of Power occurrance"); fHPowerProbability->SetXTitle("P(f)"); fHPowerProbability->SetYTitle("Counts"); fHPowerProbability->GetYaxis()->CenterTitle(); fHPowerProbability->SetDirectory(NULL); fHPowerProbability->SetBit(kCanDelete); // // First guesses for the fit (should be as close to reality as possible, // const Double_t xmax = fHPowerProbability->GetXaxis()->GetXmax(); fFExpFit = new TF1("FExpFit","exp([0]-[1]*x)",0.,xmax); const Double_t slope_guess = (TMath::Log(fHPowerProbability->GetEntries())+1.)/xmax; const Double_t offset_guess = slope_guess*xmax; // // For the fits, we have to take special care since ROOT // has stored the function pointer in a global list which // lead to removing the object twice. We have to take out // the following functions of the global list of functions // as well: // gROOT->GetListOfFunctions()->Remove(fFExpFit); fFExpFit->SetParameters(offset_guess, slope_guess); fFExpFit->SetParNames("Offset","Slope"); fFExpFit->SetParLimits(0,offset_guess/2.,2.*offset_guess); fFExpFit->SetParLimits(1,slope_guess/1.5,1.5*slope_guess); fFExpFit->SetRange(0.,xmax); fHPowerProbability->Fit(fFExpFit,"RQL0"); if (GetExpProb() > fProbLimit) SetExpFitOK(kTRUE); // // For the moment, this is the only check, later we can add more... // SetFourierSpectrumOK(IsExpFitOK()); return; } // ---------------------------------------------------------------------------------- // // Create a graph to display the array fEvents // If the variable fEventFrequency is set, the x-axis is transformed into real time. // void MHGausEvents::CreateGraphEvents() { fEvents.StripZeros(); const Int_t n = fEvents.GetSize(); if (n==0) return; const Float_t freq = fEventFrequency ? fEventFrequency : 1; MArrayF xaxis(n); for (Int_t i=0; iSetTitle("Evolution of Events with time"); fGraphEvents->GetXaxis()->SetTitle(fEventFrequency ? "Time [s]" : "Event Nr."); fGraphEvents->GetYaxis()->SetTitle(fHGausHist.GetXaxis()->GetTitle()); fGraphEvents->GetYaxis()->CenterTitle(); } // ---------------------------------------------------------------------------------- // // Create a graph to display the array fPowerSpectrum // If the variable fEventFrequency is set, the x-axis is transformed into real frequency. // void MHGausEvents::CreateGraphPowerSpectrum() { fPowerSpectrum->StripZeros(); const Int_t n = fPowerSpectrum->GetSize(); const Float_t freq = fEventFrequency ? fEventFrequency : 1; MArrayF xaxis(n); for (Int_t i=0; iGetArray()); fGraphPowerSpectrum->SetTitle("Power Spectrum Density"); fGraphPowerSpectrum->GetXaxis()->SetTitle(fEventFrequency ? "Frequency [Hz]" : "Frequency"); fGraphPowerSpectrum->GetYaxis()->SetTitle("P(f)"); fGraphPowerSpectrum->GetYaxis()->CenterTitle(); } // ----------------------------------------------------------------------------- // // Default draw: // // The following options can be chosen: // // "EVENTS": displays a TGraph of the array fEvents // "FOURIER": display a TGraph of the fourier transform of fEvents // displays the projection of the fourier transform with the fit // // The following picture shows a typical outcome of call to Draw("fourierevents"): // - The first plot shows the distribution of the values with the Gauss fit // (which did not succeed, in this case, for obvious reasons) // - The second plot shows the TGraph with the events vs. time // - The third plot shows the fourier transform and a small peak at about 85 Hz. // - The fourth plot shows the projection of the fourier components and an exponential // fit, with the result that the observed deviation is still statistical with a // probability of 0.5%. // //Begin_Html /* */ //End_Html // void MHGausEvents::Draw(const Option_t *opt) { TVirtualPad *pad = gPad ? gPad : MH::MakeDefCanvas(this,600, 600); TString option(opt); option.ToLower(); Int_t win = 1; Int_t nofit = 0; if (option.Contains("events")) win += 1; if (option.Contains("fourier")) win += 2; if (IsEmpty()) win--; if (option.Contains("nofit")) { option.ReplaceAll("nofit",""); nofit++; } pad->SetBorderMode(0); if (win > 1) pad->Divide(1,win); Int_t cwin = 1; gPad->SetTicks(); if (!IsEmpty()) { pad->cd(cwin++); if (!IsOnlyOverflow() && !IsOnlyUnderflow()) gPad->SetLogy(); fHGausHist.Draw(option); if (!nofit) if (fFGausFit) { fFGausFit->SetLineColor(IsGausFitOK() ? kGreen : kRed); fFGausFit->Draw("same"); } } if (option.Contains("events")) { pad->cd(cwin++); DrawEvents(); } if (option.Contains("fourier")) { pad->cd(cwin++); DrawPowerSpectrum(); pad->cd(cwin); DrawPowerProjection(); } } // ----------------------------------------------------------------------------- // // DrawEvents: // // Will draw the graph with the option "A", unless the option: // "SAME" has been chosen // void MHGausEvents::DrawEvents(Option_t *opt) { if (!fGraphEvents) CreateGraphEvents(); if (!fGraphEvents) return; fGraphEvents->SetBit(kCanDelete); fGraphEvents->SetTitle("Events with time"); TString option(opt); option.ToLower(); if (option.Contains("same")) { option.ReplaceAll("same",""); fGraphEvents->Draw(option+"L"); } else fGraphEvents->Draw(option+"AL"); } // ----------------------------------------------------------------------------- // // DrawPowerSpectrum // // Will draw the fourier spectrum of the events sequence with the option "A", unless the option: // "SAME" has been chosen // void MHGausEvents::DrawPowerSpectrum(Option_t *option) { TString opt(option); if (!fPowerSpectrum) CreateFourierSpectrum(); if (fPowerSpectrum) { if (!fGraphPowerSpectrum) CreateGraphPowerSpectrum(); if (!fGraphPowerSpectrum) return; if (opt.Contains("same")) { opt.ReplaceAll("same",""); fGraphPowerSpectrum->Draw(opt+"L"); } else { fGraphPowerSpectrum->Draw(opt+"AL"); fGraphPowerSpectrum->SetBit(kCanDelete); } } } // ----------------------------------------------------------------------------- // // DrawPowerProjection // // Will draw the projection of the fourier spectrum onto the power probability axis // with the possible options of TH1D // void MHGausEvents::DrawPowerProjection(Option_t *option) { TString opt(option); if (!fHPowerProbability) CreateFourierSpectrum(); if (fHPowerProbability && fHPowerProbability->GetEntries() > 0) { gPad->SetLogy(); fHPowerProbability->Draw(opt.Data()); if (fFExpFit) { fFExpFit->SetLineColor(IsExpFitOK() ? kGreen : kRed); fFExpFit->Draw("same"); } } } // -------------------------------------------------------------------------- // // Fill fEvents with f // If size of fEvents is 0, initializes it to 512 // If size of fEvents is smaller than fCurrentSize, double the size // Increase fCurrentSize by 1 // void MHGausEvents::FillArray(const Float_t f) { if (fEvents.GetSize() == 0) fEvents.Set(512); if (fCurrentSize >= fEvents.GetSize()) fEvents.Set(fEvents.GetSize()*2); fEvents.AddAt(f,fCurrentSize++); } // -------------------------------------------------------------------------- // // Fills fHGausHist with f // Returns kFALSE, if overflow or underflow occurred, else kTRUE // Bool_t MHGausEvents::FillHist(const Float_t f) { return fHGausHist.Fill(f) > -1; } // -------------------------------------------------------------------------- // // Executes: // - FillArray() // - FillHist() // Bool_t MHGausEvents::FillHistAndArray(const Float_t f) { FillArray(f); return FillHist(f); } // ------------------------------------------------------------------- // // Fit fGausHist with a Gaussian after stripping zeros from both ends // and rebinned to the number of bins specified in fBinsAfterStripping // // The fit results are retrieved and stored in class-own variables. // // A flag IsGausFitOK() is set according to whether the fit probability // is smaller or bigger than fProbLimit, whether the NDF is bigger than // fNDFLimit and whether results are NaNs. // Bool_t MHGausEvents::FitGaus(Option_t *option, const Double_t xmin, const Double_t xmax) { if (IsGausFitOK()) return kTRUE; // // First, strip the zeros from the edges which contain only zeros and rebin // to fBinsAfterStripping bins. If fBinsAfterStripping is 0, reduce bins only by // a factor 10. // // (ATTENTION: The Chisquare method is more sensitive, // the _less_ bins, you have!) // StripZeros(&fHGausHist, fBinsAfterStripping ? fBinsAfterStripping : (fNbins > 1000 ? fNbins/10 : 0)); TAxis *axe = fHGausHist.GetXaxis(); // // Get the fitting ranges // Axis_t rmin = ((xmin==0.) && (xmax==0.)) ? fHGausHist.GetBinCenter(axe->GetFirst()) : xmin; Axis_t rmax = ((xmin==0.) && (xmax==0.)) ? fHGausHist.GetBinCenter(axe->GetLast()) : xmax; // // First guesses for the fit (should be as close to reality as possible, // const Stat_t entries = fHGausHist.Integral(axe->FindBin(rmin),axe->FindBin(rmax),"width"); const Double_t mu_guess = fHGausHist.GetBinCenter(fHGausHist.GetMaximumBin()); const Double_t sigma_guess = fHGausHist.GetRMS(); const Double_t area_guess = entries/TMath::Sqrt(TMath::TwoPi())/sigma_guess; fFGausFit = new TF1("GausFit","gaus",rmin,rmax); if (!fFGausFit) { *fLog << warn << dbginf << "WARNING: Could not create fit function for Gauss fit " << "in: " << fName << endl; return kFALSE; } // // For the fits, we have to take special care since ROOT // has stored the function pointer in a global list which // lead to removing the object twice. We have to take out // the following functions of the global list of functions // as well: // gROOT->GetListOfFunctions()->Remove(fFGausFit); fFGausFit->SetParameters(area_guess,mu_guess,sigma_guess); fFGausFit->SetParNames("Area","#mu","#sigma"); fFGausFit->SetParLimits(0,0.,area_guess*25.); fFGausFit->SetParLimits(1,rmin,rmax); fFGausFit->SetParLimits(2,0.,rmax-rmin); fFGausFit->SetRange(rmin,rmax); fHGausHist.Fit(fFGausFit,option); fMean = fFGausFit->GetParameter(1); fSigma = fFGausFit->GetParameter(2); fMeanErr = fFGausFit->GetParError(1); fSigmaErr = fFGausFit->GetParError(2); fProb = fFGausFit->GetProb(); // // The fit result is accepted under condition: // 1) The results are not NaN's (not a number) // 2) The results are all finite // 3) The NDF is not smaller than fNDFLimit (default: fgNDFLimit) // 4) The Probability is greater than fProbLimit (default: fgProbLimit) // // !Finitite means either infinite or not-a-number if ( !TMath::Finite(fMean) || !TMath::Finite(fMeanErr) || !TMath::Finite(fProb) || !TMath::Finite(fSigma) || !TMath::Finite(fSigmaErr) || fFGausFit->GetNDF() < fNDFLimit || fProb < fProbLimit ) return kFALSE; SetGausFitOK(kTRUE); return kTRUE; } // -------------------------------------------------------------------------- // // Default InitBins, can be overloaded. // // Executes: // - fHGausHist.SetBins(fNbins,fFirst,fLast) // void MHGausEvents::InitBins() { // const TAttAxis att(fHGausHist.GetXaxis()); fHGausHist.SetBins(fNbins,fFirst,fLast); // att.Copy(fHGausHist.GetXaxis()); } // ----------------------------------------------------------------------------------- // // A default print // void MHGausEvents::Print(const Option_t *o) const { *fLog << all << endl; *fLog << all << "Results of the Gauss Fit in: " << fName << endl; *fLog << all << "Mean: " << GetMean() << endl; *fLog << all << "Sigma: " << GetSigma() << endl; *fLog << all << "Chisquare: " << GetChiSquare() << endl; *fLog << all << "DoF: " << GetNdf() << endl; *fLog << all << "Probability: " << GetProb() << endl; *fLog << all << endl; } // -------------------------------------------------------------------------- // // Default Reset(), can be overloaded. // // Executes: // - Clear() // - fHGausHist.Reset() // - fEvents.Set(0) // - InitBins() // void MHGausEvents::Reset() { Clear(); fHGausHist.Reset(); fEvents.Set(0); InitBins(); } // ---------------------------------------------------------------------------- // // Simulates Gaussian events and fills them into the histogram and the array // In order to do a fourier analysis, call CreateFourierSpectrum() // void MHGausEvents::SimulateGausEvents(const Float_t mean, const Float_t sigma, const Int_t nevts) { if (!IsEmpty()) *fLog << warn << "The histogram is already filled, will superimpose simulated events on it..." << endl; for (Int_t i=0;iGaus(mean,sigma); FillHistAndArray(ran); } }