testUnfold2.C: Test program for the class MyUnfold, derived from TUnfold

//  Test program for the class MyUnfold, derived from TUnfold
// Author: Stefan Schmitt
// DESY, 14.10.2008

//  Version 6a, fix problem with dynamic array allocation under windows
//
//  History:
//    Version 6, re-include class MyUnfold in the example
//    Version 5, move class MyUnfold to seperate files
//    Version 4, with bug-fix in TUnfold.C
//    Version 3, with bug-fix in TUnfold.C
//    Version 2, with changed ScanLcurve() arguments
//    Version 1, remove L curve analysis, use ScanLcurve() method instead
//    Version 0, L curve analysis included here

#include <TMath.h>
#include <TCanvas.h>
#include <TRandom3.h>
#include <TFitter.h>
#include <TF1.h>
#include <TStyle.h>
#include <TVector.h>
#include <TGraph.h>
#include "TUnfold.h"

using namespace std;

///////////////////////////////////////////////////////////////////////
// 
//  Test program for the class MyUnfold, derived from TUnfold
//
//  (1) Generate Monte Carlo and Data events
//      The events consist of
//        signal
//        background
//
//      The signal is a resonance. It is generated with a Breit-Wigner,
//      smeared by a Gaussian
//
//  (2) Unfold the data. The result is:
//      The background level
//      The shape of the resonance, corrected for detector effects
//
//      The regularisation is done on the curvature, excluding the bins
//      near the peak.
//
//  (3) fit the unfolded distribution, including the correlation matrix
//
///////////////////////////////////////////////////////////////////////

///////////////////////////////////////////////////////////////////////
// 
//  Example of a class derived from TUnfold
//
///////////////////////////////////////////////////////////////////////

class MyUnfold : public TUnfold {
public:
  MyUnfold(TH2 const *hist_A, EHistMap histmap,
           ERegMode regmode = kRegModeSize);  // constructor, in parallel to original constructor
  virtual Double_t DoUnfold(Double_t const &tau);  // derived method, to store the result of the unfolding for a given parameter tau
  using TUnfold::DoUnfold;  // otherwise TUnfold methods will be hidden
  void TauAnalysis(void); // method for the alternative analysis
  void ResetUser(Int_t const *binMap);  // reset alternative analysis
  inline Double_t GetTauUser(void) const { return fTauBest; } // query result of alternative analysis
protected:
  Int_t const *fBinMap; // bin mapping to extract the global correlation
  Double_t fTauBest;    // tau with the smallest correlation
  Double_t fRhoMin;     // smallest correlation
  ClassDef(MyUnfold,0); 
};

//ClassImp(MyUnfold)

MyUnfold::MyUnfold(TH2 const *hist_A, EHistMap histmap,ERegMode regmode)
  : TUnfold(hist_A,histmap,regmode) {
  // The arguments are passed to the parent class constructor
  // Then the local variables are initialized

  // reset members of this class
  ResetUser(0);
};

Double_t MyUnfold::DoUnfold(Double_t const &tau) {
  // The argument is passed to the corresponding method of the parent class
  // Then the new analysis code is called

  // this calls the original unfolding
  Double_t r=TUnfold::DoUnfold(tau);
  // here do our private analysis to find the best choice of tau
  TauAnalysis();

  return r;
};

void  MyUnfold::ResetUser(Int_t const *binMap) {
  // Reset the local variables
  // Arguments:
  //    binMap: the bin mapping for determining the correlation
  //            See documentation of TUnfold: Bin averaging of the output

  fBinMap=binMap;
  fTauBest=0;
  fRhoMin=1.0;
}
 
void MyUnfold::TauAnalysis(void) {
  // User analysis: extract tau with smallest correlation

  // This is a very simple analysis: the tau value with the smallest
  // globla correlation is stored
  if(GetRhoAvg()<fRhoMin) {
    fRhoMin=GetRhoAvg();
    fTauBest=fTau;
  }
}


TRandom *rnd=0;

TH2D *gHistInvEMatrix;

TVirtualFitter *gFitter=0;

void chisquare_corr(Int_t &npar, Double_t * /*gin */, Double_t &f, Double_t *u, Int_t /* flag */) {
  //  Minimization function for H1s using a Chisquare method
  //  only one-dim ensional histograms are supported
  //  Corelated errors are taken from an external inverse covariance matrix
  //  stored in a 2-dimensional histogram

  Double_t x;

  TH1 *hfit = (TH1*)gFitter->GetObjectFit();
  TF1 *f1   = (TF1*)gFitter->GetUserFunc();
   
  f1->InitArgs(&x,u);
  npar = f1->GetNpar();
  f = 0;
   
  Int_t npfit = 0;
  Int_t nPoints=hfit->GetNbinsX();
  Double_t *df=new Double_t[nPoints];
  for (Int_t i=0;i<nPoints;i++) {
    x     = hfit->GetBinCenter(i+1);
    TF1::RejectPoint(kFALSE);
    df[i] = f1->EvalPar(&x,u)-hfit->GetBinContent(i+1);
    if (TF1::RejectedPoint()) df[i]=0.0;
    else npfit++;
  }
  for (Int_t i=0;i<nPoints;i++) {
    for (Int_t j=0;j<nPoints;j++) {
      f += df[i]*df[j]*gHistInvEMatrix->GetBinContent(i+1,j+1);
    }
  }
  delete[] df;
  f1->SetNumberFitPoints(npfit);
}

Double_t bw_func(Double_t *x,Double_t *par) {
  Double_t dm=x[0]-par[1];
  return par[0]/(dm*dm+par[2]*par[2]);
}


// generate an event
// output:
//  negative mass: background event
//  positive mass: signal event
Double_t GenerateEvent(Double_t const &bgr, // relative fraction of background
                       Double_t const &mass, // peak position
                       Double_t const &gamma) // peak width
{
  Double_t t;
  if(rnd->Rndm()>bgr) {
    // generate signal event
    // with positive mass
    do {
      do {
        t=rnd->Rndm();
      } while(t>=1.0); 
      t=TMath::Tan((t-0.5)*TMath::Pi())*gamma+mass;
    } while(t<=0.0);
    return t;
  } else {
    // generate background event
    // generate events following a power-law distribution
    //   f(E) = K * TMath::power((E0+E),N0)
    static Double_t const E0=2.4;
    static Double_t const N0=2.9;
    do {
      do {
        t=rnd->Rndm();
      } while(t>=1.0);
      // the mass is returned negative
      // In our example a convenient way to indicate it is a background event.
      t= -(TMath::Power(1.-t,1./(1.-N0))-1.0)*E0;
    } while(t>=0.0);
    return t;
  }
}

// smear the event to detector level
// input:
//   mass on generator level (mTrue>0 !)
// output:
//   mass on detector level
Double_t DetectorEvent(Double_t const &mTrue) {
  // smear by double-gaussian
  static Double_t frac=0.1;
  static Double_t wideBias=0.03;
  static Double_t wideSigma=0.5;
  static Double_t smallBias=0.0;
  static Double_t smallSigma=0.1;
  if(rnd->Rndm()>frac) {
    return rnd->Gaus(mTrue+smallBias,smallSigma);
  } else {
    return rnd->Gaus(mTrue+wideBias,wideSigma);
  }
}

//int main(int argc, char *argv[])
int testUnfold2() 
{
  // switch on histogram errors
  TH1::SetDefaultSumw2();

  // show fit result
  gStyle->SetOptFit(1111);

  // random generator
  rnd=new TRandom3();

  // data and MC luminosity, cross-section
  Double_t const luminosityData=10000;
  Double_t const luminosityMC=1000000;
  Double_t const crossSection=1.0;

  Int_t const nDet=250;
  Int_t const nGen=100;
  Double_t const xminDet=0.0;
  Double_t const xmaxDet=10.0;
  Double_t const xminGen=0.0;
  Double_t const xmaxGen=10.0;

  //============================================
  // generate MC distribution
  //
  TH1D *histMgenMC=new TH1D("MgenMC",";mass(gen)",nGen,xminGen,xmaxGen);
  TH1D *histMdetMC=new TH1D("MdetMC",";mass(det)",nDet,xminDet,xmaxDet);
  TH2D *histMdetGenMC=new TH2D("MdetgenMC",";mass(det);mass(gen)",nDet,xminDet,xmaxDet,
                              nGen,xminGen,xmaxGen);
  Int_t neventMC=rnd->Poisson(luminosityMC*crossSection);
  for(Int_t i=0;i<neventMC;i++) {
    Double_t mGen=GenerateEvent(0.3, // relative fraction of background
                                4.0, // peak position in MC
                                0.2); // peak width in MC
    Double_t mDet=DetectorEvent(TMath::Abs(mGen));
    // the generated mass is negative for background
    // and positive for signal
    // so it will be filled in the underflow bin
    // this is very convenient for the unfolding:
    // the unfolded result will contain the number of background
    // events in the underflow bin

    // generated MC distribution (for comparison only)
    histMgenMC->Fill(mGen,luminosityData/luminosityMC);
    // reconstructed MC distribution (for comparison only)
    histMdetMC->Fill(mDet,luminosityData/luminosityMC);

    // matrix describing how the generator input migrates to the
    // reconstructed level. Unfolding input.
    // NOTE on underflow/overflow bins:
    //  (1) the detector level under/overflow bins are used for
    //       normalisation ("efficiency" correction)
    //       in our toy example, these bins are populated from tails
    //       of the initial MC distribution.
    //  (2) the generator level underflow/overflow bins are
    //       unfolded. In this example:
    //       underflow bin: background events reconstructed in the detector
    //       overflow bin: signal events generated at masses > xmaxDet
    // for the unfolded result these bins will be filled
    //  -> the background normalisation will be contained in the underflow bin
    histMdetGenMC->Fill(mDet,mGen,luminosityData/luminosityMC);
  }

  //============================================
  // generate data distribution
  //
  TH1D *histMgenData=new TH1D("MgenData",";mass(gen)",nGen,xminGen,xmaxGen);
  TH1D *histMdetData=new TH1D("MdetData",";mass(det)",nDet,xminDet,xmaxDet);
  Int_t neventData=rnd->Poisson(luminosityData*crossSection);
  for(Int_t i=0;i<neventData;i++) {
    Double_t mGen=GenerateEvent(0.4, // relative fraction of background
                                3.8, // peak position
                                0.15); // peak width
    Double_t mDet=DetectorEvent(TMath::Abs(mGen));
    // generated data mass for comparison plots
    // for real data, we do not have this histogram
    histMgenData->Fill(mGen);

    // reconstructed mass, unfolding input
    histMdetData->Fill(mDet);
  }

  //=========================================================================
  // set up the unfolding
  MyUnfold unfold(histMdetGenMC,TUnfold::kHistMapOutputVert,
                 TUnfold::kRegModeNone);
  // regularisation
  //----------------
  // exclude the bins near the peak, because the curvature at the peak
  // is high (and the regularisation will enforce a small curvature everywhere)
  //
  // in real life, these parameters will have to be optimized, depending on
  // the data peak position
  Double_t estimatedPeakPosition=3.8;
  Int_t nPeek=3;
  TUnfold::ERegMode regMode=TUnfold::kRegModeCurvature;
  Int_t iPeek=(Int_t)(nGen*(estimatedPeakPosition-xminGen)/(xmaxGen-xminGen)
                      // offset 1.5
                      // accounts for start bin 1
                      // and rounding errors +0.5
                      +1.5);
  // regularize output bins 1..iPeek-nPeek
  unfold.RegularizeBins(1,1,iPeek-nPeek,regMode);
  // regularize output bins iPeek+nPeek..nGen
  unfold.RegularizeBins(iPeek+nPeek,1,nGen-(iPeek+nPeek),regMode);

  // set up bin map, excluding underflow and overflow bins
  Int_t *binMap=new Int_t[nGen+2];
  for(Int_t i=1;i<=nGen;i++) binMap[i]=i;
  binMap[0]=-1;
  binMap[nGen+1]=-1;

  // unfolding
  //-----------

  // set input distribution and bias scale (=0)
  unfold.SetInput(histMdetData,0.0);
  // reset user scan and define bin map
  unfold.ResetUser(binMap);

  Int_t nScan=30;
  Double_t tauMin=1.E-8;
  Double_t tauMax=10.;
  Int_t iBest;
  TSpline *logTauX,*logTauY;
  TGraph *lCurve;
  // this method scans the parameter tau and finds the kink in the L curve
  // finally, the unfolding is done for the best choice of tau
  iBest=unfold.ScanLcurve(nScan,tauMin,tauMax,&lCurve,&logTauX,&logTauY);
  std::cout<<"tau="<<unfold.GetTau()<<"\n";  
  Double_t t[1],x[1],y[1];
  logTauX->GetKnot(iBest,t[0],x[0]);
  logTauY->GetKnot(iBest,t[0],y[0]);
  TGraph *bestLcurve=new TGraph(1,x,y);
  TGraph *bestLogTauX=new TGraph(1,t,x);

  // save point with smallest correlation as a graph
  Double_t logTau=TMath::Log10(unfold.GetTauUser());
  x[0]=logTauX->Eval(logTau);
  y[0]=lCurve->Eval(x[0]);
  TGraph *lCurveUser=new TGraph(1,x,y);
  TGraph *logTauXuser=new TGraph(1,&logTau,x);

  TH1D *histMunfold=new TH1D("Unfolded",";mass(gen)",nGen,xminGen,xmaxGen);
  unfold.GetOutput(histMunfold,binMap);
  TH1D *histMdetFold=unfold.GetFoldedOutput("FoldedBack","mass(det)",
                                              xminDet,xmaxDet);
  TH2D *histRhoij=new TH2D("rho_ij",";mass(gen);mass(gen)",
                           nGen,xminGen,xmaxGen,nGen,xminGen,xmaxGen);
  unfold.GetRhoIJ(histRhoij,binMap);

  // store global correlation coefficients with underflow/overflow bins removed
  TH1D *histRhoi=new TH1D("rho_I","mass",nGen,xminGen,xmaxGen);
  // store inverse of error matrix with underflow/overflow bins removed
  // this is needed for the fit below
  gHistInvEMatrix=new TH2D("invEmat",";mass(gen);mass(gen)",
                           nGen,xminGen,xmaxGen,nGen,xminGen,xmaxGen);
  
  unfold.GetRhoI(histRhoi,gHistInvEMatrix,binMap);

  delete[] binMap;
  binMap=0;

  //======================================================================
  // fit Breit-Wigner shape to unfolded data, using the full error matrix
  // here we use a "user" chi**2 function to take into account
  // the full covariance matrix
  gFitter=TVirtualFitter::Fitter(histMunfold);
  gFitter->SetFCN(chisquare_corr);

  TF1 *bw=new TF1("bw",bw_func,xminGen,xmaxGen,3);
  bw->SetParameter(0,1000.);
  bw->SetParameter(1,3.8);
  bw->SetParameter(2,0.2);
  // for (wrong!) fitting without correlations, drop the option "U" 
  histMunfold->Fit(bw,"UE");

  //=====================================================================
  // plot some histograms
  TCanvas output;

  // produce some plots
  output.Divide(3,2);

  // Show the matrix which connects input and output
  // There are overflow bins at the bottom, not shown in the plot
  // These contain the background shape.
  // The overflow bins to the left and right contain
  // events which are not reconstructed. These are necessary for proper MC
  // normalisation
  output.cd(1);
  histMdetGenMC->Draw("BOX");

  // draw generator-level distribution:
  //   data (red) [for real data this is not available]
  //   MC input (black) [with completely wrong peak position and shape]
  //   unfolded data (blue)
  output.cd(2);
  histMunfold->SetLineColor(kBlue);
  histMunfold->Draw();
  histMgenData->SetLineColor(kRed);
  histMgenData->Draw("SAME");
  histMgenMC->Draw("SAME HIST");

  // show detector level distributions
  //    data (red)
  //    MC (black)
  //    unfolded data (blue)
  output.cd(3);
  histMdetFold->SetLineColor(kBlue);
  histMdetFold->Draw();
  histMdetData->SetLineColor(kRed);
  histMdetData->Draw("SAME");
  histMdetMC->Draw("SAME HIST");

  // show correlation coefficients
  //     all bins outside the peak are found to be highly correlated
  //     But they are compatible with zero anyway
  //     If the peak shape is fitted,
  //     these correlations have to be taken into account, see example
  output.cd(4);
  histRhoi->Draw("BOX");

  // show rhoi_max(tau) distribution
  output.cd(5);
  logTauX->Draw();
  bestLogTauX->SetMarkerColor(kRed);
  bestLogTauX->Draw("*");
  logTauXuser->SetMarkerColor(kBlue);
  logTauXuser->Draw("*");

  output.cd(6);
  lCurve->Draw("AL");
  bestLcurve->SetMarkerColor(kRed);
  lCurveUser->SetMarkerColor(kBlue);
  bestLcurve->Draw("*");
  lCurveUser->Draw("*");

  output.SaveAs("c1.ps");
  return 0;
}