// TUnfold test program as an example for a more complex regularisation scheme
// Author: Stefan Schmitt
// DESY, 14.10.2008
// Version 16, parallel to changes in TUnfold
//
// History:
// Version 15, with automatic L-curve scan, simplified example
// Version 14, with changes in TUnfoldSys.cxx
// Version 13, with changes to TUnfold.C
// Version 12, with improvements to TUnfold.cxx
// Version 11, print chi**2 and number of degrees of freedom
// Version 10, with bug-fix in TUnfold.cxx
// Version 9, with bug-fix in TUnfold.cxx, TUnfold.h
// Version 8, with bug-fix in TUnfold.cxx, TUnfold.h
// Version 7, with bug-fix in TUnfold.cxx, TUnfold.h
// Version 6a, fix problem with dynamic array allocation under windows
// 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 as an example for a more complex regularisation scheme
//
// (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) produce some plots
//
///////////////////////////////////////////////////////////////////////
TRandom *rnd=0;
// generate an event
// output:
// negative mass: background event
// positive mass: signal event
Double_t GenerateEvent(Double_t bgr, // relative fraction of background
Double_t mass, // peak position
Double_t 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 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 testUnfold2()
{
// switch on histogram errors
TH1::SetDefaultSumw2();
// random generator
rnd=new TRandom3();
// data and MC luminosity, cross-section
Double_t const luminosityData=100000;
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
TUnfold unfold(histMdetGenMC,TUnfold::kHistMapOutputVert,
TUnfold::kRegModeNone);
// regularisation
//----------------
// the regularisation is done on the curvature (2nd derivative) of
// the output distribution
//
// One has to exclude the bins near the peak of the Breit-Wigner,
// because there the curvature is high
// (and the regularisation eventually could enforce a small
// curvature, thus biasing result)
//
// in real life, the parameters below would have to be optimized,
// depending on the data peak position and width
// Or maybe one finds a different regularisation scheme... this is
// just an example...
Double_t estimatedPeakPosition=3.8;
Int_t nPeek=3;
TUnfold::ERegMode regMode=TUnfold::kRegModeCurvature;
// calculate bin number correspoinding to estimated peak position
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);
// unfolding
//-----------
// set input distribution and bias scale (=0)
if(unfold.SetInput(histMdetData,0.0)>=10000) {
std::cout<<"Unfolding result may be wrong\n";
}
// do the unfolding here
Double_t tauMin=0.0;
Double_t tauMax=0.0;
Int_t nScan=30;
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";
std::cout<<"chi**2="<<unfold.GetChi2A()<<"+"<<unfold.GetChi2L()
<<" / "<<unfold.GetNdf()<<"\n";
// save point corresponding to the kink in the L curve as TGraph
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);
//============================================================
// extract unfolding results into histograms
// set up a bin map, excluding underflow and overflow bins
// the binMap relates the the output of the unfolding to the final
// histogram 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;
TH1D *histMunfold=new TH1D("Unfolded",";mass(gen)",nGen,xminGen,xmaxGen);
unfold.GetOutput(histMunfold,binMap);
TH1D *histMdetFold=unfold.GetFoldedOutput("FoldedBack","mass(det)",
xminDet,xmaxDet);
// store global correlation coefficients
TH1D *histRhoi=new TH1D("rho_I","mass",nGen,xminGen,xmaxGen);
unfold.GetRhoI(histRhoi,0,binMap);
delete[] binMap;
binMap=0;
//=====================================================================
// 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();
// show rhoi_max(tau) distribution
output.cd(5);
logTauX->Draw();
bestLogTauX->SetMarkerColor(kRed);
bestLogTauX->Draw("*");
output.cd(6);
lCurve->Draw("AL");
bestLcurve->SetMarkerColor(kRed);
bestLcurve->Draw("*");
output.SaveAs("testUnfold2.ps");
return 0;
}
