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Reference Guide
testUnfold2.C File Reference

Detailed Description

View in nbviewer Open in SWAN Test program as an example for a user specific 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
chi**2=160.946+4.9728 / 147
(int) 0
#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;
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
if(rnd->Rndm()>bgr) {
// generate signal event
// with positive mass
do {
do {
} while(t>=1.0);
} 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 {
} 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
// 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,
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)
// reconstructed MC distribution (for comparison only)
// 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
// 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
// reconstructed mass, unfolding input
// set up the unfolding
TUnfold unfold(histMdetGenMC,TUnfold::kHistMapOutputVert,
// 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;
// calculate bin number corresponding 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
// regularize output bins 1..iPeek-nPeek
// regularize output bins iPeek+nPeek..nGen
// 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
<<" / "<<unfold.GetNdf()<<"\n";
// save point corresponding to the kink in the L curve as TGraph
Double_t t[1],x[1],y[1];
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;
TH1D *histMunfold=new TH1D("Unfolded",";mass(gen)",nGen,xminGen,xmaxGen);
TH1D *histMdetFold=new TH1D("FoldedBack","mass(det)",nDet,xminDet,xmaxDet);
// store global correlation coefficients
TH1D *histRhoi=new TH1D("rho_I","mass",nGen,xminGen,xmaxGen);
delete[] binMap;
// plot some histograms
// produce some plots
// 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
// 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)
histMgenMC->Draw("SAME HIST");
// show detector level distributions
// data (red)
// MC (black)
// unfolded data (blue)
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
// show rhoi_max(tau) distribution
return 0;
int Int_t
Definition: RtypesCore.h:45
double Double_t
Definition: RtypesCore.h:59
@ kRed
Definition: Rtypes.h:66
@ kBlue
Definition: Rtypes.h:66
virtual void SetLineColor(Color_t lcolor)
Set the line color.
Definition: TAttLine.h:40
virtual void SetMarkerColor(Color_t mcolor=1)
Set the marker color.
Definition: TAttMarker.h:38
The Canvas class.
Definition: TCanvas.h:23
A TGraph is an object made of two arrays X and Y with npoints each.
Definition: TGraph.h:41
virtual void Draw(Option_t *chopt="")
Draw this graph with its current attributes.
Definition: TGraph.cxx:769
1-D histogram with a double per channel (see TH1 documentation)}
Definition: TH1.h:618
virtual Int_t Fill(Double_t x)
Increment bin with abscissa X by 1.
Definition: TH1.cxx:3350
static void SetDefaultSumw2(Bool_t sumw2=kTRUE)
When this static function is called with sumw2=kTRUE, all new histograms will automatically activate ...
Definition: TH1.cxx:6663
virtual void Draw(Option_t *option="")
Draw this histogram with options.
Definition: TH1.cxx:3073
2-D histogram with a double per channel (see TH1 documentation)}
Definition: TH2.h:292
Int_t Fill(Double_t)
Invalid Fill method.
Definition: TH2.cxx:294
Random number generator class based on M.
Definition: TRandom3.h:27
This is the base class for the ROOT Random number generators.
Definition: TRandom.h:27
virtual Double_t Gaus(Double_t mean=0, Double_t sigma=1)
Samples a random number from the standard Normal (Gaussian) Distribution with the given mean and sigm...
Definition: TRandom.cxx:274
virtual Int_t Poisson(Double_t mean)
Generates a random integer N according to a Poisson law.
Definition: TRandom.cxx:402
virtual Double_t Rndm()
Machine independent random number generator.
Definition: TRandom.cxx:552
Base class for spline implementation containing the Draw/Paint methods.
Definition: TSpline.h:31
virtual void Draw(Option_t *option="")
Draw this function with its current attributes.
Definition: TSpline.cxx:101
virtual void GetKnot(Int_t i, Double_t &x, Double_t &y) const =0
An algorithm to unfold distributions from detector to truth level.
Definition: TUnfold.h:103
choice of regularisation scheme
Definition: TUnfold.h:119
@ kRegModeNone
no regularisation, or defined later by RegularizeXXX() methods
Definition: TUnfold.h:122
@ kRegModeCurvature
regularize the 2nd derivative of the output distribution
Definition: TUnfold.h:131
@ kHistMapOutputVert
truth level on y-axis of the response matrix
Definition: TUnfold.h:145
Double_t y[n]
Definition: legend1.C:17
Double_t x[n]
Definition: legend1.C:17
double gamma(double x)
LongDouble_t Power(LongDouble_t x, LongDouble_t y)
Definition: TMath.h:735
constexpr Double_t Pi()
Definition: TMath.h:37
Double_t Tan(Double_t)
Definition: TMath.h:647
Short_t Abs(Short_t d)
Definition: TMathBase.h:120
static void output(int code)
Definition: gifencode.c:226

Version 17.6, in parallel to changes in TUnfold


  • Version 17.5, in parallel to changes in TUnfold
  • Version 17.4, in parallel to changes in TUnfold
  • Version 17.3, in parallel to changes in TUnfold
  • Version 17.2, in parallel to changes in TUnfold
  • Version 17.1, in parallel to changes in TUnfold
  • Version 17.0, updated for changed methods in TUnfold
  • Version 16.1, parallel to changes in TUnfold
  • Version 16.0, parallel to changes in TUnfold
  • 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 separate 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

This file is part of TUnfold.

TUnfold is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

TUnfold is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with TUnfold. If not, see http://www.gnu.org/licenses/.

Stefan Schmitt DESY, 14.10.2008

Definition in file testUnfold2.C.