ROOT   Reference Guide
TSVDUnfoldExample.C File Reference

## Detailed Description

Data unfolding using Singular Value Decomposition

TSVDUnfold example

Data unfolding using Singular Value Decomposition (hep-ph/9509307)

Example distribution and smearing model from Tim Adye (RAL)

#include <iostream>
#include "TROOT.h"
#include "TSystem.h"
#include "TStyle.h"
#include "TRandom3.h"
#include "TString.h"
#include "TMath.h"
#include "TH1D.h"
#include "TH2D.h"
#include "TLegend.h"
#include "TCanvas.h"
#include "TColor.h"
#include "TLine.h"
#include "TSVDUnfold.h"
Double_t Reconstruct( Double_t xt, TRandom3& R )
{
// apply some Gaussian smearing + bias and efficiency corrections to fake reconstruction
const Double_t cutdummy = -99999.0;
Double_t xeff = 0.3 + (1.0 - 0.3)/20.0*(xt + 10.0); // efficiency
Double_t x = R.Rndm();
if (x > xeff) return cutdummy;
else {
Double_t xsmear= R.Gaus(-2.5,0.2); // bias and smear
return xt+xsmear;
}
}
void TSVDUnfoldExample()
{
gROOT->SetStyle("Plain");
const Double_t cutdummy= -99999.0;
// --------------------------------------
// Data/MC toy generation
//
// The MC input
Int_t nbins = 40;
TH1D *xini = new TH1D("xini", "MC truth", nbins, -10.0, 10.0);
TH1D *bini = new TH1D("bini", "MC reco", nbins, -10.0, 10.0);
TH2D *Adet = new TH2D("Adet", "detector response", nbins, -10.0, 10.0, nbins, -10.0, 10.0);
// Data
TH1D *data = new TH1D("data", "data", nbins, -10.0, 10.0);
// Data "truth" distribution to test the unfolding
TH1D *datatrue = new TH1D("datatrue", "data truth", nbins, -10.0, 10.0);
// Statistical covariance matrix
TH2D *statcov = new TH2D("statcov", "covariance matrix", nbins, -10.0, 10.0, nbins, -10.0, 10.0);
// Fill the MC using a Breit-Wigner, mean 0.3 and width 2.5.
for (Int_t i= 0; i<100000; i++) {
Double_t xt = R.BreitWigner(0.3, 2.5);
xini->Fill(xt);
Double_t x = Reconstruct( xt, R );
if (x != cutdummy) {
bini->Fill(x);
}
}
// Fill the "data" with a Gaussian, mean 0 and width 2.
for (Int_t i=0; i<10000; i++) {
Double_t xt = R.Gaus(0.0, 2.0);
datatrue->Fill(xt);
Double_t x = Reconstruct( xt, R );
if (x != cutdummy)
data->Fill(x);
}
cout << "Created toy distributions and errors for: " << endl;
cout << "... \"true MC\" and \"reconstructed (smeared) MC\"" << endl;
cout << "... \"true data\" and \"reconstructed (smeared) data\"" << endl;
cout << "... the \"detector response matrix\"" << endl;
// Fill the data covariance matrix
for (int i=1; i<=data->GetNbinsX(); i++) {
statcov->SetBinContent(i,i,data->GetBinError(i)*data->GetBinError(i));
}
// ----------------------------
// Here starts the actual unfolding
//
// Create TSVDUnfold object and initialise
TSVDUnfold *tsvdunf = new TSVDUnfold( data, statcov, bini, xini, Adet );
// It is possible to normalise unfolded spectrum to unit area
tsvdunf->SetNormalize( kFALSE ); // no normalisation here
// Perform the unfolding with regularisation parameter kreg = 13
// - the larger kreg, the finer grained the unfolding, but the more fluctuations occur
// - the smaller kreg, the stronger is the regularisation and the bias
TH1D* unfres = tsvdunf->Unfold( 13 );
// Get the distribution of the d to cross check the regularization
// - choose kreg to be the point where |d_i| stop being statistically significantly >>1
TH1D* ddist = tsvdunf->GetD();
// Get the distribution of the singular values
TH1D* svdist = tsvdunf->GetSV();
// Compute the error matrix for the unfolded spectrum using toy MC
// using the measured covariance matrix as input to generate the toys
// 100 toys should usually be enough
// The same method can be used for different covariance matrices separately.
TH2D* ustatcov = tsvdunf->GetUnfoldCovMatrix( statcov, 100 );
// Now compute the error matrix on the unfolded distribution originating
// from the finite detector matrix statistics
// Sum up the two (they are uncorrelated)
//Get the computed regularized covariance matrix (always corresponding to total uncertainty passed in constructor) and add uncertainties from finite MC statistics.
TH2D* utaucov = tsvdunf->GetXtau();
//Get the computed inverse of the covariance matrix
TH2D* uinvcov = tsvdunf->GetXinv();
// ---------------------------------
// Only plotting stuff below
for (int i=1; i<=unfres->GetNbinsX(); i++) {
unfres->SetBinError(i, TMath::Sqrt(utaucov->GetBinContent(i,i)));
}
// Renormalize just to be able to plot on the same scale
xini->Scale(0.7*datatrue->Integral()/xini->Integral());
TLegend *leg = new TLegend(0.58,0.60,0.99,0.88);
leg->SetBorderSize(0);
leg->SetFillColor(0);
leg->SetFillStyle(0);
TCanvas *c1 = new TCanvas( "c1", "Unfolding toy example with TSVDUnfold", 1000, 900 );
c1->Divide(1,2);
TH1D* frame = new TH1D( *unfres );
frame->SetTitle( "Unfolding toy example with TSVDUnfold" );
frame->GetXaxis()->SetTitle( "x variable" );
frame->GetYaxis()->SetTitle( "Events" );
frame->GetXaxis()->SetTitleOffset( 1.25 );
frame->GetYaxis()->SetTitleOffset( 1.29 );
frame->Draw();
data->SetLineStyle(2);
data->SetLineColor(4);
data->SetLineWidth(2);
unfres->SetMarkerStyle(20);
datatrue->SetLineColor(2);
datatrue->SetLineWidth(2);
xini->SetLineStyle(2);
xini->SetLineColor(8);
xini->SetLineWidth(2);
// ------------------------------------------------------------
unfres->Draw("same");
datatrue->Draw("same");
data->Draw("same");
xini->Draw("same");
leg->Draw();
// covariance matrix
c12->Divide(2,1);
c2->SetRightMargin ( 0.15 );
TH2D* covframe = new TH2D( *ustatcov );
covframe->SetTitle( "TSVDUnfold covariance matrix" );
covframe->GetXaxis()->SetTitle( "x variable" );
covframe->GetYaxis()->SetTitle( "x variable" );
covframe->GetXaxis()->SetTitleOffset( 1.25 );
covframe->GetYaxis()->SetTitleOffset( 1.29 );
covframe->Draw();
ustatcov->SetLineWidth( 2 );
ustatcov->Draw( "colzsame" );
// distribution of the d quantity
c3->SetLogy();
TLine *line = new TLine( 0.,1.,40.,1. );
TH1D* dframe = new TH1D( *ddist );
dframe->SetTitle( "TSVDUnfold |d_{i}|" );
dframe->GetXaxis()->SetTitle( "i" );
dframe->GetYaxis()->SetTitle( "|d_{i}|" );
dframe->GetXaxis()->SetTitleOffset( 1.25 );
dframe->GetYaxis()->SetTitleOffset( 1.29 );
dframe->SetMinimum( 0.001 );
dframe->Draw();
ddist->SetLineWidth( 2 );
ddist->Draw( "same" );
line->Draw();
}
#define R(a, b, c, d, e, f, g, h, i)
Definition: RSha256.hxx:110
int Int_t
Definition: RtypesCore.h:45
const Bool_t kFALSE
Definition: RtypesCore.h:92
double Double_t
Definition: RtypesCore.h:59
#define gROOT
Definition: TROOT.h:406
R__EXTERN TStyle * gStyle
Definition: TStyle.h:412
virtual void SetTitleOffset(Float_t offset=1)
Set distance between the axis and the axis title.
Definition: TAttAxis.cxx:293
virtual void SetLineStyle(Style_t lstyle)
Set the line style.
Definition: TAttLine.h:42
virtual void SetLineWidth(Width_t lwidth)
Set the line width.
Definition: TAttLine.h:43
virtual void SetLineColor(Color_t lcolor)
Set the line color.
Definition: TAttLine.h:40
virtual void SetMarkerStyle(Style_t mstyle=1)
Set the marker style.
Definition: TAttMarker.h:40
The Canvas class.
Definition: TCanvas.h:23
1-D histogram with a double per channel (see TH1 documentation)}
Definition: TH1.h:618
virtual void SetTitle(const char *title)
Definition: TH1.cxx:6678
virtual Double_t GetBinError(Int_t bin) const
Return value of error associated to bin number bin.
Definition: TH1.cxx:8903
TAxis * GetXaxis()
Definition: TH1.h:320
virtual Int_t GetNbinsX() const
Definition: TH1.h:296
virtual Bool_t Add(TF1 *h1, Double_t c1=1, Option_t *option="")
Performs the operation: this = this + c1*f1 if errors are defined (see TH1::Sumw2),...
Definition: TH1.cxx:822
virtual void SetBinError(Int_t bin, Double_t error)
Set the bin Error Note that this resets the bin eror option to be of Normal Type and for the non-empt...
Definition: TH1.cxx:9046
virtual Int_t Fill(Double_t x)
Increment bin with abscissa X by 1.
Definition: TH1.cxx:3350
TAxis * GetYaxis()
Definition: TH1.h:321
virtual void SetMinimum(Double_t minimum=-1111)
Definition: TH1.h:399
virtual Double_t Integral(Option_t *option="") const
Return integral of bin contents.
Definition: TH1.cxx:7834
virtual void Draw(Option_t *option="")
Draw this histogram with options.
Definition: TH1.cxx:3073
virtual void Scale(Double_t c1=1, Option_t *option="")
Multiply this histogram by a constant c1.
Definition: TH1.cxx:6564
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
virtual Double_t GetBinContent(Int_t bin) const
Return content of bin number bin.
Definition: TH2.h:88
virtual void SetBinContent(Int_t bin, Double_t content)
Set bin content.
Definition: TH2.cxx:2507
This class displays a legend box (TPaveText) containing several legend entries.
Definition: TLegend.h:23
A simple line.
Definition: TLine.h:22
virtual void SetTitle(const char *title="")
Set the title of the TNamed.
Definition: TNamed.cxx:164
virtual void Draw(Option_t *option="")
Default Draw method for all objects.
Definition: TObject.cxx:197
Random number generator class based on M.
Definition: TRandom3.h:27
SVD Approach to Data Unfolding.
Definition: TSVDUnfold.h:46
TH1D * GetSV() const
Returns singular values vector.
Definition: TSVDUnfold.cxx:591
TH2D * GetXtau() const
Returns the computed regularized covariance matrix corresponding to total uncertainties on measured s...
Definition: TSVDUnfold.cxx:600
TH1D * Unfold(Int_t kreg)
Perform the unfolding with regularisation parameter kreg.
Definition: TSVDUnfold.cxx:241
void SetNormalize(Bool_t normalize)
Definition: TSVDUnfold.h:66
TH1D * GetD() const
Returns d vector (for choosing appropriate regularisation)
Definition: TSVDUnfold.cxx:580
TH2D * GetUnfoldCovMatrix(const TH2D *cov, Int_t ntoys, Int_t seed=1)
Determine for given input error matrix covariance matrix of unfolded spectrum from toy simulation giv...
Definition: TSVDUnfold.cxx:409
TH2D * GetAdetCovMatrix(Int_t ntoys, Int_t seed=1)
Determine covariance matrix of unfolded spectrum from finite statistics in response matrix using pseu...
Definition: TSVDUnfold.cxx:515
TH2D * GetXinv() const
Returns the computed inverse of the covariance matrix.
Definition: TSVDUnfold.cxx:608
void SetOptStat(Int_t stat=1)
The type of information printed in the histogram statistics box can be selected via the parameter mod...
Definition: TStyle.cxx:1589
TVirtualPad is an abstract base class for the Pad and Canvas classes.
virtual void Divide(Int_t nx=1, Int_t ny=1, Float_t xmargin=0.01, Float_t ymargin=0.01, Int_t color=0)=0
TLine * line
return c1
Definition: legend1.C:41
Double_t x[n]
Definition: legend1.C:17
leg
Definition: legend1.C:34
return c2
Definition: legend2.C:14
return c3
Definition: legend3.C:15
Double_t Sqrt(Double_t x)
Definition: TMath.h:691

Definition in file TSVDUnfoldExample.C.