// At each iteration, an inverse response matrix is calculated, given //
// the measured spectrum, the a priori (guessed) spectrum, //
// the efficiency spectrum and the response matrix. //
-// For each iteration, the unfolded spectrum is calculated using //
+// //
+// Then at each iteration, the unfolded spectrum is calculated using //
// the inverse response : the goal is to get an unfolded spectrum //
// similar (according to some criterion) to the a priori one. //
// If the difference is too big, another iteration is performed : //
// previous iteration, and so on so forth, until the maximum number //
// of iterations or the similarity criterion is reached. //
// //
-// Currently the similarity criterion is the Chi2 between the a priori //
-// and the unfolded spectrum. //
+// Chi2 calculation became absolute with the correlated error //
+// calculation. //
+// Errors on the unfolded distribution are not known until the end //
+// Use the convergence criterion instead //
// //
// Currently the user has to define the max. number of iterations //
// (::SetMaxNumberOfIterations) //
-// and the chi2 below which the procedure will stop //
-// (::SetMaxChi2 or ::SetMaxChi2PerDOF) //
+// and //
+// - the chi2 below which the procedure will stop //
+// (::SetMaxChi2 or ::SetMaxChi2PerDOF) (OBSOLETE) //
+// - the convergence criterion below which the procedure will stop //
+// SetMaxConvergencePerDOF(Double_t val); //
+// //
+// Correlated error calculation can be activated by using: //
+// SetUseCorrelatedErrors(Bool_t b) in combination with convergence //
+// criterion //
+// Documentation about correlated error calculation method can be //
+// found in AliCFUnfolding::CalculateCorrelatedErrors() //
+// Author: marta.verweij@cern.ch //
// //
// An optional possibility is to smooth the unfolded spectrum at the //
// end of each iteration, either using a fit function //
// If no argument is passed to this function, then the second option //
// is used. //
// //
+// IMPORTANT: //
+//----------- //
+// With this approach, the efficiency map must be calculated //
+// with *simulated* values only, otherwise the method won't work. //
+// //
+// ex: efficiency(bin_pt) = number_rec(bin_pt) / number_sim(bin_pt) //
+// //
+// the pt bin "bin_pt" must always be the same in both the efficiency //
+// numerator and denominator. //
+// This is why the efficiency map has to be created by a method //
+// from which both reconstructed and simulated values are accessible //
+// simultaneously. //
+// //
+// //
//---------------------------------------------------------------------//
// Author : renaud.vernet@cern.ch //
//---------------------------------------------------------------------//
#include "AliCFUnfolding.h"
#include "TMath.h"
#include "TAxis.h"
-#include "AliLog.h"
#include "TF1.h"
#include "TH1D.h"
#include "TH2D.h"
#include "TH3D.h"
+#include "TRandom3.h"
+
ClassImp(AliCFUnfolding)
AliCFUnfolding::AliCFUnfolding() :
TNamed(),
- fResponse(0x0),
- fPrior(0x0),
- fEfficiency(0x0),
- fMeasured(0x0),
+ fResponseOrig(0x0),
+ fPriorOrig(0x0),
+ fEfficiencyOrig(0x0),
+ fMeasuredOrig(0x0),
fMaxNumIterations(0),
fNVariables(0),
- fMaxChi2(0),
fUseSmoothing(kFALSE),
fSmoothFunction(0x0),
- fSmoothOption(""),
- fOriginalPrior(0x0),
+ fSmoothOption("iremn"),
+ fMaxConvergence(0),
+ fNRandomIterations(0),
+ fResponse(0x0),
+ fPrior(0x0),
+ fEfficiency(0x0),
+ fMeasured(0x0),
fInverseResponse(0x0),
fMeasuredEstimate(0x0),
fConditional(0x0),
- fProjResponseInT(0x0),
fUnfolded(0x0),
+ fUnfoldedFinal(0x0),
fCoordinates2N(0x0),
fCoordinatesN_M(0x0),
- fCoordinatesN_T(0x0)
+ fCoordinatesN_T(0x0),
+ fRandomResponse(0x0),
+ fRandomEfficiency(0x0),
+ fRandomMeasured(0x0),
+ fRandom3(0x0),
+ fDeltaUnfoldedP(0x0),
+ fDeltaUnfoldedN(0x0),
+ fNCalcCorrErrors(0),
+ fRandomSeed(0)
{
//
// default constructor
//______________________________________________________________
AliCFUnfolding::AliCFUnfolding(const Char_t* name, const Char_t* title, const Int_t nVar,
- const THnSparse* response, const THnSparse* efficiency, const THnSparse* measured, const THnSparse* prior) :
+ const THnSparse* response, const THnSparse* efficiency, const THnSparse* measured, const THnSparse* prior ,
+ Double_t maxConvergencePerDOF, UInt_t randomSeed, Int_t maxNumIterations
+ ) :
TNamed(name,title),
+ fResponseOrig((THnSparse*)response->Clone()),
+ fPriorOrig(0x0),
+ fEfficiencyOrig((THnSparse*)efficiency->Clone()),
+ fMeasuredOrig((THnSparse*)measured->Clone()),
+ fMaxNumIterations(maxNumIterations),
+ fNVariables(nVar),
+ fUseSmoothing(kFALSE),
+ fSmoothFunction(0x0),
+ fSmoothOption("iremn"),
+ fMaxConvergence(0),
+ fNRandomIterations(maxNumIterations),
fResponse((THnSparse*)response->Clone()),
fPrior(0x0),
fEfficiency((THnSparse*)efficiency->Clone()),
fMeasured((THnSparse*)measured->Clone()),
- fMaxNumIterations(0),
- fNVariables(nVar),
- fMaxChi2(0),
- fUseSmoothing(kFALSE),
- fSmoothFunction(0x0),
- fSmoothOption(""),
- fOriginalPrior(0x0),
fInverseResponse(0x0),
fMeasuredEstimate(0x0),
fConditional(0x0),
- fProjResponseInT(0x0),
fUnfolded(0x0),
+ fUnfoldedFinal(0x0),
fCoordinates2N(0x0),
fCoordinatesN_M(0x0),
- fCoordinatesN_T(0x0)
+ fCoordinatesN_T(0x0),
+ fRandomResponse((THnSparse*)response->Clone()),
+ fRandomEfficiency((THnSparse*)efficiency->Clone()),
+ fRandomMeasured((THnSparse*)measured->Clone()),
+ fRandom3(0x0),
+ fDeltaUnfoldedP(0x0),
+ fDeltaUnfoldedN(0x0),
+ fNCalcCorrErrors(0),
+ fRandomSeed(randomSeed)
{
//
// named constructor
//
AliInfo(Form("\n\n--------------------------\nCreating an unfolder :\n--------------------------\nresponse matrix has %d dimension(s)",fResponse->GetNdimensions()));
-
+
if (!prior) CreateFlatPrior(); // if no prior distribution declared, simply use a flat distribution
else {
fPrior = (THnSparse*) prior->Clone();
- fOriginalPrior = (THnSparse*)fPrior->Clone();
+ fPriorOrig = (THnSparse*)fPrior->Clone();
if (fPrior->GetNdimensions() != fNVariables)
AliFatal(Form("The prior matrix should have %d dimensions, and it has actually %d",fNVariables,fPrior->GetNdimensions()));
}
AliInfo(Form("efficiency matrix has %d bins in dimension %d",fEfficiency->GetAxis(iVar)->GetNbins(),iVar));
AliInfo(Form("measured matrix has %d bins in dimension %d",fMeasured ->GetAxis(iVar)->GetNbins(),iVar));
}
- Init();
-}
-
-
-//______________________________________________________________
-AliCFUnfolding::AliCFUnfolding(const AliCFUnfolding& c) :
- TNamed(c),
- fResponse((THnSparse*)c.fResponse->Clone()),
- fPrior((THnSparse*)c.fPrior->Clone()),
- fEfficiency((THnSparse*)c.fEfficiency->Clone()),
- fMeasured((THnSparse*)c.fMeasured->Clone()),
- fMaxNumIterations(c.fMaxNumIterations),
- fNVariables(c.fNVariables),
- fMaxChi2(c.fMaxChi2),
- fUseSmoothing(c.fUseSmoothing),
- fSmoothFunction((TF1*)c.fSmoothFunction->Clone()),
- fSmoothOption(fSmoothOption),
- fOriginalPrior((THnSparse*)c.fOriginalPrior->Clone()),
- fInverseResponse((THnSparse*)c.fInverseResponse->Clone()),
- fMeasuredEstimate((THnSparse*)fMeasuredEstimate->Clone()),
- fConditional((THnSparse*)c.fConditional->Clone()),
- fProjResponseInT((THnSparse*)c.fProjResponseInT->Clone()),
- fUnfolded((THnSparse*)c.fUnfolded->Clone()),
- fCoordinates2N(new Int_t(*c.fCoordinates2N)),
- fCoordinatesN_M(new Int_t(*c.fCoordinatesN_M)),
- fCoordinatesN_T(new Int_t(*c.fCoordinatesN_T))
-{
- //
- // copy constructor
- //
-}
-
-//______________________________________________________________
-
-AliCFUnfolding& AliCFUnfolding::operator=(const AliCFUnfolding& c) {
- //
- // assignment operator
- //
-
- if (this!=&c) {
- TNamed::operator=(c);
- fResponse = (THnSparse*)c.fResponse->Clone() ;
- fPrior = (THnSparse*)c.fPrior->Clone() ;
- fEfficiency = (THnSparse*)c.fEfficiency->Clone() ;
- fMeasured = (THnSparse*)c.fMeasured->Clone() ;
- fMaxNumIterations = c.fMaxNumIterations ;
- fNVariables = c.fNVariables ;
- fMaxChi2 = c.fMaxChi2 ;
- fUseSmoothing = c.fUseSmoothing ;
- fSmoothFunction = (TF1*)c.fSmoothFunction->Clone();
- fSmoothOption = c.fSmoothOption ;
- fOriginalPrior = (THnSparse*)c.fOriginalPrior->Clone() ;
- fInverseResponse = (THnSparse*)c.fInverseResponse->Clone() ;
- fMeasuredEstimate = (THnSparse*)fMeasuredEstimate->Clone() ;
- fConditional = (THnSparse*)c.fConditional->Clone() ;
- fProjResponseInT = (THnSparse*)c.fProjResponseInT->Clone() ;
- fUnfolded = (THnSparse*)c.fUnfolded->Clone() ;
- fCoordinates2N = new Int_t(*c.fCoordinates2N) ;
- fCoordinatesN_M = new Int_t(*c.fCoordinatesN_M) ;
- fCoordinatesN_T = new Int_t(*c.fCoordinatesN_T) ;
- }
- return *this;
+ fRandomResponse ->SetTitle("Randomized response matrix");
+ fRandomEfficiency->SetTitle("Randomized efficiency");
+ fRandomMeasured ->SetTitle("Randomized measured");
+ SetMaxConvergencePerDOF(maxConvergencePerDOF) ;
+ Init();
}
//______________________________________________________________
if (fResponse) delete fResponse;
if (fPrior) delete fPrior;
if (fEfficiency) delete fEfficiency;
+ if (fEfficiencyOrig) delete fEfficiencyOrig;
if (fMeasured) delete fMeasured;
+ if (fMeasuredOrig) delete fMeasuredOrig;
if (fSmoothFunction) delete fSmoothFunction;
- if (fOriginalPrior) delete fOriginalPrior;
+ if (fPriorOrig) delete fPriorOrig;
if (fInverseResponse) delete fInverseResponse;
if (fMeasuredEstimate) delete fMeasuredEstimate;
if (fConditional) delete fConditional;
- if (fProjResponseInT) delete fProjResponseInT;
+ if (fUnfolded) delete fUnfolded;
+ if (fUnfoldedFinal) delete fUnfoldedFinal;
if (fCoordinates2N) delete [] fCoordinates2N;
if (fCoordinatesN_M) delete [] fCoordinatesN_M;
if (fCoordinatesN_T) delete [] fCoordinatesN_T;
+ if (fRandomResponse) delete fRandomResponse;
+ if (fRandomEfficiency) delete fRandomEfficiency;
+ if (fRandomMeasured) delete fRandomMeasured;
+ if (fRandom3) delete fRandom3;
+ if (fDeltaUnfoldedP) delete fDeltaUnfoldedP;
+ if (fDeltaUnfoldedN) delete fDeltaUnfoldedN;
+
}
//______________________________________________________________
// initialisation function : creates internal settings
//
+ fRandom3 = new TRandom3(fRandomSeed);
+
fCoordinates2N = new Int_t[2*fNVariables];
fCoordinatesN_M = new Int_t[fNVariables];
fCoordinatesN_T = new Int_t[fNVariables];
// create the matrix of conditional probabilities P(M|T)
- CreateConditional();
+ CreateConditional(); //done only once at initialization
// create the frame of the inverse response matrix
fInverseResponse = (THnSparse*) fResponse->Clone();
// create the frame of the unfolded spectrum
fUnfolded = (THnSparse*) fPrior->Clone();
+ fUnfolded->SetTitle("Unfolded");
// create the frame of the measurement estimate spectrum
fMeasuredEstimate = (THnSparse*) fMeasured->Clone();
+
+ // create the frame of the delta profiles
+ fDeltaUnfoldedP = (THnSparse*)fPrior->Clone();
+ fDeltaUnfoldedP->SetTitle("#Delta unfolded");
+ fDeltaUnfoldedP->Reset();
+ fDeltaUnfoldedN = (THnSparse*)fPrior->Clone();
+ fDeltaUnfoldedN->SetTitle("");
+ fDeltaUnfoldedN->Reset();
+
+
}
+
//______________________________________________________________
void AliCFUnfolding::CreateEstMeasured() {
// fill it
for (Long_t iBin=0; iBin<fConditional->GetNbins(); iBin++) {
Double_t conditionalValue = fConditional->GetBinContent(iBin,fCoordinates2N);
- Double_t conditionalError = fConditional->GetBinError (iBin);
GetCoordinates();
Double_t priorTimesEffValue = priorTimesEff->GetBinContent(fCoordinatesN_T);
- Double_t priorTimesEffError = priorTimesEff->GetBinError (fCoordinatesN_T);
Double_t fill = conditionalValue * priorTimesEffValue ;
if (fill>0.) {
fMeasuredEstimate->AddBinContent(fCoordinatesN_M,fill);
-
- // error calculation : gaussian error propagation (may be overestimated...)
- Double_t err2 = TMath::Power(fMeasuredEstimate->GetBinError(fCoordinatesN_M),2) ;
- err2 += TMath::Power(conditionalValue*priorTimesEffError,2) + TMath::Power(conditionalError*priorTimesEffValue,2) ;
- Double_t err = TMath::Sqrt(err2);
- fMeasuredEstimate->SetBinError(fCoordinatesN_M,err);
+ fMeasuredEstimate->SetBinError(fCoordinatesN_M,0.);
}
}
delete priorTimesEff ;
for (Long_t iBin=0; iBin<fConditional->GetNbins(); iBin++) {
Double_t conditionalValue = fConditional->GetBinContent(iBin,fCoordinates2N);
- Double_t conditionalError = fConditional->GetBinError (iBin);
GetCoordinates();
Double_t estMeasuredValue = fMeasuredEstimate->GetBinContent(fCoordinatesN_M);
- Double_t estMeasuredError = fMeasuredEstimate->GetBinError (fCoordinatesN_M);
Double_t priorTimesEffValue = priorTimesEff ->GetBinContent(fCoordinatesN_T);
- Double_t priorTimesEffError = priorTimesEff ->GetBinError (fCoordinatesN_T);
Double_t fill = (estMeasuredValue>0. ? conditionalValue * priorTimesEffValue / estMeasuredValue : 0. ) ;
- // error calculation : gaussian error propagation (may be overestimated...)
- Double_t err = 0. ;
- if (estMeasuredValue>0.) {
- err = TMath::Sqrt( TMath::Power(conditionalError * priorTimesEffValue * estMeasuredValue ,2) +
- TMath::Power(conditionalValue * priorTimesEffError * estMeasuredValue ,2) +
- TMath::Power(conditionalValue * priorTimesEffValue * estMeasuredError ,2) )
- / TMath::Power(estMeasuredValue,2) ;
- }
if (fill>0. || fInverseResponse->GetBinContent(fCoordinates2N)>0.) {
fInverseResponse->SetBinContent(fCoordinates2N,fill);
- fInverseResponse->SetBinError (fCoordinates2N,err );
+ fInverseResponse->SetBinError (fCoordinates2N,0.);
}
}
delete priorTimesEff ;
void AliCFUnfolding::Unfold() {
//
// Main routine called by the user :
- // it calculates the unfolded spectrum from the response matrix and the measured spectrum
- // several iterations are performed until a reasonable chi2 is reached
+ // it calculates the unfolded spectrum from the response matrix, measured spectrum and efficiency
+ // several iterations are performed until a reasonable chi2 or convergence criterion is reached
//
- Int_t iIterBayes=0 ;
- Double_t chi2=0 ;
+ Int_t iIterBayes = 0 ;
+ Double_t convergence = 0.;
for (iIterBayes=0; iIterBayes<fMaxNumIterations; iIterBayes++) { // bayes iterations
- CreateEstMeasured();
- CreateInvResponse();
- CreateUnfolded();
- chi2 = GetChi2();
- AliDebug(0,Form("Chi2 at iteration %d is %e",iIterBayes,chi2));
- if (fMaxChi2>0. && chi2<fMaxChi2) {
+
+ CreateEstMeasured(); // create measured estimate from prior
+ CreateInvResponse(); // create inverse response from prior
+ CreateUnfolded(); // create unfoled spectrum from measured and inverse response
+
+ convergence = GetConvergence();
+ AliDebug(0,Form("convergence at iteration %d is %e",iIterBayes,convergence));
+
+ if (fMaxConvergence>0. && convergence<fMaxConvergence && fNCalcCorrErrors == 0) {
+ fNRandomIterations = iIterBayes;
+ AliDebug(0,Form("convergence is met at iteration %d",iIterBayes));
break;
}
- // update the prior distribution
+
if (fUseSmoothing) {
if (Smooth()) {
AliError("Couldn't smooth the unfolded spectrum!!");
- AliInfo(Form("\n\n=======================\nFinished at iteration %d : Chi2 is %e and you required it to be < %e\n=======================\n\n",iIterBayes,chi2,fMaxChi2));
+ if (fNCalcCorrErrors>0) {
+ AliInfo(Form("=======================\nUnfold of randomized distribution finished at iteration %d with convergence %e \n",iIterBayes,convergence));
+ }
+ else {
+ AliInfo(Form("\n\n=======================\nFinish at iteration %d : convergence is %e and you required it to be < %e\n=======================\n\n",iIterBayes,convergence,fMaxConvergence));
+ }
return;
}
}
- fPrior = (THnSparse*)fUnfolded->Clone() ; // this should be changed (memory)
+
+ // update the prior distribution
+ if (fPrior) delete fPrior ;
+ fPrior = (THnSparse*)fUnfolded->Clone() ;
+ fPrior->SetTitle("Prior");
+
+ } // end bayes iteration
+
+ if (fNCalcCorrErrors==0) fUnfoldedFinal = (THnSparse*) fUnfolded->Clone() ;
+
+ //
+ //for (Long_t iBin=0; iBin<fUnfoldedFinal->GetNbins(); iBin++) AliDebug(2,Form("%e\n",fUnfoldedFinal->GetBinError(iBin)));
+ //
+
+ if (fNCalcCorrErrors == 0) {
+ AliInfo("\n================================================\nFinished bayes iteration, now calculating errors...\n================================================\n");
+ fNCalcCorrErrors = 1;
+ CalculateCorrelatedErrors();
+ }
+
+ if (fNCalcCorrErrors >1 ) {
+ AliInfo(Form("\n\n=======================\nFinished at iteration %d : convergence is %e and you required it to be < %e\n=======================\n\n",iIterBayes,convergence,fMaxConvergence));
+ }
+ else if(fNCalcCorrErrors>0) {
+ AliInfo(Form("=======================\nUnfolding of randomized distribution finished at iteration %d with convergence %e \n",iIterBayes,convergence));
}
- AliInfo(Form("\n\n=======================\nFinished at iteration %d : Chi2 is %e and you required it to be < %e\n=======================\n\n",iIterBayes,chi2,fMaxChi2));
}
//______________________________________________________________
// clear the unfolded spectrum
+ // if in the process of error calculation, the random unfolded spectrum is created
+ // otherwise the normal unfolded spectrum is created
+
fUnfolded->Reset();
for (Long_t iBin=0; iBin<fInverseResponse->GetNbins(); iBin++) {
Double_t invResponseValue = fInverseResponse->GetBinContent(iBin,fCoordinates2N);
- Double_t invResponseError = fInverseResponse->GetBinError (iBin);
GetCoordinates();
Double_t effValue = fEfficiency->GetBinContent(fCoordinatesN_T);
- Double_t effError = fEfficiency->GetBinError (fCoordinatesN_T);
Double_t measuredValue = fMeasured ->GetBinContent(fCoordinatesN_M);
- Double_t measuredError = fMeasured ->GetBinError (fCoordinatesN_M);
Double_t fill = (effValue>0. ? invResponseValue * measuredValue / effValue : 0.) ;
-
+
if (fill>0.) {
+ // set errors to zero
+ // true errors will be filled afterwards
+ Double_t err = 0.;
+ fUnfolded->SetBinError (fCoordinatesN_T,err);
fUnfolded->AddBinContent(fCoordinatesN_T,fill);
-
- // error calculation : gaussian error propagation (may be overestimated...)
- Double_t err2 = TMath::Power(fUnfolded->GetBinError(fCoordinatesN_T),2) ;
- err2 += TMath::Power(invResponseError * measuredValue * effValue,2) / TMath::Power(effValue,4) ;
- err2 += TMath::Power(invResponseValue * measuredError * effValue,2) / TMath::Power(effValue,4) ;
- err2 += TMath::Power(invResponseValue * measuredValue * effError,2) / TMath::Power(effValue,4) ;
- Double_t err = TMath::Sqrt(err2);
- fUnfolded->SetBinError(fCoordinatesN_T,err);
}
}
}
+
+//______________________________________________________________
+
+void AliCFUnfolding::CalculateCorrelatedErrors() {
+
+ // Step 1: Create randomized distribution (fRandomXXXX) of each bin of
+ // the measured spectrum to calculate correlated errors.
+ // Poisson statistics: mean = measured value of bin
+ // Step 2: Unfold randomized distribution
+ // Step 3: Store difference of unfolded spectrum from measured distribution and
+ // unfolded distribution from randomized distribution
+ // -> fDeltaUnfoldedP (TProfile with option "S")
+ // Step 4: Repeat Step 1-3 several times (fNRandomIterations)
+ // Step 5: The spread of fDeltaUnfoldedP for each bin is the error on the unfolded spectrum of that specific bin
+
+
+ //Do fNRandomIterations = bayes iterations performed
+ for (int i=0; i<fNRandomIterations; i++) {
+ // reset prior to original one
+ if (fPrior) delete fPrior ;
+ fPrior = (THnSparse*) fPriorOrig->Clone();
+
+ // create randomized distribution and stick measured spectrum to it
+ CreateRandomizedDist();
+
+ if (fResponse) delete fResponse ;
+ fResponse = (THnSparse*) fRandomResponse->Clone();
+ fResponse->SetTitle("Response");
+
+ if (fEfficiency) delete fEfficiency ;
+ fEfficiency = (THnSparse*) fRandomEfficiency->Clone();
+ fEfficiency->SetTitle("Efficiency");
+
+ if (fMeasured) delete fMeasured ;
+ fMeasured = (THnSparse*) fRandomMeasured->Clone();
+ fMeasured->SetTitle("Measured");
+
+ //unfold with randomized distributions
+ Unfold();
+ FillDeltaUnfoldedProfile();
+ }
+
+ // Get statistical errors for final unfolded spectrum
+ // ie. spread of each pt bin in fDeltaUnfoldedP
+ Double_t meanx2 = 0.;
+ Double_t mean = 0.;
+ Double_t checksigma = 0.;
+ Double_t entriesInBin = 0.;
+ for (Long_t iBin=0; iBin<fUnfoldedFinal->GetNbins(); iBin++) {
+ fUnfoldedFinal->GetBinContent(iBin,fCoordinatesN_M);
+ mean = fDeltaUnfoldedP->GetBinContent(fCoordinatesN_M);
+ meanx2 = fDeltaUnfoldedP->GetBinError(fCoordinatesN_M);
+ entriesInBin = fDeltaUnfoldedN->GetBinContent(fCoordinatesN_M);
+ if(entriesInBin > 1.) checksigma = TMath::Sqrt((entriesInBin/(entriesInBin-1.))*TMath::Abs(meanx2-mean*mean));
+ //printf("mean %f, meanx2 %f, sigmacheck %f, nentries %f\n",mean, meanx2, checksigma,entriesInBin);
+ //AliDebug(2,Form("filling error %e\n",sigma));
+ fUnfoldedFinal->SetBinError(fCoordinatesN_M,checksigma);
+ }
+
+ // now errors are calculated
+ fNCalcCorrErrors = 2;
+}
+
+//______________________________________________________________
+void AliCFUnfolding::CreateRandomizedDist() {
+ //
+ // Create randomized dist from original measured distribution
+ // This distribution is created several times, each time with a different random number
+ //
+
+ for (Long_t iBin=0; iBin<fResponseOrig->GetNbins(); iBin++) {
+ Double_t val = fResponseOrig->GetBinContent(iBin,fCoordinatesN_M); //used as mean
+ Double_t err = fResponseOrig->GetBinError(fCoordinatesN_M); //used as sigma
+ Double_t ran = fRandom3->Gaus(val,err);
+ // random = fRandom3->PoissonD(measuredValue); //doesn't work for normalized spectra, use Gaus (assuming raw counts in bin is large >10)
+ fRandomResponse->SetBinContent(iBin,ran);
+ }
+ for (Long_t iBin=0; iBin<fEfficiencyOrig->GetNbins(); iBin++) {
+ Double_t val = fEfficiencyOrig->GetBinContent(iBin,fCoordinatesN_M); //used as mean
+ Double_t err = fEfficiencyOrig->GetBinError(fCoordinatesN_M); //used as sigma
+ Double_t ran = fRandom3->Gaus(val,err);
+ // random = fRandom3->PoissonD(measuredValue); //doesn't work for normalized spectra, use Gaus (assuming raw counts in bin is large >10)
+ fRandomEfficiency->SetBinContent(iBin,ran);
+ }
+ for (Long_t iBin=0; iBin<fMeasuredOrig->GetNbins(); iBin++) {
+ Double_t val = fMeasuredOrig->GetBinContent(iBin,fCoordinatesN_M); //used as mean
+ Double_t err = fMeasuredOrig->GetBinError(fCoordinatesN_M); //used as sigma
+ Double_t ran = fRandom3->Gaus(val,err);
+ // random = fRandom3->PoissonD(measuredValue); //doesn't work for normalized spectra, use Gaus (assuming raw counts in bin is large >10)
+ fRandomMeasured->SetBinContent(iBin,ran);
+ }
+}
+
+//______________________________________________________________
+void AliCFUnfolding::FillDeltaUnfoldedProfile() {
+ //
+ // Store difference of unfolded spectrum from measured distribution and unfolded spectrum from randomized distribution
+ // The delta profile has been set to a THnSparse to handle N dimension
+ // The THnSparse contains in each bin the mean value and spread of the difference
+ // This function updates the profile wrt to its previous mean and error
+ // The relation between iterations (n+1) and n is as follows :
+ // mean_{n+1} = (n*mean_n + value_{n+1}) / (n+1)
+ // sigma_{n+1} = sqrt { 1/(n+1) * [ n*sigma_n^2 + (n^2+n)*(mean_{n+1}-mean_n)^2 ] } (can this be optimized?)
+
+ for (Long_t iBin=0; iBin<fUnfoldedFinal->GetNbins(); iBin++) {
+ Double_t deltaInBin = fUnfoldedFinal->GetBinContent(iBin,fCoordinatesN_M) - fUnfolded->GetBinContent(fCoordinatesN_M);
+ Double_t entriesInBin = fDeltaUnfoldedN->GetBinContent(fCoordinatesN_M);
+ //AliDebug(2,Form("%e %e ==> delta = %e\n",fUnfoldedFinal->GetBinContent(iBin,fCoordinatesN_M),fUnfolded->GetBinContent(iBin),deltaInBin));
+
+ //printf("deltaInBin %f\n",deltaInBin);
+ //printf("pt %f\n",ptaxis->GetBinCenter(iBin+1));
+
+ Double_t mean_n = fDeltaUnfoldedP->GetBinContent(fCoordinatesN_M) ;
+ Double_t mean_nplus1 = mean_n ;
+ mean_nplus1 *= entriesInBin ;
+ mean_nplus1 += deltaInBin ;
+ mean_nplus1 /= (entriesInBin+1) ;
+
+ Double_t meanx2_n = fDeltaUnfoldedP->GetBinError(fCoordinatesN_M) ;
+ Double_t meanx2_nplus1 = meanx2_n ;
+ meanx2_nplus1 *= entriesInBin ;
+ meanx2_nplus1 += (deltaInBin*deltaInBin) ;
+ meanx2_nplus1 /= (entriesInBin+1) ;
+
+ //AliDebug(2,Form("sigma = %e\n",sigma));
+
+ fDeltaUnfoldedP->SetBinError(fCoordinatesN_M,meanx2_nplus1) ;
+ fDeltaUnfoldedP->SetBinContent(fCoordinatesN_M,mean_nplus1) ;
+ fDeltaUnfoldedN->SetBinContent(fCoordinatesN_M,entriesInBin+1);
+ }
+}
+
//______________________________________________________________
void AliCFUnfolding::GetCoordinates() {
// --> R*(i,j) = R(i,j) / SUM_k{ R(k,j) }
//
- fConditional = (THnSparse*) fResponse->Clone(); // output of this function
- fProjResponseInT = (THnSparse*) fPrior->Clone(); // output denominator :
- // projection of the response matrix on the TRUE axis
+ fConditional = (THnSparse*) fResponse->Clone(); // output of this function
+
Int_t* dim = new Int_t [fNVariables];
for (Int_t iDim=0; iDim<fNVariables; iDim++) dim[iDim] = fNVariables+iDim ; //dimensions corresponding to TRUE values (i.e. from N to 2N-1)
- fProjResponseInT = fConditional->Projection(fNVariables,dim,"E"); //project
+
+ THnSparse* responseInT = fConditional->Projection(fNVariables,dim,"E"); // output denominator :
+ // projection of the response matrix on the TRUE axis
delete [] dim;
-
+
// fill the conditional probability matrix
for (Long_t iBin=0; iBin<fResponse->GetNbins(); iBin++) {
Double_t responseValue = fResponse->GetBinContent(iBin,fCoordinates2N);
- Double_t responseError = fResponse->GetBinError (iBin);
GetCoordinates();
- Double_t projValue = fProjResponseInT->GetBinContent(fCoordinatesN_T);
- Double_t projError = fProjResponseInT->GetBinError (fCoordinatesN_T);
-
+ Double_t projValue = responseInT->GetBinContent(fCoordinatesN_T);
+
Double_t fill = responseValue / projValue ;
if (fill>0. || fConditional->GetBinContent(fCoordinates2N)>0.) {
fConditional->SetBinContent(fCoordinates2N,fill);
- // gaussian error for the moment
- Double_t err2 = TMath::Power(responseError*projValue,2) + TMath::Power(responseValue*projError,2) ;
- Double_t err = TMath::Sqrt(err2);
- err /= TMath::Power(projValue,2) ;
+ Double_t err = 0.;
fConditional->SetBinError (fCoordinates2N,err);
}
}
+ delete responseInT ;
+}
+//______________________________________________________________
+
+Int_t AliCFUnfolding::GetDOF() {
+ //
+ // number of dof = number of bins
+ //
+
+ Int_t nDOF = 1 ;
+ for (Int_t iDim=0; iDim<fNVariables; iDim++) {
+ nDOF *= fPrior->GetAxis(iDim)->GetNbins();
+ }
+ AliDebug(0,Form("Number of degrees of freedom = %d",nDOF));
+ return nDOF;
}
//______________________________________________________________
Double_t AliCFUnfolding::GetChi2() {
//
// Returns the chi2 between unfolded and a priori spectrum
+ // This function became absolute with the correlated error calculation.
+ // Errors on the unfolded distribution are not known until the end
+ // Use the convergence criterion instead
//
- Double_t chi2 = 0. ;
+ Double_t chi2 = 0. ;
+ Double_t error_unf = 0.;
for (Long_t iBin=0; iBin<fPrior->GetNbins(); iBin++) {
Double_t priorValue = fPrior->GetBinContent(iBin,fCoordinatesN_T);
- Double_t error_unf = fUnfolded->GetBinError(fCoordinatesN_T);
+ error_unf = fUnfolded->GetBinError(fCoordinatesN_T);
chi2 += (error_unf > 0. ? TMath::Power((fUnfolded->GetBinContent(fCoordinatesN_T) - priorValue)/error_unf,2) / priorValue : 0.) ;
}
return chi2;
//______________________________________________________________
-void AliCFUnfolding::SetMaxChi2PerDOF(Double_t val) {
+Double_t AliCFUnfolding::GetConvergence() {
//
- // Max. chi2 per degree of freedom : user setting
+ // Returns convergence criterion = \sum_t ((U_t^{n-1}-U_t^n)/U_t^{n-1})^2
+ // U is unfolded spectrum, t is the bin, n = current, n-1 = previous
//
+ Double_t convergence = 0.;
+ Double_t priorValue = 0.;
+ Double_t currentValue = 0.;
+ for (Long_t iBin=0; iBin < fPrior->GetNbins(); iBin++) {
+ priorValue = fPrior->GetBinContent(iBin,fCoordinatesN_T);
+ currentValue = fUnfolded->GetBinContent(fCoordinatesN_T);
- Int_t nDOF = 1 ;
- for (Int_t iDim=0; iDim<fNVariables; iDim++) {
- nDOF *= fPrior->GetAxis(iDim)->GetNbins();
+ if (priorValue > 0.)
+ convergence += ((priorValue-currentValue)/priorValue)*((priorValue-currentValue)/priorValue);
+ else
+ AliWarning(Form("priorValue = %f. Adding 0 to convergence criterion.",priorValue));
}
- AliInfo(Form("Number of degrees of freedom = %d",nDOF));
- fMaxChi2 = val * nDOF ;
+ return convergence;
+}
+
+//______________________________________________________________
+
+void AliCFUnfolding::SetMaxConvergencePerDOF(Double_t val) {
+ //
+ // Max. convergence criterion per degree of freedom : user setting
+ // convergence criterion = DOF*val; DOF = number of bins
+ // In Jan-Fiete's multiplicity note: Convergence criterion = DOF*0.001^2
+ //
+
+ Int_t nDOF = GetDOF() ;
+ fMaxConvergence = val * nDOF ;
+ AliInfo(Form("MaxConvergence = %e. Number of degrees of freedom = %d",fMaxConvergence,nDOF));
}
//______________________________________________________________
AliDebug(2,Form("Smoothing spectrum with fit function %p",fSmoothFunction));
return SmoothUsingFunction();
}
- else return SmoothUsingNeighbours();
+ else return SmoothUsingNeighbours(fUnfolded);
}
//______________________________________________________________
-Short_t AliCFUnfolding::SmoothUsingNeighbours() {
+Short_t AliCFUnfolding::SmoothUsingNeighbours(THnSparse* hist) {
//
// Smoothes the unfolded spectrum using neighouring bins
//
- Int_t* numBins = new Int_t[fNVariables];
- for (Int_t iVar=0; iVar<fNVariables; iVar++) numBins[iVar]=fUnfolded->GetAxis(iVar)->GetNbins();
+ Int_t const nDimensions = hist->GetNdimensions() ;
+ Int_t* coordinates = new Int_t[nDimensions];
+
+ Int_t* numBins = new Int_t[nDimensions];
+ for (Int_t iVar=0; iVar<nDimensions; iVar++) numBins[iVar] = hist->GetAxis(iVar)->GetNbins();
- //need a copy because fUnfolded will be updated during the loop, and this creates problems
- THnSparse* copy = (THnSparse*)fUnfolded->Clone();
+ //need a copy because hist will be updated during the loop, and this creates problems
+ THnSparse* copy = (THnSparse*)hist->Clone();
for (Long_t iBin=0; iBin<copy->GetNbins(); iBin++) { //loop on non-empty bins
- Double_t content = copy->GetBinContent(iBin,fCoordinatesN_T);
+ Double_t content = copy->GetBinContent(iBin,coordinates);
Double_t error2 = TMath::Power(copy->GetBinError(iBin),2);
// skip the under/overflow bins...
Bool_t isOutside = kFALSE ;
- for (Int_t iVar=0; iVar<fNVariables; iVar++) {
- if (fCoordinatesN_T[iVar]<1 || fCoordinatesN_T[iVar]>numBins[iVar]) {
+ for (Int_t iVar=0; iVar<nDimensions; iVar++) {
+ if (coordinates[iVar]<1 || coordinates[iVar]>numBins[iVar]) {
isOutside=kTRUE;
break;
}
Int_t neighbours = 0; // number of neighbours to average with
- for (Int_t iVar=0; iVar<fNVariables; iVar++) {
- if (fCoordinatesN_T[iVar] > 1) { // must not be on low edge border
- fCoordinatesN_T[iVar]-- ; //get lower neighbouring bin
- content += copy->GetBinContent(fCoordinatesN_T);
- error2 += TMath::Power(copy->GetBinError(fCoordinatesN_T),2);
+ for (Int_t iVar=0; iVar<nDimensions; iVar++) {
+ if (coordinates[iVar] > 1) { // must not be on low edge border
+ coordinates[iVar]-- ; //get lower neighbouring bin
+ content += copy->GetBinContent(coordinates);
+ error2 += TMath::Power(copy->GetBinError(coordinates),2);
neighbours++;
- fCoordinatesN_T[iVar]++ ; //back to initial coordinate
+ coordinates[iVar]++ ; //back to initial coordinate
}
- if (fCoordinatesN_T[iVar] < numBins[iVar]) { // must not be on up edge border
- fCoordinatesN_T[iVar]++ ; //get upper neighbouring bin
- content += copy->GetBinContent(fCoordinatesN_T);
- error2 += TMath::Power(copy->GetBinError(fCoordinatesN_T),2);
+ if (coordinates[iVar] < numBins[iVar]) { // must not be on up edge border
+ coordinates[iVar]++ ; //get upper neighbouring bin
+ content += copy->GetBinContent(coordinates);
+ error2 += TMath::Power(copy->GetBinError(coordinates),2);
neighbours++;
- fCoordinatesN_T[iVar]-- ; //back to initial coordinate
+ coordinates[iVar]-- ; //back to initial coordinate
}
}
// make an average
- fUnfolded->SetBinContent(fCoordinatesN_T,content/(1.+neighbours));
- fUnfolded->SetBinError (fCoordinatesN_T,TMath::Sqrt(error2)/(1.+neighbours));
+ hist->SetBinContent(coordinates,content/(1.+neighbours));
+ hist->SetBinError (coordinates,TMath::Sqrt(error2)/(1.+neighbours));
}
delete [] numBins;
+ delete [] coordinates ;
delete copy;
return 0;
}
x[iVar] = fUnfolded->GetAxis(iVar)->GetBinCenter(bin[iVar]);
}
Double_t functionValue = fSmoothFunction->Eval(x[0],x[1],x[2]) ;
+ fUnfolded->SetBinError (bin,fUnfolded->GetBinError(bin)*functionValue/fUnfolded->GetBinContent(bin));
fUnfolded->SetBinContent(bin,functionValue);
- fUnfolded->SetBinError (bin,functionValue*fUnfolded->GetBinError(bin));
}
+ delete [] bins;
+ delete [] bin ;
return 0;
}
// create the frame of the THnSparse given (for example) the one from the efficiency map
fPrior = (THnSparse*) fEfficiency->Clone();
+ fPrior->SetTitle("Prior");
if (fNVariables != fPrior->GetNdimensions())
AliFatal(Form("The prior matrix should have %d dimensions, and it has actually %d",fNVariables,fPrior->GetNdimensions()));
fPrior->SetBinError (bin,0.); // put 0 everywhere
}
- fOriginalPrior = (THnSparse*)fPrior->Clone();
+ fPriorOrig = (THnSparse*)fPrior->Clone();
delete [] bin;
delete [] bins;
git://git.uio.no / u / mrichter / AliRoot.git / blobdiff