rf701_efficiencyfit.C File Reference

Detailed Description

'SPECIAL PDFS' RooFit tutorial macro #701

Unbinned maximum likelihood fit of an efficiency eff(x) function to a dataset D(x,cut), where cut is a category encoding a selection, of which the efficiency as function of x should be described by eff(x)

 
 
␛[1mRooFit v3.60 -- Developed by Wouter Verkerke and David Kirkby␛[0m 
                Copyright (C) 2000-2013 NIKHEF, University of California & Stanford University
                All rights reserved, please read http://roofit.sourceforge.net/license.txt
 
[#1] INFO:Minization -- RooMinimizer::optimizeConst: activating const optimization
 **********
 **    1 **SET PRINT           1
 **********
 **********
 **    2 **SET NOGRAD
 **********
 PARAMETER DEFINITIONS:
    NO.   NAME         VALUE      STEP SIZE      LIMITS
     1 a            4.00000e-01  1.00000e-01    0.00000e+00  1.00000e+00
     2 c           -1.00000e+00  2.00000e+00   -1.00000e+01  1.00000e+01
 **********
 **    3 **SET ERR         0.5
 **********
 **********
 **    4 **SET PRINT           1
 **********
 **********
 **    5 **SET STR           1
 **********
 NOW USING STRATEGY  1: TRY TO BALANCE SPEED AGAINST RELIABILITY
 **********
 **    6 **MIGRAD        1000           1
 **********
 FIRST CALL TO USER FUNCTION AT NEW START POINT, WITH IFLAG=4.
 START MIGRAD MINIMIZATION.  STRATEGY  1.  CONVERGENCE WHEN EDM .LT. 1.00e-03
 FCN=3887.11 FROM MIGRAD    STATUS=INITIATE        8 CALLS           9 TOTAL
                     EDM= unknown      STRATEGY= 1      NO ERROR MATRIX       
  EXT PARAMETER               CURRENT GUESS       STEP         FIRST   
  NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE 
   1  a            4.00000e-01   1.00000e-01   2.05758e-01   8.51804e+01
   2  c           -1.00000e+00   2.00000e+00   2.02430e-01   7.00873e+01
                               ERR DEF= 0.5
 MIGRAD MINIMIZATION HAS CONVERGED.
 MIGRAD WILL VERIFY CONVERGENCE AND ERROR MATRIX.
 COVARIANCE MATRIX CALCULATED SUCCESSFULLY
 FCN=3886.26 FROM MIGRAD    STATUS=CONVERGED      30 CALLS          31 TOTAL
                     EDM=2.277e-05    STRATEGY= 1      ERROR MATRIX ACCURATE 
  EXT PARAMETER                                   STEP         FIRST   
  NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE 
   1  a            3.89817e-01   8.14984e-03   6.58343e-04  -2.65715e-01
   2  c           -9.91750e-01   6.56208e-02   2.58326e-04  -6.57933e-01
                               ERR DEF= 0.5
 EXTERNAL ERROR MATRIX.    NDIM=  25    NPAR=  2    ERR DEF=0.5
  6.643e-05 -2.189e-04 
 -2.189e-04  4.306e-03 
 PARAMETER  CORRELATION COEFFICIENTS  
       NO.  GLOBAL      1      2
        1  0.40934   1.000 -0.409
        2  0.40934  -0.409  1.000
 **********
 **    7 **SET ERR         0.5
 **********
 **********
 **    8 **SET PRINT           1
 **********
 **********
 **    9 **HESSE        1000
 **********
 COVARIANCE MATRIX CALCULATED SUCCESSFULLY
 FCN=3886.26 FROM HESSE     STATUS=OK             10 CALLS          41 TOTAL
                     EDM=2.27764e-05    STRATEGY= 1      ERROR MATRIX ACCURATE 
  EXT PARAMETER                                INTERNAL      INTERNAL  
  NO.   NAME      VALUE            ERROR       STEP SIZE       VALUE   
   1  a            3.89817e-01   8.14814e-03   1.31669e-04  -2.22191e-01
   2  c           -9.91750e-01   6.56071e-02   5.16653e-05  -9.93383e-02
                               ERR DEF= 0.5
 EXTERNAL ERROR MATRIX.    NDIM=  25    NPAR=  2    ERR DEF=0.5
  6.640e-05 -2.186e-04 
 -2.186e-04  4.304e-03 
 PARAMETER  CORRELATION COEFFICIENTS  
       NO.  GLOBAL      1      2
        1  0.40891   1.000 -0.409
        2  0.40891  -0.409  1.000
[#1] INFO:Minization -- RooMinimizer::optimizeConst: deactivating const optimization
[#1] INFO:Plotting -- RooTreeData::plotOn: plotting 8176 events out of 10000 total events

 
 
#include "RooRealVar.h"
#include "RooDataSet.h"
#include "RooGaussian.h"
#include "RooConstVar.h"
#include "RooFormulaVar.h"
#include "RooProdPdf.h"
#include "RooEfficiency.h"
#include "RooPolynomial.h"
#include "RooCategory.h"
#include "TCanvas.h"
#include "TAxis.h"
#include "RooPlot.h"
using namespace RooFit ;
 
 
void rf701_efficiencyfit()
{
   // C o n s t r u c t   e f f i c i e n c y   f u n c t i o n   e ( x ) 
   // -------------------------------------------------------------------
 
   // Declare variables x,mean,sigma with associated name, title, initial value and allowed range
   RooRealVar x("x","x",-10,10) ;
 
   // Efficiency function eff(x;a,b) 
   RooRealVar a("a","a",0.4,0,1) ;
   RooRealVar b("b","b",5) ;
   RooRealVar c("c","c",-1,-10,10) ;
   RooFormulaVar effFunc("effFunc","(1-a)+a*cos((x-c)/b)",RooArgList(a,b,c,x)) ;
 
 
 
   // C o n s t r u c t   c o n d i t i o n a l    e f f i c i e n c y   p d f   E ( c u t | x ) 
   // ------------------------------------------------------------------------------------------
 
   // Acceptance state cut (1 or 0)
   RooCategory cut("cut","cutr") ;
   cut.defineType("accept",1) ;
   cut.defineType("reject",0) ;
 
   // Construct efficiency p.d.f eff(cut|x)
   RooEfficiency effPdf("effPdf","effPdf",effFunc,cut,"accept") ;
 
 
 
   // G e n e r a t e   d a t a   ( x ,   c u t )   f r o m   a   t o y   m o d e l 
   // -----------------------------------------------------------------------------
 
   // Construct global shape p.d.f shape(x) and product model(x,cut) = eff(cut|x)*shape(x) 
   // (These are _only_ needed to generate some toy MC here to be used later)
   RooPolynomial shapePdf("shapePdf","shapePdf",x,RooConst(-0.095)) ;
   RooProdPdf model("model","model",shapePdf,Conditional(effPdf,cut)) ;
 
   // Generate some toy data from model
   RooDataSet* data = model.generate(RooArgSet(x,cut),10000) ;
 
 
 
   // F i t   c o n d i t i o n a l   e f f i c i e n c y   p d f   t o   d a t a 
   // --------------------------------------------------------------------------
 
   // Fit conditional efficiency p.d.f to data
   effPdf.fitTo(*data,ConditionalObservables(x)) ;
 
 
 
   // P l o t   f i t t e d ,   d a t a   e f f i c i e n c y  
   // --------------------------------------------------------
 
   // Plot distribution of all events and accepted fraction of events on frame
   RooPlot* frame1 = x.frame(Bins(20),Title("Data (all, accepted)")) ;
   data->plotOn(frame1) ;
   data->plotOn(frame1,Cut("cut==cut::accept"),MarkerColor(kRed),LineColor(kRed)) ;
 
   // Plot accept/reject efficiency on data overlay fitted efficiency curve
   RooPlot* frame2 = x.frame(Bins(20),Title("Fitted efficiency")) ;
   data->plotOn(frame2,Efficiency(cut)) ; // needs ROOT version >= 5.21
   effFunc.plotOn(frame2,LineColor(kRed)) ;
 
 
 
   // Draw all frames on a canvas
   TCanvas* ca = new TCanvas("rf701_efficiency","rf701_efficiency",800,400) ;
   ca->Divide(2) ;
   ca->cd(1) ; gPad->SetLeftMargin(0.15) ; frame1->GetYaxis()->SetTitleOffset(1.6) ; frame1->Draw() ;
   ca->cd(2) ; gPad->SetLeftMargin(0.15) ; frame2->GetYaxis()->SetTitleOffset(1.4) ; frame2->Draw() ;
   
 
}

Author

07/2008 - Wouter Verkerke

Definition in file rf701_efficiencyfit.C.