rf701_efficiencyfit.C File Reference

Detailed Description

Speecial p.d.f.

's: 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
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 **********
 **    2 **SET NOGRAD
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 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
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 **********
 **    4 **SET PRINT           1
 **********
 **********
 **    5 **SET STR           1
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 NOW USING STRATEGY  1: TRY TO BALANCE SPEED AGAINST RELIABILITY
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 **    6 **MIGRAD        1000           1
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 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
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 **    7 **SET ERR         0.5
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 **********
 **    8 **SET PRINT           1
 **********
 **********
 **    9 **HESSE        1000
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 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.