rf703_effpdfprod.C File Reference

Detailed Description

'SPECIAL PDFS' RooFit tutorial macro #703

Using a product of an (acceptance) efficiency and a p.d.f as p.d.f.

Processing /mnt/build/workspace/root-makedoc-v614/rootspi/rdoc/src/v6-14-00-patches/tutorials/roofit/rf703_effpdfprod.C...

RooFit v3.60 -- Developed by Wouter Verkerke and David Kirkby 
                Copyright (C) 2000-2013 NIKHEF, University of California & Stanford University
                All rights reserved, please read http://roofit.sourceforge.net/license.txt

[#1] INFO:NumericIntegration -- RooRealIntegral::init(modelEff_clone_Int[t]) using numeric integrator RooIntegrator1D to calculate Int(t)
[#1] INFO:NumericIntegration -- RooRealIntegral::init(modelEff_clone_Int[t]) using numeric integrator RooIntegrator1D to calculate Int(t)
[#1] INFO:Minization -- RooMinimizer::optimizeConst: activating const optimization
[#1] INFO:Minization --  The following expressions have been identified as constant and will be precalculated and cached: (eff)
 **********
 **    1 **SET PRINT           1
 **********
 **********
 **    2 **SET NOGRAD
 **********
 PARAMETER DEFINITIONS:
    NO.   NAME         VALUE      STEP SIZE      LIMITS
     1 tau         -1.54000e+00  3.90000e-01   -4.00000e+00 -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         500           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=9696.74 FROM MIGRAD    STATUS=INITIATE        4 CALLS           5 TOTAL
                     EDM= unknown      STRATEGY= 1      NO ERROR MATRIX       
  EXT PARAMETER               CURRENT GUESS       STEP         FIRST   
  NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE 
   1  tau         -1.54000e+00   3.90000e-01   2.09076e-01   1.80888e+02
                               ERR DEF= 0.5
 MIGRAD MINIMIZATION HAS CONVERGED.
 MIGRAD WILL VERIFY CONVERGENCE AND ERROR MATRIX.
 COVARIANCE MATRIX CALCULATED SUCCESSFULLY
 FCN=9695.84 FROM MIGRAD    STATUS=CONVERGED      12 CALLS          13 TOTAL
                     EDM=2.41592e-05    STRATEGY= 1      ERROR MATRIX ACCURATE 
  EXT PARAMETER                                   STEP         FIRST   
  NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE 
   1  tau         -1.55887e+00   1.40931e-02   5.05936e-04   6.58163e-01
                               ERR DEF= 0.5
 EXTERNAL ERROR MATRIX.    NDIM=  25    NPAR=  1    ERR DEF=0.5
  1.986e-04 
 **********
 **    7 **SET ERR         0.5
 **********
 **********
 **    8 **SET PRINT           1
 **********
 **********
 **    9 **HESSE         500
 **********
 COVARIANCE MATRIX CALCULATED SUCCESSFULLY
 FCN=9695.84 FROM HESSE     STATUS=OK              5 CALLS          18 TOTAL
                     EDM=2.41576e-05    STRATEGY= 1      ERROR MATRIX ACCURATE 
  EXT PARAMETER                                INTERNAL      INTERNAL  
  NO.   NAME      VALUE            ERROR       STEP SIZE       VALUE   
   1  tau         -1.55887e+00   1.40931e-02   1.01187e-04   2.54601e-01
                               ERR DEF= 0.5
 EXTERNAL ERROR MATRIX.    NDIM=  25    NPAR=  1    ERR DEF=0.5
  1.986e-04 
[#1] INFO:Minization -- RooMinimizer::optimizeConst: deactivating const optimization
[#1] INFO:NumericIntegration -- RooRealIntegral::init(modelEff_clone_Int[t]) using numeric integrator RooIntegrator1D to calculate Int(t)

#include "RooRealVar.h"
#include "RooDataSet.h"
#include "RooGaussian.h"
#include "RooConstVar.h"
#include "RooExponential.h"
#include "RooEffProd.h"
#include "RooFormulaVar.h"
#include "TCanvas.h"
#include "TAxis.h"
#include "RooPlot.h"
using namespace RooFit ;


void rf703_effpdfprod()
{
   // D e f i n e   o b s e r v a b l e s   a n d   d e c a y   p d f
   // ---------------------------------------------------------------

   // Declare observables
   RooRealVar t("t","t",0,5) ;

   // Make pdf
   RooRealVar tau("tau","tau",-1.54,-4,-0.1) ;
   RooExponential model("model","model",t,tau) ;



   // D e f i n e   e f f i c i e n c y   f u n c t i o n
   // ---------------------------------------------------
   
   // Use error function to simulate turn-on slope
   RooFormulaVar eff("eff","0.5*(TMath::Erf((t-1)/0.5)+1)",t) ;



   // D e f i n e   d e c a y   p d f   w i t h   e f f i c i e n c y 
   // ---------------------------------------------------------------

   // Multiply pdf(t) with efficiency in t
   RooEffProd modelEff("modelEff","model with efficiency",model,eff) ;

   

   // P l o t   e f f i c i e n c y ,   p d f  
   // ----------------------------------------

   RooPlot* frame1 = t.frame(Title("Efficiency")) ;
   eff.plotOn(frame1,LineColor(kRed)) ;

   RooPlot* frame2 = t.frame(Title("Pdf with and without efficiency")) ;

   model.plotOn(frame2,LineStyle(kDashed)) ;
   modelEff.plotOn(frame2) ;



   // G e n e r a t e   t o y   d a t a ,   f i t   m o d e l E f f   t o   d a t a
   // ------------------------------------------------------------------------------

   // Generate events. If the input pdf has an internal generator, the internal generator
   // is used and an accept/reject sampling on the efficiency is applied. 
   RooDataSet* data = modelEff.generate(t,10000) ;

   // Fit pdf. The normalization integral is calculated numerically. 
   modelEff.fitTo(*data) ;

   // Plot generated data and overlay fitted pdf
   RooPlot* frame3 = t.frame(Title("Fitted pdf with efficiency")) ;
   data->plotOn(frame3) ;
   modelEff.plotOn(frame3) ;

   
   TCanvas* c = new TCanvas("rf703_effpdfprod","rf703_effpdfprod",1200,400) ;
   c->Divide(3) ;
   c->cd(1) ; gPad->SetLeftMargin(0.15) ; frame1->GetYaxis()->SetTitleOffset(1.4) ; frame1->Draw() ;
   c->cd(2) ; gPad->SetLeftMargin(0.15) ; frame2->GetYaxis()->SetTitleOffset(1.6) ; frame2->Draw() ;
   c->cd(3) ; gPad->SetLeftMargin(0.15) ; frame3->GetYaxis()->SetTitleOffset(1.6) ; frame3->Draw() ;

}

Author

07/2008 - Wouter Verkerke

Definition in file rf703_effpdfprod.C.