## From \$ROOTSYS/tutorials/roofit/rf701_efficiencyfit.C

```//////////////////////////////////////////////////////////////////////////
//
// '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)
//
// 07/2008 - Wouter Verkerke
//
/////////////////////////////////////////////////////////////////////////

#ifndef __CINT__
#include "RooGlobalFunc.h"
#endif
#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() ;

}
```
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