## From \$ROOTSYS/tutorials/roofit/rf702_efficiencyfit_2D.C

```//////////////////////////////////////////////////////////////////////////
//
// 'SPECIAL PDFS' RooFit tutorial macro #702
//
// Unbinned maximum likelihood fit of an efficiency eff(x) function to
// a dataset D(x,cut), where cut is a category encoding a selection whose
// efficiency as function of x should be described by eff(x)
//
//
/////////////////////////////////////////////////////////////////////////

#ifndef __CINT__
#include "RooGlobalFunc.h"
#endif
#include "RooRealVar.h"
#include "RooDataSet.h"
#include "RooGaussian.h"
#include "RooConstVar.h"
#include "RooCategory.h"
#include "RooEfficiency.h"
#include "RooPolynomial.h"
#include "RooProdPdf.h"
#include "RooFormulaVar.h"
#include "TCanvas.h"
#include "TAxis.h"
#include "TH1.h"
#include "RooPlot.h"
using namespace RooFit ;

void rf702_efficiencyfit_2D(Bool_t flat=kFALSE)
{
// 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 , y )
// -----------------------------------------------------------------------

// Declare variables x,mean,sigma with associated name, title, initial value and allowed range
RooRealVar x("x","x",-10,10) ;
RooRealVar y("y","y",-10,10) ;

// Efficiency function eff(x;a,b)
RooRealVar ax("ax","ay",0.6,0,1) ;
RooRealVar bx("bx","by",5) ;
RooRealVar cx("cx","cy",-1,-10,10) ;

RooRealVar ay("ay","ay",0.2,0,1) ;
RooRealVar by("by","by",5) ;
RooRealVar cy("cy","cy",-1,-10,10) ;

RooFormulaVar effFunc("effFunc","((1-ax)+ax*cos((x-cx)/bx))*((1-ay)+ay*cos((y-cy)/by))",RooArgList(ax,bx,cx,x,ay,by,cy,y)) ;

// Acceptance state cut (1 or 0)
RooCategory cut("cut","cutr") ;
cut.defineType("accept",1) ;
cut.defineType("reject",0) ;

// 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 , y )
// ---------------------------------------------------------------------------------------------

// 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 , y , 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 shapePdfX("shapePdfX","shapePdfX",x,RooConst(flat?0:-0.095)) ;
RooPolynomial shapePdfY("shapePdfY","shapePdfY",y,RooConst(flat?0:+0.095)) ;
RooProdPdf shapePdf("shapePdf","shapePdf",RooArgSet(shapePdfX,shapePdfY)) ;
RooProdPdf model("model","model",shapePdf,Conditional(effPdf,cut)) ;

// Generate some toy data from model
RooDataSet* data = model.generate(RooArgSet(x,y,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(RooArgSet(x,y))) ;

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

// Make 2D histograms of all data, selected data and efficiency function
TH1* hh_data_all = data->createHistogram("hh_data_all",x,Binning(8),YVar(y,Binning(8))) ;
TH1* hh_data_sel = data->createHistogram("hh_data_sel",x,Binning(8),YVar(y,Binning(8)),Cut("cut==cut::accept")) ;
TH1* hh_eff      = effFunc.createHistogram("hh_eff",x,Binning(50),YVar(y,Binning(50))) ;

// Some adjustsment for good visualization
hh_data_all->SetMinimum(0) ;
hh_data_sel->SetMinimum(0) ;
hh_eff->SetMinimum(0) ;
hh_eff->SetLineColor(kBlue) ;

// Draw all frames on a canvas
TCanvas* ca = new TCanvas("rf702_efficiency_2D","rf702_efficiency_2D",1200,400) ;
ca->Divide(3) ;
ca->cd(1) ; gPad->SetLeftMargin(0.15) ; hh_data_all->GetZaxis()->SetTitleOffset(1.8) ; hh_data_all->Draw("lego") ;
ca->cd(2) ; gPad->SetLeftMargin(0.15) ; hh_data_sel->GetZaxis()->SetTitleOffset(1.8) ; hh_data_sel->Draw("lego") ;
ca->cd(3) ; gPad->SetLeftMargin(0.15) ; hh_eff->GetZaxis()->SetTitleOffset(1.8) ; hh_eff->Draw("surf") ;

return ;

}
```
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