/// \file
/// \ingroup tutorial_roofit
/// \notebook -js
///  'SPECIAL PDFS' RooFit tutorial macro #703
///
///  Using a product of an (acceptance) efficiency and a p.d.f as p.d.f.
///
/// \macro_image
/// \macro_output
/// \macro_code
/// \author 07/2008 - Wouter Verkerke 


#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() ;

}