/// Example demonstrating problem with projections
/// Based on 'MULTIDIMENSIONAL MODELS' RooFit tutorial macro #310


#include "RooRealVar.h"
#include "RooDataSet.h"
#include "RooGaussian.h"
#include "RooConstVar.h"
#include "RooProdPdf.h"
#include "RooAddPdf.h"
#include "RooPolynomial.h"
#include "TCanvas.h"
#include "TAxis.h"
#include "RooPlot.h"
using namespace RooFit ;


void min_example()
{

   // C r e a t e   3 D   p d f   a n d   d a t a 
   // -------------------------------------------

   // Create observables
   RooRealVar x("x","x",-5,5) ;
   RooRealVar y("y","y",-5,5) ;
   RooRealVar z("z","z",-5,5) ;

   // Create signal pdf gauss(x)*gauss(y)*gauss(z) 
   RooGaussian gx("gx","gx",x,RooConst(0),RooConst(1)) ;
   RooGaussian gy("gy","gy",y,RooConst(0),RooConst(1)) ;
   RooGaussian gz("gz","gz",z,RooConst(0),RooConst(1)) ;
   RooProdPdf sig("sig","sig",RooArgSet(gx,gy,gz)) ;

   // Create RooHistPdf for signal shape
   RooDataSet* signal_data = sig.generate(RooArgSet(x,y,z),20000) ;
   x.setBins(40);
   y.setBins(40);
   RooDataHist dh("dh","binned version of d",RooArgSet(x,y),*signal_data);
   RooHistPdf sig_xy_hist("sig_xy_hist","sig_xy_hist",RooArgSet(x,y), dh);
   RooProdPdf sig_hist("sig_hist","sig_hist",RooArgSet(sig_xy_hist,gz)) ;


   // Create background pdf poly(x)*poly(y)*poly(z) 
   RooPolynomial px("px","px",x,RooArgSet(RooConst(-0.1),RooConst(0.004))) ;
   RooPolynomial py("py","py",y,RooArgSet(RooConst(0.1),RooConst(-0.004))) ;
   RooPolynomial pz("pz","pz",z) ;
   RooProdPdf bkg("bkg","bkg",RooArgSet(px,py,pz)) ;

   // Create composite pdf sig+bkg
   RooRealVar fsig("fsig","signal fraction",0.1,0.,1.) ;
   RooAddPdf model("model","model",RooArgList(sig,bkg),fsig) ;
   RooAddPdf model_hist("model_hist","model_hist",RooArgList(sig_hist,bkg),fsig) ;

   RooDataSet* data = model.generate(RooArgSet(x,y,z),20000) ;



   // P r o j e c t   p d f   a n d   d a t a   o n   x
   // -------------------------------------------------

   // Make plain projection of data and pdf on x observable
   RooPlot* frame = x.frame(Title("Projection of 3D data and pdf on X"),Bins(40)) ;
   data->plotOn(frame) ;
   model.plotOn(frame) ;

   // Do the same thing for the model with RooHistPdf
   RooPlot* frame_hist = x.frame(Title("Projection of 3D data and pdf on X"),Bins(40)) ;
   data->plotOn(frame_hist) ;
   model_hist.plotOn(frame_hist) ;


   // P r o j e c t   p d f   a n d   d a t a   o n   x   i n   s i g n a l   r a n g e
   // ----------------------------------------------------------------------------------

   // Define signal region in y and z observables
   y.setRange("sigRegion",-1,1) ;
   z.setRange("sigRegion",-1,1) ;

   // Make plot frame
   RooPlot* frame2 = x.frame(Title("Same projection on X in signal range of (Y,Z)"),Bins(40)) ;
   RooPlot* frame2_hist = x.frame(Title("Same projection on X in signal range of (Y,Z)"),Bins(40)) ;

   // Plot subset of data in which all observables are inside "sigRegion"
   // For observables that do not have an explicit "sigRegion" range defined (e.g. observable)
   // an implicit definition is used that is identical to the full range (i.e. [-5,5] for x)
   data->plotOn(frame2,CutRange("sigRegion")) ;
   data->plotOn(frame2_hist,CutRange("sigRegion")) ;

   // Project model on x, integrating projected observables (y,z) only in "sigRegion"
   model.plotOn(frame2,ProjectionRange("sigRegion")) ;
   // And the same thing for model with RooHistPdf
   model_hist.plotOn(frame2_hist,ProjectionRange("sigRegion")) ;



   TCanvas* c = new TCanvas("rf311_rangeplot","rf310_rangeplot",800,400) ;
   c->Divide(2) ;
   c->cd(1) ; gPad->SetLeftMargin(0.15) ; frame->GetYaxis()->SetTitleOffset(1.4) ; frame->Draw() ;
   c->cd(2) ; gPad->SetLeftMargin(0.15) ; frame2->GetYaxis()->SetTitleOffset(1.4) ; frame2->Draw() ;

   TCanvas* c_hist = new TCanvas("rf311_rangeplot_hist","rf310_rangeplot_hist",800,400) ;
   c_hist->Divide(2) ;
   c_hist->cd(1) ; gPad->SetLeftMargin(0.15) ; frame_hist->GetYaxis()->SetTitleOffset(1.4) ; frame_hist->Draw() ;
   c_hist->cd(2) ; gPad->SetLeftMargin(0.15) ; frame2_hist->GetYaxis()->SetTitleOffset(1.4) ; frame2_hist->Draw() ;


}