/// \file
/// \ingroup tutorial_roofit
/// \notebook -js
///
/// Multidimensional models: projecting p.d.f and data ranges in continuous observables
///
/// \macro_image
/// \macro_output
/// \macro_code
///
/// \date 07/2008
/// \author Wouter Verkerke

#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 rf311_rangeplot()
{

   // 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 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);

   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);

   // 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));

   // 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"));

   // Project model on x, integrating projected observables (y,z) only in "sigRegion"
   model.plotOn(frame2, 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();
}