rf201_composite.C

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/// \file
/// \ingroup tutorial_roofit
/// \notebook -js
/// Addition and convolution: composite p.d.f with signal and background component
///
///  pdf = f_bkg * bkg(x,a0,a1) + (1-fbkg) * (f_sig1 * sig1(x,m,s1 + (1-f_sig1) * sig2(x,m,s2)))
///
/// \macro_image
/// \macro_output
/// \macro_code
/// \author 07/2008 - Wouter Verkerke

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

void rf201_composite()
{
   // S e t u p   c o m p o n e n t   p d f s
   // ---------------------------------------

   // Declare observable x
   RooRealVar x("x", "x", 0, 10);

   // Create two Gaussian PDFs g1(x,mean1,sigma) anf g2(x,mean2,sigma) and their parameters
   RooRealVar mean("mean", "mean of gaussians", 5);
   RooRealVar sigma1("sigma1", "width of gaussians", 0.5);
   RooRealVar sigma2("sigma2", "width of gaussians", 1);

   RooGaussian sig1("sig1", "Signal component 1", x, mean, sigma1);
   RooGaussian sig2("sig2", "Signal component 2", x, mean, sigma2);

   // Build Chebychev polynomial p.d.f.
   RooRealVar a0("a0", "a0", 0.5, 0., 1.);
   RooRealVar a1("a1", "a1", 0.2, 0., 1.);
   RooChebychev bkg("bkg", "Background", x, RooArgSet(a0, a1));

   // ---------------------------------------------
   // M E T H O D   1 - T w o   R o o A d d P d f s
   // =============================================

   // A d d   s i g n a l   c o m p o n e n t s
   // ------------------------------------------

   // Sum the signal components into a composite signal p.d.f.
   RooRealVar sig1frac("sig1frac", "fraction of component 1 in signal", 0.8, 0., 1.);
   RooAddPdf sig("sig", "Signal", RooArgList(sig1, sig2), sig1frac);

   // A d d  s i g n a l   a n d   b a c k g r o u n d
   // ------------------------------------------------

   // Sum the composite signal and background
   RooRealVar bkgfrac("bkgfrac", "fraction of background", 0.5, 0., 1.);
   RooAddPdf model("model", "g1+g2+a", RooArgList(bkg, sig), bkgfrac);

   // S a m p l e ,   f i t   a n d   p l o t   m o d e l
   // ---------------------------------------------------

   // Generate a data sample of 1000 events in x from model
   RooDataSet *data = model.generate(x, 1000);

   // Fit model to data
   model.fitTo(*data);

   // Plot data and PDF overlaid
   RooPlot *xframe = x.frame(Title("Example of composite pdf=(sig1+sig2)+bkg"));
   data->plotOn(xframe);
   model.plotOn(xframe);

   // Overlay the background component of model with a dashed line
   model.plotOn(xframe, Components(bkg), LineStyle(kDashed));

   // Overlay the background+sig2 components of model with a dotted line
   model.plotOn(xframe, Components(RooArgSet(bkg, sig2)), LineStyle(kDotted));

   // Print structure of composite p.d.f.
   model.Print("t");

   // ---------------------------------------------------------------------------------------------
   // M E T H O D   2 - O n e   R o o A d d P d f   w i t h   r e c u r s i v e   f r a c t i o n s
   // =============================================================================================

   // Construct sum of models on one go using recursive fraction interpretations
   //
   //   model2 = bkg + (sig1 + sig2)
   //
   RooAddPdf model2("model", "g1+g2+a", RooArgList(bkg, sig1, sig2), RooArgList(bkgfrac, sig1frac), kTRUE);

   // NB: Each coefficient is interpreted as the fraction of the
   // left-hand component of the i-th recursive sum, i.e.
   //
   //   sum4 = A + ( B + ( C + D)  with fraction fA, fB and fC expands to
   //
   //   sum4 = fA*A + (1-fA)*(fB*B + (1-fB)*(fC*C + (1-fC)*D))

   // P l o t   r e c u r s i v e   a d d i t i o n   m o d e l
   // ---------------------------------------------------------
   model2.plotOn(xframe, LineColor(kRed), LineStyle(kDashed));
   model2.plotOn(xframe, Components(RooArgSet(bkg, sig2)), LineColor(kRed), LineStyle(kDashed));
   model2.Print("t");

   // Draw the frame on the canvas
   new TCanvas("rf201_composite", "rf201_composite", 600, 600);
   gPad->SetLeftMargin(0.15);
   xframe->GetYaxis()->SetTitleOffset(1.4);
   xframe->Draw();
}