rf201_composite.C File Reference

Detailed Description

Addition and convolution: composite pdf 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)))

 
#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 pdf
   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 pdf
   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
   std::unique_ptr<RooDataSet> data{model.generate(x, 1000)};
 
   // Fit model to data
   model.fitTo(*data, PrintLevel(-1));
 
   // 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 pdf
   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), true);
 
   // 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();
}

[#0] WARNING:InputArguments -- The parameter 'sigma1' with range [-inf, inf] of the RooGaussian 'sig1' exceeds the safe range of (0, inf). Advise to limit its range.
[#0] WARNING:InputArguments -- The parameter 'sigma2' with range [-inf, inf] of the RooGaussian 'sig2' exceeds the safe range of (0, inf). Advise to limit its range.
[#1] INFO:Fitting -- RooAbsPdf::fitTo(model) fixing normalization set for coefficient determination to observables in data
[#1] INFO:Fitting -- using generic CPU library compiled with no vectorizations
[#1] INFO:Fitting -- Creation of NLL object took 526.311 μs
[#1] INFO:Fitting -- RooAddition::defaultErrorLevel(nll_model_modelData) Summation contains a RooNLLVar, using its error level
[#1] INFO:Minimization -- [fitFCN] No discrete parameters, performing continuous minimization only
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) directly selected PDF components: (bkg)
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) indirectly selected PDF components: ()
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) directly selected PDF components: (bkg,sig2)
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) indirectly selected PDF components: (sig)
0x7ffeb5d357d0 RooAddPdf::model = 0.898624/1 [Auto,Clean] 
  0x7ffeb5d34eb8/V- RooChebychev::bkg = 0.79893 [Auto,Dirty] 
    0x7ffeb5d353e8/V- RooRealVar::x = 5
    0x7ffeb5d32eb8/V- RooRealVar::a0 = 0.441621 +/- 0.0731875
    0x7ffeb5d332a0/V- RooRealVar::a1 = 0.20107 +/- 0.117637
  0x7ffeb5d34578/V- RooRealVar::bkgfrac = 0.504184 +/- 0.0359091
  0x7ffeb5d33688/V- RooAddPdf::sig = 1/1 [Auto,Clean] 
    0x7ffeb5d32190/V- RooGaussian::sig1 = 1 [Auto,Dirty] 
      0x7ffeb5d353e8/V- RooRealVar::x = 5
      0x7ffeb5d33da8/V- RooRealVar::mean = 5
      0x7ffeb5d326e8/V- RooRealVar::sigma1 = 0.5
    0x7ffeb5d34190/V- RooRealVar::sig1frac = 0.837334 +/- 0.116852
    0x7ffeb5d34960/V- RooGaussian::sig2 = 1 [Auto,Dirty] 
      0x7ffeb5d353e8/V- RooRealVar::x = 5
      0x7ffeb5d33da8/V- RooRealVar::mean = 5
      0x7ffeb5d32ad0/V- RooRealVar::sigma2 = 1
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) directly selected PDF components: (bkg,sig2)
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) indirectly selected PDF components: ()
0x7ffeb5d35ef0 RooAddPdf::model = 0.898624/1 [Auto,Clean] 
  0x7ffeb5d34eb8/V- RooChebychev::bkg = 0.79893 [Auto,Dirty] 
    0x7ffeb5d353e8/V- RooRealVar::x = 5
    0x7ffeb5d32eb8/V- RooRealVar::a0 = 0.441621 +/- 0.0731875
    0x7ffeb5d332a0/V- RooRealVar::a1 = 0.20107 +/- 0.117637
  0x7ffeb5d34578/V- RooRealVar::bkgfrac = 0.504184 +/- 0.0359091
  0x7ffeb5d32190/V- RooGaussian::sig1 = 1 [Auto,Dirty] 
    0x7ffeb5d353e8/V- RooRealVar::x = 5
    0x7ffeb5d33da8/V- RooRealVar::mean = 5
    0x7ffeb5d326e8/V- RooRealVar::sigma1 = 0.5
  0x150a89e0/V- RooRecursiveFraction::model_recursive_fraction_sig1_2 = 0.415163 [Auto,Clean] 
    0x7ffeb5d34190/V- RooRealVar::sig1frac = 0.837334 +/- 0.116852
    0x7ffeb5d34578/V- RooRealVar::bkgfrac = 0.504184 +/- 0.0359091
  0x7ffeb5d34960/V- RooGaussian::sig2 = 1 [Auto,Dirty] 
    0x7ffeb5d353e8/V- RooRealVar::x = 5
    0x7ffeb5d33da8/V- RooRealVar::mean = 5
    0x7ffeb5d32ad0/V- RooRealVar::sigma2 = 1
  0x150aa0d0/V- RooRecursiveFraction::model_recursive_fraction_sig2_3 = 0.0806524 [Auto,Clean] 
    0x1762d140/V- RooConstVar::1 = 1
    0x7ffeb5d34190/V- RooRealVar::sig1frac = 0.837334 +/- 0.116852
    0x7ffeb5d34578/V- RooRealVar::bkgfrac = 0.504184 +/- 0.0359091

Date

July 2008

Author

Wouter Verkerke

Definition in file rf201_composite.C.