Logo ROOT  
Reference Guide
rf210_angularconv.C
Go to the documentation of this file.
1/// \file
2/// \ingroup tutorial_roofit
3/// \notebook -js
4/// Addition and convolution: convolution in cyclical angular observables theta
5///
6/// and construction of pdf in terms of transformed angular coordinates, e.g. cos(theta),
7/// where the convolution is performed in theta rather than cos(theta)
8///
9/// ```
10/// pdf(theta) = T(theta) (x) gauss(theta)
11/// pdf(cosTheta) = T(acos(cosTheta)) (x) gauss(acos(cosTheta))
12/// ```
13///
14/// This tutorial requires FFT3 to be enabled.
15///
16/// \macro_image
17/// \macro_output
18/// \macro_code
19///
20/// \date April 2009
21/// \author Wouter Verkerke
22
23#include "RooRealVar.h"
24#include "RooDataSet.h"
25#include "RooGaussian.h"
26#include "RooGenericPdf.h"
27#include "RooFormulaVar.h"
28#include "RooFFTConvPdf.h"
29#include "RooPlot.h"
30#include "TCanvas.h"
31#include "TAxis.h"
32#include "TH1.h"
33using namespace RooFit;
34
35void rf210_angularconv()
36{
37 // S e t u p c o m p o n e n t p d f s
38 // ---------------------------------------
39
40 // Define angle psi
41 RooRealVar psi("psi", "psi", 0, 3.14159268);
42
43 // Define physics pdf T(psi)
44 RooGenericPdf Tpsi("Tpsi", "1+sin(2*@0)", psi);
45
46 // Define resolution R(psi)
47 RooRealVar gbias("gbias", "gbias", 0.2, 0., 1);
48 RooRealVar greso("greso", "greso", 0.3, 0.1, 1.0);
49 RooGaussian Rpsi("Rpsi", "Rpsi", psi, gbias, greso);
50
51 // Define cos(psi) and function psif that calculates psi from cos(psi)
52 RooRealVar cpsi("cpsi", "cos(psi)", -1, 1);
53 RooFormulaVar psif("psif", "acos(cpsi)", cpsi);
54
55 // Define physics pdf also as function of cos(psi): T(psif(cpsi)) = T(cpsi) ;
56 RooGenericPdf Tcpsi("T", "1+sin(2*@0)", psif);
57
58 // C o n s t r u c t c o n v o l u t i o n p d f i n p s i
59 // --------------------------------------------------------------
60
61 // Define convoluted pdf as function of psi: M=[T(x)R](psi) = M(psi)
62 RooFFTConvPdf Mpsi("Mf", "Mf", psi, Tpsi, Rpsi);
63
64 // Set the buffer fraction to zero to obtain a true cyclical convolution
65 Mpsi.setBufferFraction(0);
66
67 // S a m p l e , f i t a n d p l o t c o n v o l u t e d p d f ( p s i )
68 // --------------------------------------------------------------------------------
69
70 // Generate some events in observable psi
71 RooDataSet *data_psi = Mpsi.generate(psi, 10000);
72
73 // Fit convoluted model as function of angle psi
74 Mpsi.fitTo(*data_psi);
75
76 // Plot cos(psi) frame with Mf(cpsi)
77 RooPlot *frame1 = psi.frame(Title("Cyclical convolution in angle psi"));
78 data_psi->plotOn(frame1);
79 Mpsi.plotOn(frame1);
80
81 // Overlay comparison to unsmeared physics pdf T(psi)
82 Tpsi.plotOn(frame1, LineColor(kRed));
83
84 // C o n s t r u c t c o n v o l u t i o n p d f i n c o s ( p s i )
85 // --------------------------------------------------------------------------
86
87 // Define convoluted pdf as function of cos(psi): M=[T(x)R](psif(cpsi)) = M(cpsi)
88 //
89 // Need to give both observable psi here (for definition of convolution)
90 // and function psif here (for definition of observables, ultimately in cpsi)
91 RooFFTConvPdf Mcpsi("Mf", "Mf", psif, psi, Tpsi, Rpsi);
92
93 // Set the buffer fraction to zero to obtain a true cyclical convolution
94 Mcpsi.setBufferFraction(0);
95
96 // S a m p l e , f i t a n d p l o t c o n v o l u t e d p d f ( c o s p s i )
97 // --------------------------------------------------------------------------------
98
99 // Generate some events
100 RooDataSet *data_cpsi = Mcpsi.generate(cpsi, 10000);
101
102 // set psi constant to exclude to be a parameter of the fit
103 psi.setConstant(true);
104
105 // Fit convoluted model as function of cos(psi)
106 Mcpsi.fitTo(*data_cpsi);
107
108 // Plot cos(psi) frame with Mf(cpsi)
109 RooPlot *frame2 = cpsi.frame(Title("Same convolution in psi, expressed in cos(psi)"));
110 data_cpsi->plotOn(frame2);
111 Mcpsi.plotOn(frame2);
112
113 // Overlay comparison to unsmeared physics pdf Tf(cpsi)
114 Tcpsi.plotOn(frame2, LineColor(kRed));
115
116 // Draw frame on canvas
117 TCanvas *c = new TCanvas("rf210_angularconv", "rf210_angularconv", 800, 400);
118 c->Divide(2);
119 c->cd(1);
120 gPad->SetLeftMargin(0.15);
121 frame1->GetYaxis()->SetTitleOffset(1.4);
122 frame1->Draw();
123 c->cd(2);
124 gPad->SetLeftMargin(0.15);
125 frame2->GetYaxis()->SetTitleOffset(1.4);
126 frame2->Draw();
127}
#define c(i)
Definition: RSha256.hxx:101
@ kRed
Definition: Rtypes.h:66
#define gPad
Definition: TVirtualPad.h:287
virtual RooPlot * plotOn(RooPlot *frame, const RooCmdArg &arg1=RooCmdArg::none(), const RooCmdArg &arg2=RooCmdArg::none(), const RooCmdArg &arg3=RooCmdArg::none(), const RooCmdArg &arg4=RooCmdArg::none(), const RooCmdArg &arg5=RooCmdArg::none(), const RooCmdArg &arg6=RooCmdArg::none(), const RooCmdArg &arg7=RooCmdArg::none(), const RooCmdArg &arg8=RooCmdArg::none()) const
Definition: RooAbsData.cxx:547
RooDataSet is a container class to hold unbinned data.
Definition: RooDataSet.h:33
PDF for the numerical (FFT) convolution of two PDFs.
Definition: RooFFTConvPdf.h:25
A RooFormulaVar is a generic implementation of a real-valued object, which takes a RooArgList of serv...
Definition: RooFormulaVar.h:30
Plain Gaussian p.d.f.
Definition: RooGaussian.h:24
RooGenericPdf is a concrete implementation of a probability density function, which takes a RooArgLis...
Definition: RooGenericPdf.h:25
A RooPlot is a plot frame and a container for graphics objects within that frame.
Definition: RooPlot.h:44
TAxis * GetYaxis() const
Definition: RooPlot.cxx:1263
static RooPlot * frame(const RooAbsRealLValue &var, Double_t xmin, Double_t xmax, Int_t nBins)
Create a new frame for a given variable in x.
Definition: RooPlot.cxx:249
virtual void Draw(Option_t *options=0)
Draw this plot and all of the elements it contains.
Definition: RooPlot.cxx:691
RooRealVar represents a variable that can be changed from the outside.
Definition: RooRealVar.h:39
virtual void SetTitleOffset(Float_t offset=1)
Set distance between the axis and the axis title.
Definition: TAttAxis.cxx:293
The Canvas class.
Definition: TCanvas.h:23
RooCmdArg LineColor(Color_t color)
The namespace RooFit contains mostly switches that change the behaviour of functions of PDFs (or othe...
const char * Title
Definition: TXMLSetup.cxx:68