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rf308_normintegration2d.C
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1/// \file
2/// \ingroup tutorial_roofit
3/// \notebook
4/// Multidimensional models: normalization and integration of pdfs, construction of
5/// cumulative distribution functions from pdfs in two dimensions
6///
7/// \macro_image
8/// \macro_output
9/// \macro_code
10///
11/// \date July 2008
12/// \author Wouter Verkerke
13
14#include "RooRealVar.h"
15#include "RooGaussian.h"
16#include "RooConstVar.h"
17#include "RooProdPdf.h"
18#include "RooAbsReal.h"
19#include "RooPlot.h"
20#include "TCanvas.h"
21#include "TAxis.h"
22#include "TH1.h"
23using namespace RooFit;
24
26{
27 // S e t u p m o d e l
28 // ---------------------
29
30 // Create observables x,y
31 RooRealVar x("x", "x", -10, 10);
32 RooRealVar y("y", "y", -10, 10);
33
34 // Create pdf gaussx(x,-2,3), gaussy(y,2,2)
35 RooGaussian gx("gx", "gx", x, RooConst(-2), RooConst(3));
36 RooGaussian gy("gy", "gy", y, RooConst(+2), RooConst(2));
37
38 // Create gxy = gx(x)*gy(y)
39 RooProdPdf gxy("gxy", "gxy", RooArgSet(gx, gy));
40
41 // R e t r i e v e r a w & n o r m a l i z e d v a l u e s o f R o o F i t p . d . f . s
42 // --------------------------------------------------------------------------------------------------
43
44 // Return 'raw' unnormalized value of gx
45 cout << "gxy = " << gxy.getVal() << endl;
46
47 // Return value of gxy normalized over x _and_ y in range [-10,10]
48 RooArgSet nset_xy(x, y);
49 cout << "gx_Norm[x,y] = " << gxy.getVal(&nset_xy) << endl;
50
51 // Create object representing integral over gx
52 // which is used to calculate gx_Norm[x,y] == gx / gx_Int[x,y]
53 RooAbsReal *igxy = gxy.createIntegral(RooArgSet(x, y));
54 cout << "gx_Int[x,y] = " << igxy->getVal() << endl;
55
56 // NB: it is also possible to do the following
57
58 // Return value of gxy normalized over x in range [-10,10] (i.e. treating y as parameter)
59 RooArgSet nset_x(x);
60 cout << "gx_Norm[x] = " << gxy.getVal(&nset_x) << endl;
61
62 // Return value of gxy normalized over y in range [-10,10] (i.e. treating x as parameter)
63 RooArgSet nset_y(y);
64 cout << "gx_Norm[y] = " << gxy.getVal(&nset_y) << endl;
65
66 // I n t e g r a t e n o r m a l i z e d p d f o v e r s u b r a n g e
67 // ----------------------------------------------------------------------------
68
69 // Define a range named "signal" in x from -5,5
70 x.setRange("signal", -5, 5);
71 y.setRange("signal", -3, 3);
72
73 // Create an integral of gxy_Norm[x,y] over x and y in range "signal"
74 // This is the fraction of of pdf gxy_Norm[x,y] which is in the
75 // range named "signal"
76 RooAbsReal *igxy_sig = gxy.createIntegral(RooArgSet(x, y), NormSet(RooArgSet(x, y)), Range("signal"));
77 cout << "gx_Int[x,y|signal]_Norm[x,y] = " << igxy_sig->getVal() << endl;
78
79 // C o n s t r u c t c u m u l a t i v e d i s t r i b u t i o n f u n c t i o n f r o m p d f
80 // -----------------------------------------------------------------------------------------------------
81
82 // Create the cumulative distribution function of gx
83 // i.e. calculate Int[-10,x] gx(x') dx'
84 RooAbsReal *gxy_cdf = gxy.createCdf(RooArgSet(x, y));
85
86 // Plot cdf of gx versus x
87 TH1 *hh_cdf = gxy_cdf->createHistogram("hh_cdf", x, Binning(40), YVar(y, Binning(40)));
88 hh_cdf->SetLineColor(kBlue);
89
90 new TCanvas("rf308_normintegration2d", "rf308_normintegration2d", 600, 600);
91 gPad->SetLeftMargin(0.15);
92 hh_cdf->GetZaxis()->SetTitleOffset(1.8);
93 hh_cdf->Draw("surf");
94}
@ kBlue
Definition: Rtypes.h:66
#define gPad
Definition: TVirtualPad.h:287
RooAbsReal is the common abstract base class for objects that represent a real value and implements f...
Definition: RooAbsReal.h:61
TH1 * createHistogram(const char *varNameList, Int_t xbins=0, Int_t ybins=0, Int_t zbins=0) const
Create and fill a ROOT histogram TH1, TH2 or TH3 with the values of this function for the variables w...
Double_t getVal(const RooArgSet *normalisationSet=nullptr) const
Evaluate object.
Definition: RooAbsReal.h:91
RooAbsReal * createIntegral(const RooArgSet &iset, const RooCmdArg &arg1, 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
Create an object that represents the integral of the function over one or more observables listed in ...
Definition: RooAbsReal.cxx:570
RooArgSet is a container object that can hold multiple RooAbsArg objects.
Definition: RooArgSet.h:29
Plain Gaussian p.d.f.
Definition: RooGaussian.h:24
RooProdPdf is an efficient implementation of a product of PDFs of the form.
Definition: RooProdPdf.h:37
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
virtual void SetLineColor(Color_t lcolor)
Set the line color.
Definition: TAttLine.h:40
The Canvas class.
Definition: TCanvas.h:23
TH1 is the base class of all histogram classes in ROOT.
Definition: TH1.h:58
TAxis * GetZaxis()
Definition: TH1.h:322
virtual void Draw(Option_t *option="")
Draw this histogram with options.
Definition: TH1.cxx:3073
RooCmdArg NormSet(const RooArgSet &nset)
RooCmdArg YVar(const RooAbsRealLValue &var, const RooCmdArg &arg=RooCmdArg::none())
RooConstVar & RooConst(Double_t val)
RooCmdArg Binning(const RooAbsBinning &binning)
Double_t y[n]
Definition: legend1.C:17
Double_t x[n]
Definition: legend1.C:17
The namespace RooFit contains mostly switches that change the behaviour of functions of PDFs (or othe...
Ta Range(0, 0, 1, 1)