# rf301_composition¶

Multidimensional models: multi-dimensional pdfs through composition e.g. substituting a pdf parameter with a function that depends on other observables

pdf = gauss(x,f(y),s) with f(y) = a0 + a1*y

Author: Wouter Verkerke
This notebook tutorial was automatically generated with ROOTBOOK-izer from the macro found in the ROOT repository on Monday, September 26, 2022 at 09:38 AM.

In :
%%cpp -d
#include "RooRealVar.h"
#include "RooDataSet.h"
#include "RooGaussian.h"
#include "RooPolyVar.h"
#include "RooPlot.h"
#include "TCanvas.h"
#include "TAxis.h"
#include "TH1.h"
using namespace RooFit;


## Setup composed model gauss(x,m(y),s)¶

Create observables

In :
RooRealVar x("x", "x", -5, 5);
RooRealVar y("y", "y", -5, 5);


Create function f(y) = a0 + a1*y

In :
RooRealVar a0("a0", "a0", -0.5, -5, 5);
RooRealVar a1("a1", "a1", -0.5, -1, 1);
RooPolyVar fy("fy", "fy", y, RooArgSet(a0, a1));


Create gauss(x,f(y),s)

In :
RooRealVar sigma("sigma", "width of gaussian", 0.5);
RooGaussian model("model", "Gaussian with shifting mean", x, fy, sigma);

[#0] WARNING:InputArguments -- The parameter 'sigma' with range [-1e+30, 1e+30] of the RooGaussian 'model' exceeds the safe range of (0, inf). Advise to limit its range.


## Sample data, plot data and pdf on x and y¶

Generate 10000 events in x and y from model

In :
RooDataSet *data = model.generate(RooArgSet(x, y), 10000);

[#1] INFO:NumericIntegration -- RooRealIntegral::init(model_Int[x,y]) using numeric integrator RooIntegrator1D to calculate Int(y)
[#1] INFO:NumericIntegration -- RooRealIntegral::init(model_Int[x,y]) using numeric integrator RooIntegrator1D to calculate Int(y)
[#1] INFO:NumericIntegration -- RooRealIntegral::init(model_Int[x,y]) using numeric integrator RooIntegrator1D to calculate Int(y)

input_line_51:2:2: warning: 'data' shadows a declaration with the same name in the 'std' namespace; use '::data' to reference this declaration
RooDataSet *data = model.generate(RooArgSet(x, y), 10000);
^


Plot x distribution of data and projection of model on x = Int(dy) model(x,y)

In :
RooPlot *xframe = x.frame();
data->plotOn(xframe);
model.plotOn(xframe);

input_line_52:3:1: error: reference to 'data' is ambiguous
data->plotOn(xframe);
^
input_line_51:2:14: note: candidate found by name lookup is '__cling_N524::data'
RooDataSet *data = model.generate(RooArgSet(x, y), 10000);
^
/usr/include/c++/9/bits/range_access.h:318:5: note: candidate found by name lookup is 'std::data'
data(initializer_list<_Tp> __il) noexcept
^
/usr/include/c++/9/bits/range_access.h:289:5: note: candidate found by name lookup is 'std::data'
data(_Container& __cont) noexcept(noexcept(__cont.data()))
^
/usr/include/c++/9/bits/range_access.h:299:5: note: candidate found by name lookup is 'std::data'
data(const _Container& __cont) noexcept(noexcept(__cont.data()))
^
/usr/include/c++/9/bits/range_access.h:309:5: note: candidate found by name lookup is 'std::data'
data(_Tp (&__array)[_Nm]) noexcept
^


Plot x distribution of data and projection of model on y = Int(dx) model(x,y)

In :
RooPlot *yframe = y.frame();
data->plotOn(yframe);
model.plotOn(yframe);

input_line_53:3:1: error: reference to 'data' is ambiguous
data->plotOn(yframe);
^
input_line_51:2:14: note: candidate found by name lookup is '__cling_N524::data'
RooDataSet *data = model.generate(RooArgSet(x, y), 10000);
^
/usr/include/c++/9/bits/range_access.h:318:5: note: candidate found by name lookup is 'std::data'
data(initializer_list<_Tp> __il) noexcept
^
/usr/include/c++/9/bits/range_access.h:289:5: note: candidate found by name lookup is 'std::data'
data(_Container& __cont) noexcept(noexcept(__cont.data()))
^
/usr/include/c++/9/bits/range_access.h:299:5: note: candidate found by name lookup is 'std::data'
data(const _Container& __cont) noexcept(noexcept(__cont.data()))
^
/usr/include/c++/9/bits/range_access.h:309:5: note: candidate found by name lookup is 'std::data'
data(_Tp (&__array)[_Nm]) noexcept
^


Make two-dimensional plot in x vs y

In :
TH1 *hh_model = model.createHistogram("hh_model", x, Binning(50), YVar(y, Binning(50)));
hh_model->SetLineColor(kBlue);

[#1] INFO:NumericIntegration -- RooRealIntegral::init(model_Int[x,y]) using numeric integrator RooIntegrator1D to calculate Int(y)


Make canvas and draw RooPlots

In :
TCanvas *c = new TCanvas("rf301_composition", "rf301_composition", 1200, 400);
c->Divide(3);
c->cd(1);
xframe->GetYaxis()->SetTitleOffset(1.4);
xframe->Draw();
c->cd(2);
yframe->GetYaxis()->SetTitleOffset(1.4);
yframe->Draw();
c->cd(3);
hh_model->GetZaxis()->SetTitleOffset(2.5);
hh_model->Draw("surf");

input_line_56:2:3: error: use of undeclared identifier 'xframe'
(xframe->GetYaxis()->SetTitleOffset(1.3999999999999999))
^
Error in <HandleInterpreterException>: Error evaluating expression (xframe->GetYaxis()->SetTitleOffset(1.3999999999999999))
Execution of your code was aborted.


Draw all canvases

In :
gROOT->GetListOfCanvases()->Draw() 