# rf309_ndimplot¶

Multidimensional models: making 2/3 dimensional plots of pdfs and datasets

Author: Wouter Verkerke
This notebook tutorial was automatically generated with ROOTBOOK-izer from the macro found in the ROOT repository on Wednesday, November 30, 2022 at 11:22 AM.

In [1]:
%%cpp -d
#include "RooRealVar.h"
#include "RooDataSet.h"
#include "RooConstVar.h"
#include "RooGaussian.h"
#include "RooProdPdf.h"
#include "TCanvas.h"
#include "TAxis.h"
#include "TH1.h"
#include "RooPlot.h"
using namespace RooFit;


## Create 2D model and dataset¶

Create observables

In [2]:
RooRealVar x("x", "x", -5, 5);
RooRealVar y("y", "y", -5, 5);


Create parameters

In [3]:
RooRealVar a0("a0", "a0", -3.5, -5, 5);
RooRealVar a1("a1", "a1", -1.5, -1, 1);
RooRealVar sigma("sigma", "width of gaussian", 1.5);


Create interpreted function f(y) = a0 - a1sqrt(10abs(y))

In [4]:
RooFormulaVar fy("fy", "a0-a1*sqrt(10*abs(y))", RooArgSet(y, a0, a1));


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

In [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 dataset from gauss(x,y)

In [6]:
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_57:2:2: 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);
^


## Make 2D plots of data and model¶

Create and fill ROOT 2D histogram (20x20 bins) with contents of dataset

In [7]:
TH1 *hh_data = data->createHistogram("x,y", Binning(20), Binning(20));

input_line_58:2:17: error: reference to 'data' is ambiguous
TH1 *hh_data = data->createHistogram("x,y", Binning(20), Binning(20));
^
input_line_57:2:14: note: candidate found by name lookup is '__cling_N525::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
^


Create and fill ROOT 2D histogram (50x50 bins) with sampling of pdf TH2D* hh_pdf = model.createHistogram("hh_model",x,Binning(50),YVar(y,Binning(50))) ;

In [8]:
TH1 *hh_pdf = model.createHistogram("x,y", 50, 50);
hh_pdf->SetLineColor(kBlue);

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


## Create 3D model and dataset¶

Create observables

In [9]:
RooRealVar z("z", "z", -5, 5);

RooGaussian gz("gz", "gz", z, RooConst(0), RooConst(2));
RooProdPdf model3("model3", "model3", RooArgSet(model, gz));

RooDataSet *data3 = model3.generate(RooArgSet(x, y, z), 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)


## Make 3D plots of data and model¶

Create and fill ROOT 2D histogram (8x8x8 bins) with contents of dataset

In [10]:
TH1 *hh_data3 = data3->createHistogram("hh_data3", x, Binning(8), YVar(y, Binning(8)), ZVar(z, Binning(8)));


Create and fill ROOT 2D histogram (20x20x20 bins) with sampling of pdf

In [11]:
TH1 *hh_pdf3 = model3.createHistogram("hh_model3", x, Binning(20), YVar(y, Binning(20)), ZVar(z, Binning(20)));
hh_pdf3->SetFillColor(kBlue);

TCanvas *c1 = new TCanvas("rf309_2dimplot", "rf309_2dimplot", 800, 800);
c1->Divide(2, 2);
c1->cd(1);
hh_data->GetZaxis()->SetTitleOffset(1.4);
hh_data->Draw("lego");
c1->cd(2);
hh_pdf->GetZaxis()->SetTitleOffset(2.5);
hh_pdf->Draw("surf");
c1->cd(3);
hh_data->GetZaxis()->SetTitleOffset(1.4);
hh_data->Draw("box");
c1->cd(4);
hh_pdf->GetZaxis()->SetTitleOffset(2.5);
hh_pdf->Draw("cont3");

TCanvas *c2 = new TCanvas("rf309_3dimplot", "rf309_3dimplot", 800, 400);
c2->Divide(2);
c2->cd(1);
hh_data3->GetZaxis()->SetTitleOffset(1.4);
hh_data3->Draw("lego");
c2->cd(2);
hh_pdf3->GetZaxis()->SetTitleOffset(1.4);
hh_pdf3->Draw("iso");

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

input_line_63:2:3: error: use of undeclared identifier 'hh_data'
(hh_data->GetZaxis()->SetTitleOffset(1.3999999999999999))
^
Error in <HandleInterpreterException>: Error evaluating expression (hh_data->GetZaxis()->SetTitleOffset(1.3999999999999999))
Execution of your code was aborted.


Draw all canvases

In [12]:
gROOT->GetListOfCanvases()->Draw()