Rf 2 0 7_Comptools¶

Addition and convolution: tools and utilities for manipulation of composite objects

Author: Wouter Verkerke
This notebook tutorial was automatically generated with ROOTBOOK-izer from the macro found in the ROOT repository on Monday, January 17, 2022 at 09:54 AM.

In :
%%cpp -d
#include "RooRealVar.h"
#include "RooDataSet.h"
#include "RooGaussian.h"
#include "RooChebychev.h"
#include "RooExponential.h"
#include "RooPlot.h"
#include "RooCustomizer.h"
#include "TCanvas.h"
#include "TAxis.h"
#include "TH1.h"
In :
%%cpp -d
// This is a workaround to make sure the namespace is used inside functions
using namespace RooFit;

Setup composite pdf, dataset¶

Declare observable x

In :
RooRealVar x("x", "x", 0, 10);
RooFit v3.60 -- Developed by Wouter Verkerke and David Kirkby
Copyright (C) 2000-2013 NIKHEF, University of California & Stanford University

Create two gaussian pdfs g1(x,mean1,sigma) anf g2(x,mean2,sigma) and their parameters

In :
RooRealVar mean("mean", "mean of gaussians", 5);
RooRealVar sigma("sigma", "width of gaussians", 0.5);
RooGaussian sig("sig", "Signal component 1", x, mean, sigma);
[#0] WARNING:InputArguments -- The parameter 'sigma' with range [-1e+30, 1e+30] of the RooGaussian 'sig' exceeds the safe range of (0, inf). Advise to limit its range.

Build chebychev polynomial pdf

In :
RooRealVar a0("a0", "a0", 0.5, 0., 1.);
RooRealVar a1("a1", "a1", 0.2, 0., 1.);
RooChebychev bkg1("bkg1", "Background 1", x, RooArgSet(a0, a1));

Build exponential pdf

In :
RooRealVar alpha("alpha", "alpha", -1);
RooExponential bkg2("bkg2", "Background 2", x, alpha);

Sum the background components into a composite background pdf

In :
RooRealVar bkg1frac("bkg1frac", "fraction of component 1 in background", 0.2, 0., 1.);
RooAddPdf bkg("bkg", "Signal", RooArgList(bkg1, bkg2), bkg1frac);

Sum the composite signal and background

In :
RooRealVar bkgfrac("bkgfrac", "fraction of background", 0.5, 0., 1.);
RooAddPdf model("model", "g1+g2+a", RooArgList(bkg, sig), bkgfrac);

Create dummy dataset that has more observables than the above pdf

In :
RooRealVar y("y", "y", -10, 10);
RooDataSet data("data", "data", RooArgSet(x, y));

Basic information requests¶

Get list of observables¶

Get list of observables of pdf in context of a dataset

Observables are define each context as the variables shared between a model and a dataset. In this case that is the variable 'x'

In :
RooArgSet *model_obs = model.getObservables(data);
model_obs->Print("v");
input_line_60:2:46: error: reference to 'data' is ambiguous
RooArgSet *model_obs = model.getObservables(data);
^
input_line_59:3:12: note: candidate found by name lookup is '__cling_N527::data'
RooDataSet data("data", "data", RooArgSet(x, y));
^
/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
^

Get list of parameters¶

Get list of parameters, given list of observables

In :
RooArgSet *model_params = model.getParameters(x);
model_params->Print("v");
1) 0x7ff2a5541000 RooRealVar::       a0 = 0.5  L(0 - 1)  "a0"
2) 0x7ff2a55413d8 RooRealVar::       a1 = 0.2  L(0 - 1)  "a1"
3) 0x7ff2d0263400 RooRealVar::    alpha = -1 C  L(-INF - +INF)  "alpha"
4) 0x7ff2a553c000 RooRealVar:: bkg1frac = 0.2  L(0 - 1)  "fraction of component 1 in background"
5) 0x7ff2a5539000 RooRealVar::  bkgfrac = 0.5  L(0 - 1)  "fraction of background"
6) 0x7ff2a5885000 RooRealVar::     mean = 5 C  L(-INF - +INF)  "mean of gaussians"
7) 0x7ff2a58853d8 RooRealVar::    sigma = 0.5 C  L(-INF - +INF)  "width of gaussians"

Get list of parameters, given a dataset (Gives identical results to operation above)

In :
RooArgSet *model_params2 = model.getParameters(data);
model_params2->Print();
input_line_62:2:49: error: reference to 'data' is ambiguous
RooArgSet *model_params2 = model.getParameters(data);
^
input_line_59:3:12: note: candidate found by name lookup is '__cling_N527::data'
RooDataSet data("data", "data", RooArgSet(x, y));
^
/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
^

Get list of components¶

Get list of component objects, including top-level node

In :
RooArgSet *model_comps = model.getComponents();
model_comps->Print("v");
1) 0x7ff2a55393d8 RooAddPdf:: model[ bkgfrac * bkg + [%] * sig ] = 0.582695  "g1+g2+a"
2) 0x7ff2a553c3d8 RooAddPdf::   bkg[ bkg1frac * bkg1 + [%] * bkg2 ] = 0.16539  "Signal"
3) 0x7ff2a55417b0 RooChebychev::  bkg1[ x=x coefficients=(a0,a1) ] = 0.8  "Background 1"
4) 0x7ff2d02637d8 RooExponential::  bkg2[ x=x c=alpha ] = 0.00673795  "Background 2"
5) 0x7ff2a58857b0 RooGaussian::   sig[ x=x mean=mean sigma=sigma ] = 1  "Signal component 1"

Modifications to structure of composites¶

Create a second gaussian

In :
RooRealVar sigma2("sigma2", "width of gaussians", 1);
RooGaussian sig2("sig2", "Signal component 1", x, mean, sigma2);
[#0] WARNING:InputArguments -- The parameter 'sigma2' with range [-1e+30, 1e+30] of the RooGaussian 'sig2' exceeds the safe range of (0, inf). Advise to limit its range.

Create a sum of the original gaussian plus the new second gaussian

In :
RooRealVar sig1frac("sig1frac", "fraction of component 1 in signal", 0.8, 0., 1.);
RooAddPdf sigsum("sigsum", "sig+sig2", RooArgList(sig, sig2), sig1frac);

Construct a customizer utility to customize model

In :
RooCustomizer cust(model, "cust");

Instruct the customizer to replace node 'sig' with node 'sigsum'

In :
cust.replaceArg(sig, sigsum);

Build a clone of the input pdf according to the above customization instructions. Each node that requires modified is clone so that the original pdf remained untouched. The name of each cloned node is that of the original node suffixed by the name of the customizer object

The returned head node own all nodes that were cloned as part of the build process so when cust_clone is deleted so will all other nodes that were created in the process.

In :
RooAbsPdf *cust_clone = (RooAbsPdf *)cust.build(kTRUE);
[#1] INFO:ObjectHandling -- RooCustomizer::build(model): tree node sig will be replaced by sigsum
[#1] INFO:ObjectHandling -- RooCustomizer::build(model) Branch node RooAddPdf::model cloned: depends on a replaced parameter
[#1] INFO:ObjectHandling -- RooCustomizer::build(model) Branch node sig is already replaced

Print structure of clone of model with sig->sigsum replacement.

In :
cust_clone->Print("t");

delete cust_clone;
0x7ff2a55417b0/V- RooChebychev::bkg1 = 0.8 [Auto,Dirty]
0x7ff2d0263028/V- RooRealVar::x = 5
0x7ff2a5541000/V- RooRealVar::a0 = 0.5
0x7ff2a55413d8/V- RooRealVar::a1 = 0.2
0x7ff2a553c000/V- RooRealVar::bkg1frac = 0.2
0x7ff2d02637d8/V- RooExponential::bkg2 = 0.00673795 [Auto,Dirty]
0x7ff2d0263028/V- RooRealVar::x = 5
0x7ff2d0263400/V- RooRealVar::alpha = -1
0x7ff2a5539000/V- RooRealVar::bkgfrac = 0.5