Multidimensional models: performing fits in multiple (disjoint) ranges in one or more dimensions
Author: Wouter Verkerke
This notebook tutorial was automatically generated with ROOTBOOK-izer from the macro found in the ROOT repository on Tuesday, March 19, 2024 at 07:15 PM.
%%cpp -d
#include "RooRealVar.h"
#include "RooDataSet.h"
#include "RooGaussian.h"
#include "RooProdPdf.h"
#include "RooAddPdf.h"
#include "RooPolynomial.h"
#include "TCanvas.h"
#include "TAxis.h"
#include "RooPlot.h"
#include "RooFitResult.h"
using namespace RooFit;
Define observables x,y
RooRealVar x("x", "x", -10, 10);
RooRealVar y("y", "y", -10, 10);
Construct the signal pdf gauss(x)*gauss(y)
RooRealVar mx("mx", "mx", 1, -10, 10);
RooRealVar my("my", "my", 1, -10, 10);
RooGaussian gx("gx", "gx", x, mx, 1.0);
RooGaussian gy("gy", "gy", y, my, 1.0);
RooProdPdf sig("sig", "sig", gx, gy);
Construct the background pdf (flat in x,y)
RooPolynomial px("px", "px", x);
RooPolynomial py("py", "py", y);
RooProdPdf bkg("bkg", "bkg", px, py);
Construct the composite model sig+bkg
RooRealVar f("f", "f", 0., 1.);
RooAddPdf model("model", "model", RooArgList(sig, bkg), f);
Sample 10000 events in (x,y) from the model
std::unique_ptr<RooDataSet> modelData{model.generate({x, y}, 10000)};
Construct the SideBand1,SideBand2,Signal regions
| +-------------+-----------+ | | | | Side | Sig | | Band1 | nal | | | | --+-------------+-----------+-- | | | Side | | Band2 | | | +-------------+-----------+ |
x.setRange("SB1", -10, +10);
y.setRange("SB1", -10, 0);
x.setRange("SB2", -10, 0);
y.setRange("SB2", 0, +10);
x.setRange("SIG", 0, +10);
y.setRange("SIG", 0, +10);
x.setRange("FULL", -10, +10);
y.setRange("FULL", -10, +10);
[#1] INFO:Eval -- RooRealVar::setRange(x) new range named 'SB1' created with bounds [-10,10] [#1] INFO:Eval -- RooRealVar::setRange(y) new range named 'SB1' created with bounds [-10,0] [#1] INFO:Eval -- RooRealVar::setRange(x) new range named 'SB2' created with bounds [-10,0] [#1] INFO:Eval -- RooRealVar::setRange(y) new range named 'SB2' created with bounds [0,10] [#1] INFO:Eval -- RooRealVar::setRange(x) new range named 'SIG' created with bounds [0,10] [#1] INFO:Eval -- RooRealVar::setRange(y) new range named 'SIG' created with bounds [0,10] [#1] INFO:Eval -- RooRealVar::setRange(x) new range named 'FULL' created with bounds [-10,10] [#1] INFO:Eval -- RooRealVar::setRange(y) new range named 'FULL' created with bounds [-10,10]
Perform fit in SideBand1 region (RooAddPdf coefficients will be interpreted in full range)
std::unique_ptr<RooFitResult> r_sb1{model.fitTo(*modelData, Range("SB1"), Save(), PrintLevel(-1))};
[#1] INFO:Eval -- RooRealVar::setRange(x) new range named 'fit_nll_model_modelData' created with bounds [-10,10] [#1] INFO:Eval -- RooRealVar::setRange(y) new range named 'fit_nll_model_modelData' created with bounds [-10,0] [#1] INFO:Fitting -- RooAbsPdf::fitTo(model) fixing normalization set for coefficient determination to observables in data [#1] INFO:Fitting -- using CPU computation library compiled with -mavx2 [#1] INFO:Fitting -- RooAddition::defaultErrorLevel(nll_model_modelData) Summation contains a RooNLLVar, using its error level [#1] INFO:Minimization -- RooAbsMinimizerFcn::setOptimizeConst: activating const optimization [#1] INFO:Minimization -- RooAbsMinimizerFcn::setOptimizeConst: deactivating const optimization
Perform fit in SideBand2 region (RooAddPdf coefficients will be interpreted in full range)
std::unique_ptr<RooFitResult> r_sb2{model.fitTo(*modelData, Range("SB2"), Save(), PrintLevel(-1))};
[#1] INFO:Fitting -- RooAbsPdf::fitTo(model) fixing normalization set for coefficient determination to observables in data [#1] INFO:Fitting -- RooAddition::defaultErrorLevel(nll_model_modelData) Summation contains a RooNLLVar, using its error level [#1] INFO:Minimization -- RooAbsMinimizerFcn::setOptimizeConst: activating const optimization [#1] INFO:Minimization -- RooAbsMinimizerFcn::setOptimizeConst: deactivating const optimization
Now perform fit to joint 'L-shaped' sideband region 'SB1|SB2' (RooAddPdf coefficients will be interpreted in full range)
std::unique_ptr<RooFitResult> r_sb12{model.fitTo(*modelData, Range("SB1,SB2"), Save(), PrintLevel(-1))};
[#1] INFO:Eval -- RooRealVar::setRange(x) new range named 'fit_nll_model_modelData_SB1' created with bounds [-10,10] [#1] INFO:Eval -- RooRealVar::setRange(y) new range named 'fit_nll_model_modelData_SB1' created with bounds [-10,0] [#1] INFO:Eval -- RooRealVar::setRange(x) new range named 'fit_nll_model_modelData_SB2' created with bounds [-10,0] [#1] INFO:Eval -- RooRealVar::setRange(y) new range named 'fit_nll_model_modelData_SB2' created with bounds [0,10] [#1] INFO:Fitting -- RooAbsPdf::fitTo(model) fixing normalization set for coefficient determination to observables in data [#1] INFO:Fitting -- RooAddition::defaultErrorLevel(nll_model_modelData) Summation contains a RooNLLVar, using its error level [#1] INFO:Minimization -- RooAbsMinimizerFcn::setOptimizeConst: activating const optimization [#1] INFO:Minimization -- RooAbsMinimizerFcn::setOptimizeConst: deactivating const optimization
Print results for comparison
r_sb1->Print();
r_sb2->Print();
r_sb12->Print();
RooFitResult: minimized FCN value: 16261.4, estimated distance to minimum: 5.06415e-07 covariance matrix quality: Full, accurate covariance matrix Status : MINIMIZE=0 HESSE=0 Floating Parameter FinalValue +/- Error -------------------- -------------------------- f 5.1135e-01 +/- 3.58e-02 mx 9.8740e-01 +/- 4.03e-02 my 9.9305e-01 +/- 9.39e-02 RooFitResult: minimized FCN value: 7578.28, estimated distance to minimum: 3.07865e-06 covariance matrix quality: Full, accurate covariance matrix Status : MINIMIZE=0 HESSE=0 Floating Parameter FinalValue +/- Error -------------------- -------------------------- f 5.4586e-01 +/- 4.46e-02 mx 1.1276e+00 +/- 1.10e-01 my 9.6462e-01 +/- 5.60e-02 RooFitResult: minimized FCN value: 27252.6, estimated distance to minimum: 2.25202e-06 covariance matrix quality: Full, accurate covariance matrix Status : MINIMIZE=0 HESSE=0 Floating Parameter FinalValue +/- Error -------------------- -------------------------- f 5.0082e-01 +/- 1.29e-02 mx 1.0100e+00 +/- 3.26e-02 my 9.6348e-01 +/- 3.31e-02