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rf204_extrangefit.C File Reference
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View in nbviewer Open in SWAN 'ADDITION AND CONVOLUTION' RooFit tutorial macro #204

Extended maximum likelihood fit with alternate range definition for observed number of events. If multiple ranges are used, or only a part of the data is fitted, it is advisable to use a RooAddPdf to extend the model. See tutorial 204a.

␛[1mRooFit v3.60 -- Developed by Wouter Verkerke and David Kirkby␛[0m
Copyright (C) 2000-2013 NIKHEF, University of California & Stanford University
All rights reserved, please read http://roofit.sourceforge.net/license.txt
[#1] INFO:Eval -- RooRealVar::setRange(x) new range named 'signalRange' created with bounds [4,6]
[#1] INFO:Minization -- p.d.f. provides expected number of events, including extended term in likelihood.
[#1] INFO:Minization -- RooMinimizer::optimizeConst: activating const optimization
[#1] INFO:Minization -- The following expressions have been identified as constant and will be precalculated and cached: (sig1,sig2)
[#1] INFO:Minization -- The following expressions will be evaluated in cache-and-track mode: (bkg)
**********
** 1 **SET PRINT 1
**********
**********
** 2 **SET NOGRAD
**********
PARAMETER DEFINITIONS:
NO. NAME VALUE STEP SIZE LIMITS
1 a0 5.00000e-01 1.00000e-01 0.00000e+00 1.00000e+00
2 a1 2.00000e-01 1.00000e-01 0.00000e+00 1.00000e+00
3 nbkg 5.00000e+02 2.50000e+02 0.00000e+00 1.00000e+04
4 nsig 5.00000e+02 2.50000e+02 0.00000e+00 1.00000e+04
5 sig1frac 8.00000e-01 1.00000e-01 0.00000e+00 1.00000e+00
**********
** 3 **SET ERR 0.5
**********
**********
** 4 **SET PRINT 1
**********
**********
** 5 **SET STR 1
**********
NOW USING STRATEGY 1: TRY TO BALANCE SPEED AGAINST RELIABILITY
**********
** 6 **MIGRAD 2500 1
**********
FIRST CALL TO USER FUNCTION AT NEW START POINT, WITH IFLAG=4.
START MIGRAD MINIMIZATION. STRATEGY 1. CONVERGENCE WHEN EDM .LT. 1.00e-03
FCN=-3945.08 FROM MIGRAD STATUS=INITIATE 14 CALLS 15 TOTAL
EDM= unknown STRATEGY= 1 NO ERROR MATRIX
EXT PARAMETER CURRENT GUESS STEP FIRST
NO. NAME VALUE ERROR SIZE DERIVATIVE
1 a0 5.00000e-01 1.00000e-01 2.01358e-01 5.55992e+00
2 a1 2.00000e-01 1.00000e-01 2.57889e-01 -1.57427e+00
3 nbkg 5.00000e+02 2.50000e+02 1.18625e-01 2.53685e+00
4 nsig 5.00000e+02 2.50000e+02 1.18625e-01 -2.53775e+00
5 sig1frac 8.00000e-01 1.00000e-01 2.57889e-01 -2.02142e+00
ERR DEF= 0.5
MIGRAD MINIMIZATION HAS CONVERGED.
MIGRAD WILL VERIFY CONVERGENCE AND ERROR MATRIX.
COVARIANCE MATRIX CALCULATED SUCCESSFULLY
FCN=-3945.49 FROM MIGRAD STATUS=CONVERGED 98 CALLS 99 TOTAL
EDM=1.34919e-05 STRATEGY= 1 ERROR MATRIX ACCURATE
EXT PARAMETER STEP FIRST
NO. NAME VALUE ERROR SIZE DERIVATIVE
1 a0 4.41701e-01 7.31971e-02 6.37371e-03 -2.20459e-02
2 a1 2.01081e-01 1.18245e-01 8.18002e-03 7.34208e-03
3 nbkg 5.04206e+02 3.94549e+01 4.96630e-04 1.70657e-02
4 nsig 4.95799e+02 3.93537e+01 4.96929e-04 6.32308e-03
5 sig1frac 8.37341e-01 1.17266e-01 8.52165e-03 -5.56324e-04
ERR DEF= 0.5
EXTERNAL ERROR MATRIX. NDIM= 25 NPAR= 5 ERR DEF=0.5
5.397e-03 1.216e-03 -3.098e-01 3.099e-01 -1.021e-03
1.216e-03 1.441e-02 -3.254e+00 3.254e+00 -9.763e-03
-3.098e-01 -3.254e+00 1.557e+03 -1.053e+03 3.292e+00
3.099e-01 3.254e+00 -1.053e+03 1.549e+03 -3.293e+00
-1.021e-03 -9.763e-03 3.292e+00 -3.293e+00 1.424e-02
PARAMETER CORRELATION COEFFICIENTS
NO. GLOBAL 1 2 3 4 5
1 0.14135 1.000 0.138 -0.107 0.107 -0.116
2 0.77063 0.138 1.000 -0.687 0.689 -0.682
3 0.77292 -0.107 -0.687 1.000 -0.678 0.699
4 0.77488 0.107 0.689 -0.678 1.000 -0.701
5 0.78168 -0.116 -0.682 0.699 -0.701 1.000
**********
** 7 **SET ERR 0.5
**********
**********
** 8 **SET PRINT 1
**********
**********
** 9 **HESSE 2500
**********
COVARIANCE MATRIX CALCULATED SUCCESSFULLY
FCN=-3945.49 FROM HESSE STATUS=OK 31 CALLS 130 TOTAL
EDM=1.34689e-05 STRATEGY= 1 ERROR MATRIX ACCURATE
EXT PARAMETER INTERNAL INTERNAL
NO. NAME VALUE ERROR STEP SIZE VALUE
1 a0 4.41701e-01 7.31850e-02 1.27474e-03 -1.16864e-01
2 a1 2.01081e-01 1.17613e-01 3.27201e-04 -6.40802e-01
3 nbkg 5.04206e+02 3.93107e+01 9.93261e-05 -1.11784e+00
4 nsig 4.95799e+02 3.92054e+01 1.98772e-05 -1.12170e+00
5 sig1frac 8.37341e-01 1.16841e-01 3.40866e-04 7.40533e-01
ERR DEF= 0.5
EXTERNAL ERROR MATRIX. NDIM= 25 NPAR= 5 ERR DEF=0.5
5.395e-03 1.200e-03 -3.051e-01 3.051e-01 -1.005e-03
1.200e-03 1.425e-02 -3.209e+00 3.209e+00 -9.625e-03
-3.051e-01 -3.209e+00 1.545e+03 -1.041e+03 3.258e+00
3.051e-01 3.209e+00 -1.041e+03 1.537e+03 -3.258e+00
-1.005e-03 -9.625e-03 3.258e+00 -3.258e+00 1.413e-02
PARAMETER CORRELATION COEFFICIENTS
NO. GLOBAL 1 2 3 4 5
1 0.14023 1.000 0.137 -0.106 0.106 -0.115
2 0.76770 0.137 1.000 -0.684 0.686 -0.678
3 0.77101 -0.106 -0.684 1.000 -0.676 0.697
4 0.77292 0.106 0.686 -0.676 1.000 -0.699
5 0.77980 -0.115 -0.678 0.697 -0.699 1.000
[#1] INFO:Minization -- RooMinimizer::optimizeConst: deactivating const optimization
RooFitResult: minimized FCN value: -3945.49, estimated distance to minimum: 1.34689e-05
covariance matrix quality: Full, accurate covariance matrix
Status : MINIMIZE=0 HESSE=0
Floating Parameter FinalValue +/- Error
-------------------- --------------------------
a0 4.4170e-01 +/- 7.32e-02
a1 2.0108e-01 +/- 1.18e-01
nbkg 5.0421e+02 +/- 3.93e+01
nsig 4.9580e+02 +/- 3.92e+01
sig1frac 8.3734e-01 +/- 1.17e-01
#include "RooRealVar.h"
#include "RooDataSet.h"
#include "RooGaussian.h"
#include "RooChebychev.h"
#include "RooAddPdf.h"
#include "RooExtendPdf.h"
#include "RooFitResult.h"
#include "TCanvas.h"
#include "TAxis.h"
#include "RooPlot.h"
using namespace RooFit;
void rf204_extrangefit()
{
// S e t u p c o m p o n e n t p d f s
// ---------------------------------------
// Declare observable x
RooRealVar x("x", "x", 0, 10);
// Create two Gaussian PDFs g1(x,mean1,sigma) anf g2(x,mean2,sigma) and their parameters
RooRealVar mean("mean", "mean of gaussians", 5);
RooRealVar sigma1("sigma1", "width of gaussians", 0.5);
RooRealVar sigma2("sigma2", "width of gaussians", 1);
RooGaussian sig1("sig1", "Signal component 1", x, mean, sigma1);
RooGaussian sig2("sig2", "Signal component 2", x, mean, sigma2);
// Build Chebychev polynomial p.d.f.
RooRealVar a0("a0", "a0", 0.5, 0., 1.);
RooRealVar a1("a1", "a1", 0.2, 0., 1.);
RooChebychev bkg("bkg", "Background", x, RooArgSet(a0, a1));
// Sum the signal components into a composite signal p.d.f.
RooRealVar sig1frac("sig1frac", "fraction of component 1 in signal", 0.8, 0., 1.);
RooAddPdf sig("sig", "Signal", RooArgList(sig1, sig2), sig1frac);
// C o n s t r u c t e x t e n d e d c o m p s wi t h r a n g e s p e c
// ------------------------------------------------------------------------------
// Define signal range in which events counts are to be defined
x.setRange("signalRange", 4, 6);
// Associated nsig/nbkg as expected number of events with sig/bkg _in_the_range_ "signalRange"
RooRealVar nsig("nsig", "number of signal events in signalRange", 500, 0., 10000) ;
RooRealVar nbkg("nbkg", "number of background events in signalRange", 500, 0, 10000) ;
// Use AddPdf to extend the model:
RooAddPdf model("model","(g1+g2)+a", RooArgList(bkg,sig), RooArgList(nbkg,nsig)) ;
// Clone these models here because the interpretation of normalisation coefficients changes
// when different ranges are used:
RooAddPdf model2(model);
RooAddPdf model3(model);
// S a m p l e d a t a , f i t m o d e l
// -------------------------------------------
// Generate 1000 events from model so that nsig,nbkg come out to numbers <<500 in fit
RooDataSet *data = model.generate(x, 1000);
auto canv = new TCanvas("Canvas", "Canvas", 1500, 600);
canv->Divide(3,1);
// Fit full range
// -------------------------------------------
canv->cd(1);
// Perform unbinned ML fit to data, full range
RooFitResult* r = model.fitTo(*data,Save()) ;
r->Print() ;
}
r
ROOT::R::TRInterface & r
Definition: Object.C:4
RooAddPdf
RooAddPdf is an efficient implementation of a sum of PDFs of the form.
Definition: RooAddPdf.h:29
RooArgList
RooArgList is a container object that can hold multiple RooAbsArg objects.
Definition: RooArgList.h:21
RooArgSet
RooArgSet is a container object that can hold multiple RooAbsArg objects.
Definition: RooArgSet.h:28
RooChebychev
Chebychev polynomial p.d.f.
Definition: RooChebychev.h:25
RooDataSet
RooDataSet is a container class to hold unbinned data.
Definition: RooDataSet.h:31
RooFitResult
RooFitResult is a container class to hold the input and output of a PDF fit to a dataset.
Definition: RooFitResult.h:40
RooGaussian
Plain Gaussian p.d.f.
Definition: RooGaussian.h:25
RooRealVar
RooRealVar represents a fundamental (non-derived) real valued object.
Definition: RooRealVar.h:36
TCanvas
The Canvas class.
Definition: TCanvas.h:31
TObject::Print
virtual void Print(Option_t *option="") const
This method must be overridden when a class wants to print itself.
Definition: TObject.cxx:550
x
Double_t x[n]
Definition: legend1.C:17
RooFit
Template specialisation used in RooAbsArg:
Definition: RooCFunction1Binding.h:29
RooFit::Save
RooCmdArg Save(Bool_t flag=kTRUE)
Definition: RooGlobalFunc.cxx:184
rf204_extrangefit
Definition: rf204_extrangefit.py:1
Author
07/2008 - Wouter Verkerke

Definition in file rf204_extrangefit.C.