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rf702_efficiencyfit_2D.C File Reference
Tutorials » RooFit Tutorials

Detailed Description

View in nbviewer Open in SWAN Special pdf's: unbinned maximum likelihood fit of an efficiency eff(x) function to a dataset D(x,cut), cut is a category encoding a selection whose efficiency as function of x should be described by eff(x)

␛[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
[#0] WARNING:Generation -- RooAcceptReject::ctor(effPdf_Int[]_Norm[cut]) WARNING: performing accept/reject sampling on a p.d.f in 2 dimensions without prior knowledge on maximum value of p.d.f. Determining maximum value by taking 200000 trial samples. If p.d.f contains sharp peaks smaller than average distance between trial sampling points these may be missed and p.d.f. may be sampled incorrectly.
[#0] WARNING:Generation -- RooAcceptReject::ctor(effPdf_Int[]_Norm[cut]): WARNING: 200000 trial samples requested by p.d.f for 2-dimensional accept/reject sampling, this may take some time
[#1] INFO:Minimization -- RooAbsMinimizerFcn::setOptimizeConst: activating const optimization
**********
** 1 **SET PRINT 1
**********
**********
** 2 **SET NOGRAD
**********
PARAMETER DEFINITIONS:
NO. NAME VALUE STEP SIZE LIMITS
1 ax 6.00000e-01 1.00000e-01 0.00000e+00 1.00000e+00
2 ay 2.00000e-01 1.00000e-01 0.00000e+00 1.00000e+00
3 cx -1.00000e+00 2.00000e+00 -1.00000e+01 1.00000e+01
4 cy -1.00000e+00 2.00000e+00 -1.00000e+01 1.00000e+01
**********
** 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 2000 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=5447.45 FROM MIGRAD STATUS=INITIATE 16 CALLS 17 TOTAL
EDM= unknown STRATEGY= 1 NO ERROR MATRIX
EXT PARAMETER CURRENT GUESS STEP FIRST
NO. NAME VALUE ERROR SIZE DERIVATIVE
1 ax 6.00000e-01 1.00000e-01 2.05758e-01 2.07611e+01
2 ay 2.00000e-01 1.00000e-01 2.57889e-01 6.35766e+01
3 cx -1.00000e+00 2.00000e+00 2.02430e-01 3.98906e+02
4 cy -1.00000e+00 2.00000e+00 2.02430e-01 -1.37299e+02
ERR DEF= 0.5
MIGRAD MINIMIZATION HAS CONVERGED.
MIGRAD WILL VERIFY CONVERGENCE AND ERROR MATRIX.
COVARIANCE MATRIX CALCULATED SUCCESSFULLY
FCN=5441.98 FROM MIGRAD STATUS=CONVERGED 79 CALLS 80 TOTAL
EDM=2.10777e-05 STRATEGY= 1 ERROR MATRIX ACCURATE
EXT PARAMETER STEP FIRST
NO. NAME VALUE ERROR SIZE DERIVATIVE
1 ax 6.10442e-01 9.85749e-03 8.90018e-04 1.06907e-01
2 ay 2.06325e-01 1.06819e-02 9.76478e-04 2.34590e-01
3 cx -1.13975e+00 5.97322e-02 2.77681e-04 6.58278e-02
4 cy -5.30427e-01 2.15761e-01 8.34515e-04 -2.03235e-01
ERR DEF= 0.5
EXTERNAL ERROR MATRIX. NDIM= 25 NPAR= 4 ERR DEF=0.5
9.718e-05 -2.419e-05 -2.246e-04 2.779e-05
-2.419e-05 1.141e-04 -2.514e-05 1.447e-03
-2.246e-04 -2.514e-05 3.568e-03 1.894e-05
2.779e-05 1.447e-03 1.894e-05 4.656e-02
PARAMETER CORRELATION COEFFICIENTS
NO. GLOBAL 1 2 3 4
1 0.50176 1.000 -0.230 -0.381 0.013
2 0.68607 -0.230 1.000 -0.039 0.628
3 0.42040 -0.381 -0.039 1.000 0.001
4 0.65573 0.013 0.628 0.001 1.000
**********
** 7 **SET ERR 0.5
**********
**********
** 8 **SET PRINT 1
**********
**********
** 9 **HESSE 2000
**********
COVARIANCE MATRIX CALCULATED SUCCESSFULLY
FCN=5441.98 FROM HESSE STATUS=OK 23 CALLS 103 TOTAL
EDM=2.1074e-05 STRATEGY= 1 ERROR MATRIX ACCURATE
EXT PARAMETER INTERNAL INTERNAL
NO. NAME VALUE ERROR STEP SIZE VALUE
1 ax 6.10442e-01 9.85365e-03 1.78004e-04 2.22720e-01
2 ay 2.06325e-01 1.06842e-02 1.95296e-04 -6.27781e-01
3 cx -1.13975e+00 5.97056e-02 5.55362e-05 -1.14223e-01
4 cy -5.30427e-01 2.15797e-01 1.66903e-04 -5.30676e-02
ERR DEF= 0.5
EXTERNAL ERROR MATRIX. NDIM= 25 NPAR= 4 ERR DEF=0.5
9.711e-05 -2.421e-05 -2.238e-04 2.765e-05
-2.421e-05 1.142e-04 -2.530e-05 1.448e-03
-2.238e-04 -2.530e-05 3.565e-03 1.965e-05
2.765e-05 1.448e-03 1.965e-05 4.658e-02
PARAMETER CORRELATION COEFFICIENTS
NO. GLOBAL 1 2 3 4
1 0.50117 1.000 -0.230 -0.380 0.013
2 0.68624 -0.230 1.000 -0.040 0.628
3 0.41953 -0.380 -0.040 1.000 0.002
4 0.65587 0.013 0.628 0.002 1.000
[#1] INFO:Minimization -- RooAbsMinimizerFcn::setOptimizeConst: deactivating const optimization
[#0] WARNING:InputArguments -- RooAbsReal::createHistogram(effFunc) WARNING extended mode requested for a non-pdf object, ignored
#include "RooRealVar.h"
#include "RooDataSet.h"
#include "RooGaussian.h"
#include "RooConstVar.h"
#include "RooCategory.h"
#include "RooEfficiency.h"
#include "RooPolynomial.h"
#include "RooProdPdf.h"
#include "RooFormulaVar.h"
#include "TCanvas.h"
#include "TAxis.h"
#include "TH1.h"
#include "RooPlot.h"
using namespace RooFit;
void rf702_efficiencyfit_2D(Bool_t flat = kFALSE)
{
// C o n s t r u c t e f f i c i e n c y f u n c t i o n e ( x , y )
// -----------------------------------------------------------------------
// Declare variables x,mean,sigma with associated name, title, initial value and allowed range
RooRealVar x("x", "x", -10, 10);
RooRealVar y("y", "y", -10, 10);
// Efficiency function eff(x;a,b)
RooRealVar ax("ax", "ay", 0.6, 0, 1);
RooRealVar bx("bx", "by", 5);
RooRealVar cx("cx", "cy", -1, -10, 10);
RooRealVar ay("ay", "ay", 0.2, 0, 1);
RooRealVar by("by", "by", 5);
RooRealVar cy("cy", "cy", -1, -10, 10);
RooFormulaVar effFunc("effFunc", "((1-ax)+ax*cos((x-cx)/bx))*((1-ay)+ay*cos((y-cy)/by))",
RooArgList(ax, bx, cx, x, ay, by, cy, y));
// Acceptance state cut (1 or 0)
RooCategory cut("cut", "cutr", { {"accept", 1}, {"reject", 0} });
// C o n s t r u c t c o n d i t i o n a l e f f i c i e n c y p d f E ( c u t | x , y )
// ---------------------------------------------------------------------------------------------
// Construct efficiency pdf eff(cut|x)
RooEfficiency effPdf("effPdf", "effPdf", effFunc, cut, "accept");
// G e n e r a t e d a t a ( x , y , c u t ) f r o m a t o y m o d e l
// -------------------------------------------------------------------------------
// Construct global shape pdf shape(x) and product model(x,cut) = eff(cut|x)*shape(x)
// (These are _only_ needed to generate some toy MC here to be used later)
RooPolynomial shapePdfX("shapePdfX", "shapePdfX", x, RooConst(flat ? 0 : -0.095));
RooPolynomial shapePdfY("shapePdfY", "shapePdfY", y, RooConst(flat ? 0 : +0.095));
RooProdPdf shapePdf("shapePdf", "shapePdf", RooArgSet(shapePdfX, shapePdfY));
RooProdPdf model("model", "model", shapePdf, Conditional(effPdf, cut));
// Generate some toy data from model
RooDataSet *data = model.generate(RooArgSet(x, y, cut), 10000);
// F i t c o n d i t i o n a l e f f i c i e n c y p d f t o d a t a
// --------------------------------------------------------------------------
// Fit conditional efficiency pdf to data
effPdf.fitTo(*data, ConditionalObservables(RooArgSet(x, y)));
// P l o t f i t t e d , d a t a e f f i c i e n c y
// --------------------------------------------------------
// Make 2D histograms of all data, selected data and efficiency function
TH1 *hh_data_all = data->createHistogram("hh_data_all", x, Binning(8), YVar(y, Binning(8)));
TH1 *hh_data_sel = data->createHistogram("hh_data_sel", x, Binning(8), YVar(y, Binning(8)), Cut("cut==cut::accept"));
TH1 *hh_eff = effFunc.createHistogram("hh_eff", x, Binning(50), YVar(y, Binning(50)));
// Some adjustment for good visualization
hh_data_all->SetMinimum(0);
hh_data_sel->SetMinimum(0);
hh_eff->SetMinimum(0);
hh_eff->SetLineColor(kBlue);
// Draw all frames on a canvas
TCanvas *ca = new TCanvas("rf702_efficiency_2D", "rf702_efficiency_2D", 1200, 400);
ca->Divide(3);
ca->cd(1);
gPad->SetLeftMargin(0.15);
hh_data_all->GetZaxis()->SetTitleOffset(1.8);
hh_data_all->Draw("lego");
ca->cd(2);
gPad->SetLeftMargin(0.15);
hh_data_sel->GetZaxis()->SetTitleOffset(1.8);
hh_data_sel->Draw("lego");
ca->cd(3);
gPad->SetLeftMargin(0.15);
hh_eff->GetZaxis()->SetTitleOffset(1.8);
hh_eff->Draw("surf");
return;
}
kFALSE
const Bool_t kFALSE
Definition RtypesCore.h:101
Bool_t
bool Bool_t
Definition RtypesCore.h:63
kBlue
@ kBlue
Definition Rtypes.h:66
gPad
#define gPad
Definition TVirtualPad.h:288
RooArgList
RooArgList is a container object that can hold multiple RooAbsArg objects.
Definition RooArgList.h:22
RooArgSet
RooArgSet is a container object that can hold multiple RooAbsArg objects.
Definition RooArgSet.h:35
RooCategory
RooCategory is an object to represent discrete states.
Definition RooCategory.h:27
RooDataSet
RooDataSet is a container class to hold unbinned data.
Definition RooDataSet.h:36
RooDataSet::createHistogram
TH2F * createHistogram(const RooAbsRealLValue &var1, const RooAbsRealLValue &var2, const char *cuts="", const char *name="hist") const
Create a TH2F histogram of the distribution of the specified variable using this dataset.
Definition RooDataSet.cxx:1428
RooEfficiency
RooEfficiency is a PDF helper class to fit efficiencies parameterized by a supplied function F.
Definition RooEfficiency.h:27
RooFormulaVar
A RooFormulaVar is a generic implementation of a real-valued object, which takes a RooArgList of serv...
Definition RooFormulaVar.h:30
RooPolynomial
RooPolynomial implements a polynomial p.d.f of the form.
Definition RooPolynomial.h:28
RooProdPdf
RooProdPdf is an efficient implementation of a product of PDFs of the form.
Definition RooProdPdf.h:33
RooRealVar
RooRealVar represents a variable that can be changed from the outside.
Definition RooRealVar.h:39
TAttAxis::SetTitleOffset
virtual void SetTitleOffset(Float_t offset=1)
Set distance between the axis and the axis title.
Definition TAttAxis.cxx:302
TAttLine::SetLineColor
virtual void SetLineColor(Color_t lcolor)
Set the line color.
Definition TAttLine.h:40
TAttPad::SetLeftMargin
virtual void SetLeftMargin(Float_t leftmargin)
Set Pad left margin in fraction of the pad width.
Definition TAttPad.cxx:109
TCanvas
The Canvas class.
Definition TCanvas.h:23
TCanvas::cd
TVirtualPad * cd(Int_t subpadnumber=0) override
Set current canvas & pad.
Definition TCanvas.cxx:706
TH1
TH1 is the base class of all histogram classes in ROOT.
Definition TH1.h:58
TH1::GetZaxis
TAxis * GetZaxis()
Definition TH1.h:322
TH1::SetMinimum
virtual void SetMinimum(Double_t minimum=-1111)
Definition TH1.h:399
TH1::Draw
virtual void Draw(Option_t *option="")
Draw this histogram with options.
Definition TH1.cxx:3074
TPad::Divide
void Divide(Int_t nx=1, Int_t ny=1, Float_t xmargin=0.01, Float_t ymargin=0.01, Int_t color=0) override
Automatic pad generation by division.
Definition TPad.cxx:1178
RooFit::YVar
RooCmdArg YVar(const RooAbsRealLValue &var, const RooCmdArg &arg=RooCmdArg::none())
Definition RooGlobalFunc.cxx:304
RooFit::RooConst
RooConstVar & RooConst(Double_t val)
Definition RooGlobalFunc.cxx:406
RooFit::Conditional
RooCmdArg Conditional(const RooArgSet &pdfSet, const RooArgSet &depSet, Bool_t depsAreCond=kFALSE)
Definition RooGlobalFunc.cxx:280
RooFit::ConditionalObservables
RooCmdArg ConditionalObservables(Args_t &&... argsOrArgSet)
Create a RooCmdArg to declare conditional observables.
Definition RooGlobalFunc.h:242
RooFit::Binning
RooCmdArg Binning(const RooAbsBinning &binning)
Definition RooGlobalFunc.cxx:126
RooFit::Cut
RooCmdArg Cut(const char *cutSpec)
Definition RooGlobalFunc.cxx:124
y
Double_t y[n]
Definition legend1.C:17
x
Double_t x[n]
Definition legend1.C:17
RooFit
The namespace RooFit contains mostly switches that change the behaviour of functions of PDFs (or othe...
Definition Common.h:18
rf702_efficiencyfit_2D
Definition rf702_efficiencyfit_2D.py:1
Date
February 2018
Authors
Clemens Lange, Wouter Verkerke (C++ version)

Definition in file rf702_efficiencyfit_2D.C.