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rf702_efficiencyfit_2D.C File Reference
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View in nbviewer Open in SWAN 'SPECIAL PDFS' RooFit tutorial macro #702

Unbinned maximum likelihood fit of an efficiency eff(x) function to a dataset D(x,cut), where cut is a category encoding a selection whose

pict1_rf702_efficiencyfit_2D.C.png
Processing /mnt/build/workspace/root-makedoc-v614/rootspi/rdoc/src/v6-14-00-patches/tutorials/roofit/rf702_efficiencyfit_2D.C...
RooFit v3.60 -- Developed by Wouter Verkerke and David Kirkby
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:Minization -- RooMinimizer::optimizeConst: 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:Minization -- RooMinimizer::optimizeConst: 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") ;
cut.defineType("accept",1) ;
cut.defineType("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 p.d.f 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 p.d.f 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 p.d.f 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 ;
}
Author
//

Definition in file rf702_efficiencyfit_2D.C.