# rf701_efficiencyfit¶

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, which the efficiency as function of x should be described by eff(x)

Author: Clemens Lange, Wouter Verkerke (C++ version)
This notebook tutorial was automatically generated with ROOTBOOK-izer from the macro found in the ROOT repository on Wednesday, November 30, 2022 at 11:24 AM.

In [1]:
import ROOT

Welcome to JupyROOT 6.27/01


## Construct efficiency function e(x)¶

Declare variables x,mean, with associated name, title, value and allowed range

In [2]:
x = ROOT.RooRealVar("x", "x", -10, 10)


Efficiency function eff(x;a,b)

In [3]:
a = ROOT.RooRealVar("a", "a", 0.4, 0, 1)
b = ROOT.RooRealVar("b", "b", 5)
c = ROOT.RooRealVar("c", "c", -1, -10, 10)
effFunc = ROOT.RooFormulaVar("effFunc", "(1-a)+a*cos((x-c)/b)", [a, b, c, x])


## Construct conditional efficiency pdf E(cut|x)¶

Acceptance state cut (1 or 0)

In [4]:
cut = ROOT.RooCategory("cut", "cutr", {"accept": 1, "reject": 0})


Construct efficiency pdf eff(cut|x)

In [5]:
effPdf = ROOT.RooEfficiency("effPdf", "effPdf", effFunc, cut, "accept")


## Generate data (x, cut) from a toy model¶

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)

In [6]:
shapePdf = ROOT.RooPolynomial("shapePdf", "shapePdf", x, [-0.095])
model = ROOT.RooProdPdf("model", "model", {shapePdf}, Conditional=({effPdf}, {cut}))


Generate some toy data from model

In [7]:
data = model.generate({x, cut}, 10000)


## Fit conditional efficiency pdf to data¶

Fit conditional efficiency pdf to data

In [8]:
effPdf.fitTo(data, ConditionalObservables={x})

Out[8]:
<cppyy.gbl.RooFitResult object at 0x(nil)>
[#1] INFO:Minimization -- RooAbsMinimizerFcn::setOptimizeConst: activating const optimization
**********
**    1 **SET PRINT           1
**********
**********
**********
PARAMETER DEFINITIONS:
NO.   NAME         VALUE      STEP SIZE      LIMITS
1 a            4.00000e-01  1.00000e-01    0.00000e+00  1.00000e+00
2 c           -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
**********
**********
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=3887.11 FROM MIGRAD    STATUS=INITIATE        8 CALLS           9 TOTAL
EDM= unknown      STRATEGY= 1      NO ERROR MATRIX
EXT PARAMETER               CURRENT GUESS       STEP         FIRST
NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE
1  a            4.00000e-01   1.00000e-01   2.05758e-01   8.51804e+01
2  c           -1.00000e+00   2.00000e+00   2.02430e-01   7.00873e+01
ERR DEF= 0.5
MIGRAD WILL VERIFY CONVERGENCE AND ERROR MATRIX.
COVARIANCE MATRIX CALCULATED SUCCESSFULLY
FCN=3886.26 FROM MIGRAD    STATUS=CONVERGED      30 CALLS          31 TOTAL
EDM=2.277e-05    STRATEGY= 1      ERROR MATRIX ACCURATE
EXT PARAMETER                                   STEP         FIRST
NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE
1  a            3.89817e-01   8.14984e-03   6.58343e-04  -2.65715e-01
2  c           -9.91750e-01   6.56208e-02   2.58326e-04  -6.57933e-01
ERR DEF= 0.5
EXTERNAL ERROR MATRIX.    NDIM=  25    NPAR=  2    ERR DEF=0.5
6.643e-05 -2.189e-04
-2.189e-04  4.306e-03
PARAMETER  CORRELATION COEFFICIENTS
NO.  GLOBAL      1      2
1  0.40934   1.000 -0.409
2  0.40934  -0.409  1.000
**********
**    7 **SET ERR         0.5
**********
**********
**    8 **SET PRINT           1
**********
**********
**    9 **HESSE        1000
**********
COVARIANCE MATRIX CALCULATED SUCCESSFULLY
FCN=3886.26 FROM HESSE     STATUS=OK             10 CALLS          41 TOTAL
EDM=2.27764e-05    STRATEGY= 1      ERROR MATRIX ACCURATE
EXT PARAMETER                                INTERNAL      INTERNAL
NO.   NAME      VALUE            ERROR       STEP SIZE       VALUE
1  a            3.89817e-01   8.14814e-03   1.31669e-04  -2.22191e-01
2  c           -9.91750e-01   6.56071e-02   5.16653e-05  -9.93383e-02
ERR DEF= 0.5
EXTERNAL ERROR MATRIX.    NDIM=  25    NPAR=  2    ERR DEF=0.5
6.640e-05 -2.186e-04
-2.186e-04  4.304e-03
PARAMETER  CORRELATION COEFFICIENTS
NO.  GLOBAL      1      2
1  0.40891   1.000 -0.409
2  0.40891  -0.409  1.000
[#1] INFO:Minimization -- RooAbsMinimizerFcn::setOptimizeConst: deactivating const optimization


## Plot fitted, data efficiency¶

Plot distribution of all events and accepted fraction of events on frame

In [9]:
frame1 = x.frame(Bins=20, Title="Data (all, accepted)")
data.plotOn(frame1)
data.plotOn(frame1, Cut="cut==cut::accept", MarkerColor="r", LineColor="r")

Out[9]:
<cppyy.gbl.RooPlot object at 0xa32e980>
[#1] INFO:Plotting -- RooTreeData::plotOn: plotting 8176 events out of 10000 total events


Plot accept/reject efficiency on data overlay fitted efficiency curve

In [10]:
frame2 = x.frame(Bins=20, Title="Fitted efficiency")
data.plotOn(frame2, Efficiency=cut)  # needs ROOT version >= 5.21
effFunc.plotOn(frame2, LineColor="r")

Out[10]:
<cppyy.gbl.RooPlot object at 0xa45a120>

Draw all frames on a canvas

In [11]:
ca = ROOT.TCanvas("rf701_efficiency", "rf701_efficiency", 800, 400)
ca.Divide(2)
ca.cd(1)
frame1.GetYaxis().SetTitleOffset(1.6)
frame1.Draw()
ca.cd(2)
frame2.GetYaxis().SetTitleOffset(1.4)
frame2.Draw()

ca.SaveAs("rf701_efficiencyfit.png")

Info in <TCanvas::Print>: png file rf701_efficiencyfit.png has been created


Draw all canvases

In [12]:
from ROOT import gROOT
gROOT.GetListOfCanvases().Draw()