Rf 1 0 1_Basics

This tutorial illustrates the basic features of RooFit.

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 Saturday, November 28, 2020 at 10:34 AM.

In [1]:
import ROOT
Welcome to JupyROOT 6.23/01

Set up model

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

In [2]:
x = ROOT.RooRealVar("x", "x", -10, 10)
mean = ROOT.RooRealVar("mean", "mean of gaussian", 1, -10, 10)
sigma = ROOT.RooRealVar("sigma", "width of gaussian", 1, 0.1, 10)
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

Build gaussian pdf in terms of x,mean and sigma

In [3]:
gauss = ROOT.RooGaussian("gauss", "gaussian PDF", x, mean, sigma)

Construct plot frame in 'x'

In [4]:
xframe = x.frame(ROOT.RooFit.Title("Gaussian pdf"))  # RooPlot

Plot model and change parameter values

Plot gauss in frame (i.e. in x)

In [5]:
gauss.plotOn(xframe)
Out[5]:
<cppyy.gbl.RooPlot object at 0x669b4e0>

Change the value of sigma to 3

In [6]:
sigma.setVal(3)

Plot gauss in frame (i.e. in x) and draw frame on canvas

In [7]:
gauss.plotOn(xframe, ROOT.RooFit.LineColor(ROOT.kRed))
Out[7]:
<cppyy.gbl.RooPlot object at 0x669b4e0>

Generate events

Generate a dataset of 1000 events in x from gauss

In [8]:
data = gauss.generate(ROOT.RooArgSet(x), 10000)  # ROOT.RooDataSet

Make a second plot frame in x and draw both the data and the pdf in the frame

In [9]:
xframe2 = x.frame(ROOT.RooFit.Title(
    "Gaussian pdf with data"))  # RooPlot
data.plotOn(xframe2)
gauss.plotOn(xframe2)
Out[9]:
<cppyy.gbl.RooPlot object at 0x6b49bf0>

Fit model to data

Fit pdf to data

In [10]:
gauss.fitTo(data)
Out[10]:
<cppyy.gbl.RooFitResult object at 0x(nil)>
[#1] INFO:Minization -- RooMinimizer::optimizeConst: activating const optimization
 **********
 **    1 **SET PRINT           1
 **********
 **********
 **    2 **SET NOGRAD
 **********
 PARAMETER DEFINITIONS:
    NO.   NAME         VALUE      STEP SIZE      LIMITS
     1 mean         1.00000e+00  2.00000e+00   -1.00000e+01  1.00000e+01
     2 sigma        3.00000e+00  9.90000e-01    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        1000           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=25019.2 FROM MIGRAD    STATUS=INITIATE       10 CALLS          11 TOTAL
                     EDM= unknown      STRATEGY= 1      NO ERROR MATRIX       
  EXT PARAMETER               CURRENT GUESS       STEP         FIRST   
  NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE 
   1  mean         1.00000e+00   2.00000e+00   2.02430e-01  -1.99004e+02
   2  sigma        3.00000e+00   9.90000e-01   2.22742e-01   1.98823e+02
                               ERR DEF= 0.5
 MIGRAD MINIMIZATION HAS CONVERGED.
 MIGRAD WILL VERIFY CONVERGENCE AND ERROR MATRIX.
 COVARIANCE MATRIX CALCULATED SUCCESSFULLY
 FCN=25018.5 FROM MIGRAD    STATUS=CONVERGED      32 CALLS          33 TOTAL
                     EDM=5.80039e-07    STRATEGY= 1      ERROR MATRIX ACCURATE 
  EXT PARAMETER                                   STEP         FIRST   
  NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE 
   1  mean         1.01746e+00   3.00149e-02   3.29345e-04  -8.41130e-02
   2  sigma        2.97870e+00   2.19221e-02   5.32112e-04   1.48724e-01
                               ERR DEF= 0.5
 EXTERNAL ERROR MATRIX.    NDIM=  25    NPAR=  2    ERR DEF=0.5
  9.009e-04  1.839e-05 
  1.839e-05  4.806e-04 
 PARAMETER  CORRELATION COEFFICIENTS  
       NO.  GLOBAL      1      2
        1  0.02795   1.000  0.028
        2  0.02795   0.028  1.000
 **********
 **    7 **SET ERR         0.5
 **********
 **********
 **    8 **SET PRINT           1
 **********
 **********
 **    9 **HESSE        1000
 **********
 COVARIANCE MATRIX CALCULATED SUCCESSFULLY
 FCN=25018.5 FROM HESSE     STATUS=OK             10 CALLS          43 TOTAL
                     EDM=5.80381e-07    STRATEGY= 1      ERROR MATRIX ACCURATE 
  EXT PARAMETER                                INTERNAL      INTERNAL  
  NO.   NAME      VALUE            ERROR       STEP SIZE       VALUE   
   1  mean         1.01746e+00   3.00144e-02   6.58691e-05   1.01922e-01
   2  sigma        2.97870e+00   2.19217e-02   2.12845e-05  -4.31732e-01
                               ERR DEF= 0.5
 EXTERNAL ERROR MATRIX.    NDIM=  25    NPAR=  2    ERR DEF=0.5
  9.009e-04  1.792e-05 
  1.792e-05  4.806e-04 
 PARAMETER  CORRELATION COEFFICIENTS  
       NO.  GLOBAL      1      2
        1  0.02723   1.000  0.027
        2  0.02723   0.027  1.000
[#1] INFO:Minization -- RooMinimizer::optimizeConst: deactivating const optimization

Print values of mean and sigma (that now reflect fitted values and errors)

In [11]:
mean.Print()
sigma.Print()
RooRealVar::mean = 1.01746 +/- 0.0300144  L(-10 - 10) 
RooRealVar::sigma = 2.9787 +/- 0.0219217  L(0.1 - 10) 

Draw all frames on a canvas

In [12]:
c = ROOT.TCanvas("rf101_basics", "rf101_basics", 800, 400)
c.Divide(2)
c.cd(1)
ROOT.gPad.SetLeftMargin(0.15)
xframe.GetYaxis().SetTitleOffset(1.6)
xframe.Draw()
c.cd(2)
ROOT.gPad.SetLeftMargin(0.15)
xframe2.GetYaxis().SetTitleOffset(1.6)
xframe2.Draw()

c.SaveAs("rf101_basics.png")
Info in <TCanvas::Print>: png file rf101_basics.png has been created

Draw all canvases

In [13]:
from ROOT import gROOT 
gROOT.GetListOfCanvases().Draw()