Rf 1 0 2_Dataimport

Basic functionality: importing data from ROOT TTrees and THx histograms.

Author: Wouter Verkerke
This notebook tutorial was automatically generated with ROOTBOOK-izer from the macro found in the ROOT repository on Monday, January 17, 2022 at 09:48 AM.

In [1]:
%%cpp -d
#include "RooRealVar.h"
#include "RooDataSet.h"
#include "RooDataHist.h"
#include "RooGaussian.h"
#include "TCanvas.h"
#include "RooPlot.h"
#include "TTree.h"
#include "TH1D.h"
#include "TRandom.h"
In [2]:
%%cpp -d
// This is a workaround to make sure the namespace is used inside functions
using namespace RooFit;
In [3]:
TH1 *makeTH1();
TTree *makeTTree();
input_line_44:2:14: warning: empty parentheses interpreted as a function declaration [-Wvexing-parse]
 TH1 *makeTH1();
             ^~
input_line_44:2:14: note: replace parentheses with an initializer to declare a variable
 TH1 *makeTH1();
             ^~
              = nullptr
input_line_44:3:17: warning: empty parentheses interpreted as a function declaration [-Wvexing-parse]
TTree *makeTTree();
                ^~
input_line_44:3:17: note: replace parentheses with an initializer to declare a variable
TTree *makeTTree();
                ^~
                 = nullptr

Create root th1 filled with a gaussian distribution

Create root ttree filled with a gaussian distribution in x and a uniform distribution in y

A helper function is created:

In [4]:
%%cpp -d
TH1 *makeTH1()
{
   TH1D *hh = new TH1D("hh", "hh", 25, -10, 10);
   for (int i = 0; i < 100; i++) {
      hh->Fill(gRandom->Gaus(0, 3));
   }
   return hh;
}

A helper function is created:

In [5]:
%%cpp -d
TTree *makeTTree()
{
   TTree *tree = new TTree("tree", "tree");
   Double_t *px = new Double_t;
   Double_t *py = new Double_t;
   tree->Branch("x", px, "x/D");
   tree->Branch("y", py, "y/D");
   for (int i = 0; i < 100; i++) {
      *px = gRandom->Gaus(0, 3);
      *py = gRandom->Uniform() * 30 - 15;
      tree->Fill();
   }
   return tree;
}

Importing ROOT histograms

Import th1 into a roodatahist

Create a root th1 histogram

In [6]:
TH1 *hh = makeTH1();

Declare observable x

In [7]:
RooRealVar x("x", "x", -10, 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

Create a binned dataset that imports contents of th1 and associates its contents to observable 'x'

In [8]:
RooDataHist dh("dh", "dh", x, Import(*hh));

Plot and fit a roodatahist

Make plot of binned dataset showing poisson error bars (roofit default)

In [9]:
RooPlot *frame = x.frame(Title("Imported TH1 with Poisson error bars"));
dh.plotOn(frame);

Fit a gaussian pdf to the data

In [10]:
RooRealVar mean("mean", "mean", 0, -10, 10);
RooRealVar sigma("sigma", "sigma", 3, 0.1, 10);
RooGaussian gauss("gauss", "gauss", x, mean, sigma);
gauss.fitTo(dh);
gauss.plotOn(frame);
[#1] INFO:Minimization -- RooAbsMinimizerFcn::setOptimizeConst: activating const optimization
 **********
 **    1 **SET PRINT           1
 **********
 **********
 **    2 **SET NOGRAD
 **********
 PARAMETER DEFINITIONS:
    NO.   NAME         VALUE      STEP SIZE      LIMITS
     1 mean         0.00000e+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=249.349 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  mean         0.00000e+00   2.00000e+00   2.01358e-01   1.15556e+01
   2  sigma        3.00000e+00   9.90000e-01   2.22742e-01   5.42294e+00
                               ERR DEF= 0.5
 MIGRAD MINIMIZATION HAS CONVERGED.
 MIGRAD WILL VERIFY CONVERGENCE AND ERROR MATRIX.
 COVARIANCE MATRIX CALCULATED SUCCESSFULLY
 FCN=249.251 FROM MIGRAD    STATUS=CONVERGED      23 CALLS          24 TOTAL
                     EDM=1.58964e-05    STRATEGY= 1      ERROR MATRIX ACCURATE 
  EXT PARAMETER                                   STEP         FIRST   
  NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE 
   1  mean        -1.05079e-01   2.95122e-01   3.29083e-04  -2.34747e-02
   2  sigma        2.93926e+00   2.13363e-01   5.44955e-04  -8.23858e-02
                               ERR DEF= 0.5
 EXTERNAL ERROR MATRIX.    NDIM=  25    NPAR=  2    ERR DEF=0.5
  8.712e-02 -9.823e-05 
 -9.823e-05  4.556e-02 
 PARAMETER  CORRELATION COEFFICIENTS  
       NO.  GLOBAL      1      2
        1  0.00156   1.000 -0.002
        2  0.00156  -0.002  1.000
 **********
 **    7 **SET ERR         0.5
 **********
 **********
 **    8 **SET PRINT           1
 **********
 **********
 **    9 **HESSE        1000
 **********
 COVARIANCE MATRIX CALCULATED SUCCESSFULLY
 FCN=249.251 FROM HESSE     STATUS=OK             10 CALLS          34 TOTAL
                     EDM=1.58906e-05    STRATEGY= 1      ERROR MATRIX ACCURATE 
  EXT PARAMETER                                INTERNAL      INTERNAL  
  NO.   NAME      VALUE            ERROR       STEP SIZE       VALUE   
   1  mean        -1.05079e-01   2.95122e-01   6.58167e-05  -1.05081e-02
   2  sigma        2.93926e+00   2.13363e-01   1.08991e-04  -4.40523e-01
                               ERR DEF= 0.5
 EXTERNAL ERROR MATRIX.    NDIM=  25    NPAR=  2    ERR DEF=0.5
  8.712e-02 -1.406e-04 
 -1.406e-04  4.556e-02 
 PARAMETER  CORRELATION COEFFICIENTS  
       NO.  GLOBAL      1      2
        1  0.00223   1.000 -0.002
        2  0.00223  -0.002  1.000
[#1] INFO:Minimization -- RooAbsMinimizerFcn::setOptimizeConst: deactivating const optimization

Plot and fit a roodatahist with internal errors

If histogram has custom error (i.e. its contents is does not originate from a poisson process but e.g. is a sum of weighted events) you can data with symmetric 'sum-of-weights' error instead (same error bars as shown by ROOT)

In [11]:
RooPlot *frame2 = x.frame(Title("Imported TH1 with internal errors"));
dh.plotOn(frame2, DataError(RooAbsData::SumW2));
gauss.plotOn(frame2);

Please note that error bars shown (poisson or sumw2) are for visualization only, the are not used in a maximum likelihood fit

A (binned) ML fit will ALWAYS assume the Poisson error interpretation of data (the mathematical definition of likelihood does not take any external definition of errors). Data with non-unit weights can only be correctly fitted with a chi^2 fit (see rf602_chi2fit.C)


Importing ROOT TTrees

Import ttree into a roodataset

In [12]:
TTree *tree = makeTTree();

Define 2nd observable y

In [13]:
RooRealVar y("y", "y", -10, 10);

Construct unbinned dataset importing tree branches x and y matching between branches and roorealvars is done by name of the branch/RRV

Note that ONLY entries for which x,y have values within their allowed ranges as defined in RooRealVar x and y are imported. Since the y values in the import tree are in the range [-15,15] and RRV y defines a range [-10,10] this means that the RooDataSet below will have less entries than the TTree 'tree'

In [14]:
RooDataSet ds("ds", "ds", RooArgSet(x, y), Import(*tree));
[#1] INFO:DataHandling -- RooTreeDataStore::loadValues(ds) Skipping event #0 because y cannot accommodate the value 14.424
[#1] INFO:DataHandling -- RooTreeDataStore::loadValues(ds) Skipping event #3 because y cannot accommodate the value -12.0022
[#1] INFO:DataHandling -- RooTreeDataStore::loadValues(ds) Skipping event #5 because y cannot accommodate the value 13.8261
[#1] INFO:DataHandling -- RooTreeDataStore::loadValues(ds) Skipping event #6 because y cannot accommodate the value -14.9925
[#1] INFO:DataHandling -- RooTreeDataStore::loadValues(ds) Skipping ...
[#0] WARNING:DataHandling -- RooTreeDataStore::loadValues(ds) Ignored 36 out-of-range events

Use ascii import/export for datasets

In [15]:
{
   // Write data to output stream
   std::ofstream outstream("rf102_testData.txt");
   // Optionally, adjust the stream here (e.g. std::setprecision)
   ds.write(outstream);
   outstream.close();
}

Read data from input stream. the variables of the dataset need to be supplied to the RooDataSet::read() function.

In [16]:
std::cout << "\n-----------------------\nReading data from ASCII\n";
RooDataSet *dataReadBack =
   RooDataSet::read("rf102_testData.txt",
                    RooArgList(x, y), // variables to be read. If the file has more fields, these are ignored.
                    "D"); // Prints if a RooFit message stream listens for debug messages. Use Q for quiet.

dataReadBack->Print("V");

std::cout << "\nOriginal data, line 20:\n";
ds.get(20)->Print("V");

std::cout << "\nRead-back data, line 20:\n";
dataReadBack->get(20)->Print("V");
-----------------------
Reading data from ASCII
[#1] INFO:DataHandling -- RooDataSet::read: reading file rf102_testData.txt
[#1] INFO:DataHandling -- RooDataSet::read: read 64 events (ignored 0 out of range events)
DataStore dataset (rf102_testData.txt)
  Contains 64 entries
  Observables: 
    1)           x = 0.0174204  L(-10 - 10)  "x"
    2)           y = 9.46654  L(-10 - 10)  "y"
    3)  blindState = Normal(idx = 0)
  "Blinding State"

Original data, line 20:
  1) RooRealVar:: x = -0.79919
  2) RooRealVar:: y = 0.0106407

Read-back data, line 20:
  1) RooRealVar::          x = -0.79919
  2) RooRealVar::          y = 0.0106407
  3) RooCategory:: blindState = Normal(idx = 0)

Plot datasets with multiple binning choices

Print number of events in dataset

In [17]:
ds.Print();
RooDataSet::ds[x,y] = 64 entries

Print unbinned dataset with default frame binning (100 bins)

In [18]:
RooPlot *frame3 = y.frame(Title("Unbinned data shown in default frame binning"));
ds.plotOn(frame3);
[#0] WARNING:Plotting -- Cannot apply a bin width correction and use Poisson errors. Not correcting for bin width.

Print unbinned dataset with custom binning choice (20 bins)

In [19]:
RooPlot *frame4 = y.frame(Title("Unbinned data shown with custom binning"));
ds.plotOn(frame4, Binning(20));

RooPlot *frame5 = y.frame(Title("Unbinned data read back from ASCII file"));
ds.plotOn(frame5, Binning(20));
dataReadBack->plotOn(frame5, Binning(20), MarkerColor(kRed), MarkerStyle(5));
[#0] WARNING:Plotting -- Cannot apply a bin width correction and use Poisson errors. Not correcting for bin width.
[#0] WARNING:Plotting -- Cannot apply a bin width correction and use Poisson errors. Not correcting for bin width.
[#0] WARNING:Plotting -- Cannot apply a bin width correction and use Poisson errors. Not correcting for bin width.

Draw all frames on a canvas

In [20]:
TCanvas *c = new TCanvas("rf102_dataimport", "rf102_dataimport", 1000, 800);
c->Divide(3, 2);
c->cd(1);
gPad->SetLeftMargin(0.15);
frame->GetYaxis()->SetTitleOffset(1.4);
frame->Draw();
c->cd(2);
gPad->SetLeftMargin(0.15);
frame2->GetYaxis()->SetTitleOffset(1.4);
frame2->Draw();

c->cd(4);
gPad->SetLeftMargin(0.15);
frame3->GetYaxis()->SetTitleOffset(1.4);
frame3->Draw();
c->cd(5);
gPad->SetLeftMargin(0.15);
frame4->GetYaxis()->SetTitleOffset(1.4);
frame4->Draw();
c->cd(6);
gPad->SetLeftMargin(0.15);
frame4->GetYaxis()->SetTitleOffset(1.4);
frame5->Draw();

Draw all canvases

In [21]:
%jsroot on
gROOT->GetListOfCanvases()->Draw()