Rf 1 0 3_Interprfuncs

Basic functionality: interpreted functions and PDFs.

Author: Wouter Verkerke
This notebook tutorial was automatically generated with ROOTBOOK-izer from the macro found in the ROOT repository on Wednesday, January 19, 2022 at 10:08 AM.

In [1]:
%%cpp -d
#include "RooRealVar.h"
#include "RooDataSet.h"
#include "RooGaussian.h"
#include "TCanvas.h"
#include "TAxis.h"
#include "RooPlot.h"
#include "RooFitResult.h"
#include "RooGenericPdf.h"
#include "RooConstVar.h"
In [2]:
%%cpp -d
// This is a workaround to make sure the namespace is used inside functions
using namespace RooFit;

Generic interpreted p.d.f.

Declare observable x

In [3]:
RooRealVar x("x", "x", -20, 20);
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

Construct generic pdf from interpreted expression

To construct a proper pdf, the formula expression is explicitly normalized internally by dividing it by a numeric integral of the expression over x in the range [-20,20]

In [4]:
RooRealVar alpha("alpha", "alpha", 5, 0.1, 10);
RooGenericPdf genpdf("genpdf", "genpdf", "(1+0.1*abs(x)+sin(sqrt(abs(x*alpha+0.1))))", RooArgSet(x, alpha));

Sample, fit and plot generic pdf

Generate a toy dataset from the interpreted pdf

In [5]:
RooDataSet *data = genpdf.generate(x, 10000);
[#1] INFO:NumericIntegration -- RooRealIntegral::init(genpdf_Int[x]) using numeric integrator RooIntegrator1D to calculate Int(x)
[#1] INFO:NumericIntegration -- RooRealIntegral::init(genpdf_Int[x]) using numeric integrator RooIntegrator1D to calculate Int(x)

Fit the interpreted pdf to the generated data

In [6]:
genpdf.fitTo(*data);
input_line_59:2:16: error: reference to 'data' is ambiguous
 genpdf.fitTo(*data);
               ^
input_line_58:2:14: note: candidate found by name lookup is '__cling_N523::data'
 RooDataSet *data = genpdf.generate(x, 10000);
             ^
/usr/include/c++/9/bits/range_access.h:318:5: note: candidate found by name lookup is 'std::data'
    data(initializer_list<_Tp> __il) noexcept
    ^
/usr/include/c++/9/bits/range_access.h:289:5: note: candidate found by name lookup is 'std::data'
    data(_Container& __cont) noexcept(noexcept(__cont.data()))
    ^
/usr/include/c++/9/bits/range_access.h:299:5: note: candidate found by name lookup is 'std::data'
    data(const _Container& __cont) noexcept(noexcept(__cont.data()))
    ^
/usr/include/c++/9/bits/range_access.h:309:5: note: candidate found by name lookup is 'std::data'
    data(_Tp (&__array)[_Nm]) noexcept
    ^

Make a plot of the data and the pdf overlaid

In [7]:
RooPlot *xframe = x.frame(Title("Interpreted expression pdf"));
data->plotOn(xframe);
genpdf.plotOn(xframe);
input_line_60:3:1: error: reference to 'data' is ambiguous
data->plotOn(xframe);
^
input_line_58:2:14: note: candidate found by name lookup is '__cling_N523::data'
 RooDataSet *data = genpdf.generate(x, 10000);
             ^
/usr/include/c++/9/bits/range_access.h:318:5: note: candidate found by name lookup is 'std::data'
    data(initializer_list<_Tp> __il) noexcept
    ^
/usr/include/c++/9/bits/range_access.h:289:5: note: candidate found by name lookup is 'std::data'
    data(_Container& __cont) noexcept(noexcept(__cont.data()))
    ^
/usr/include/c++/9/bits/range_access.h:299:5: note: candidate found by name lookup is 'std::data'
    data(const _Container& __cont) noexcept(noexcept(__cont.data()))
    ^
/usr/include/c++/9/bits/range_access.h:309:5: note: candidate found by name lookup is 'std::data'
    data(_Tp (&__array)[_Nm]) noexcept
    ^

Standard p.d.f adjust with interpreted helper function

Make a gauss(x,sqrt(mean2),sigma) from a standard RooGaussian

Construct standard pdf with formula replacing parameter

Construct parameter mean2 and sigma

In [8]:
RooRealVar mean2("mean2", "mean^2", 10, 0, 200);
RooRealVar sigma("sigma", "sigma", 3, 0.1, 10);

Construct interpreted function mean = sqrt(mean^2)

In [9]:
RooFormulaVar mean("mean", "mean", "sqrt(mean2)", mean2);

Construct a gaussian g2(x,sqrt(mean2),sigma) ;

In [10]:
RooGaussian g2("g2", "h2", x, mean, sigma);

Generate toy data

Construct a separate gaussian g1(x,10,3) to generate a toy gaussian dataset with mean 10 and width 3

In [11]:
RooGaussian g1("g1", "g1", x, RooConst(10), RooConst(3));
RooDataSet *data2 = g1.generate(x, 1000);

Fit and plot tailored standard pdf

Fit g2 to data from g1

In [12]:
RooFitResult *r = g2.fitTo(*data2, Save());
r->Print();
[#1] INFO:Minimization -- RooAbsMinimizerFcn::setOptimizeConst: activating const optimization
 **********
 **    1 **SET PRINT           1
 **********
 **********
 **    2 **SET NOGRAD
 **********
 PARAMETER DEFINITIONS:
    NO.   NAME         VALUE      STEP SIZE      LIMITS
     1 mean2        1.00000e+01  5.00000e+00    0.00000e+00  2.00000e+02
     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=5148.93 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  mean2        1.00000e+01   5.00000e+00   1.18625e-01  -5.23438e+03
   2  sigma        3.00000e+00   9.90000e-01   2.22742e-01  -7.90389e+03
                               ERR DEF= 0.5
 MIGRAD MINIMIZATION HAS CONVERGED.
 MIGRAD WILL VERIFY CONVERGENCE AND ERROR MATRIX.
 COVARIANCE MATRIX CALCULATED SUCCESSFULLY
 FCN=2551.39 FROM MIGRAD    STATUS=CONVERGED      59 CALLS          60 TOTAL
                     EDM=8.7852e-06    STRATEGY= 1      ERROR MATRIX ACCURATE 
  EXT PARAMETER                                   STEP         FIRST   
  NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE 
   1  mean2        1.00100e+02   1.98019e+00   6.89576e-04   4.58015e-02
   2  sigma        3.11719e+00   7.12427e-02   5.29831e-04   1.79331e-01
                               ERR DEF= 0.5
 EXTERNAL ERROR MATRIX.    NDIM=  25    NPAR=  2    ERR DEF=0.5
  3.922e+00  2.826e-03 
  2.826e-03  5.076e-03 
 PARAMETER  CORRELATION COEFFICIENTS  
       NO.  GLOBAL      1      2
        1  0.02003   1.000  0.020
        2  0.02003   0.020  1.000
 **********
 **    7 **SET ERR         0.5
 **********
 **********
 **    8 **SET PRINT           1
 **********
 **********
 **    9 **HESSE        1000
 **********
 COVARIANCE MATRIX CALCULATED SUCCESSFULLY
 FCN=2551.39 FROM HESSE     STATUS=OK             10 CALLS          70 TOTAL
                     EDM=8.78617e-06    STRATEGY= 1      ERROR MATRIX ACCURATE 
  EXT PARAMETER                                INTERNAL      INTERNAL  
  NO.   NAME      VALUE            ERROR       STEP SIZE       VALUE   
   1  mean2        1.00100e+02   1.98016e+00   1.37915e-04   1.00004e-03
   2  sigma        3.11719e+00   7.12418e-02   1.05966e-04  -4.01138e-01
                               ERR DEF= 0.5
 EXTERNAL ERROR MATRIX.    NDIM=  25    NPAR=  2    ERR DEF=0.5
  3.922e+00  2.730e-03 
  2.730e-03  5.076e-03 
 PARAMETER  CORRELATION COEFFICIENTS  
       NO.  GLOBAL      1      2
        1  0.01935   1.000  0.019
        2  0.01935   0.019  1.000
[#1] INFO:Minimization -- RooAbsMinimizerFcn::setOptimizeConst: deactivating const optimization

  RooFitResult: minimized FCN value: 2551.39, estimated distance to minimum: 8.78617e-06
                covariance matrix quality: Full, accurate covariance matrix
                Status : MINIMIZE=0 HESSE=0 

    Floating Parameter    FinalValue +/-  Error   
  --------------------  --------------------------
                 mean2    1.0010e+02 +/-  1.98e+00
                 sigma    3.1172e+00 +/-  7.12e-02

Plot data on frame and overlay projection of g2

In [13]:
RooPlot *xframe2 = x.frame(Title("Tailored Gaussian pdf"));
data2->plotOn(xframe2);
g2.plotOn(xframe2);
[#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 [14]:
TCanvas *c = new TCanvas("rf103_interprfuncs", "rf103_interprfuncs", 800, 400);
c->Divide(2);
c->cd(1);
gPad->SetLeftMargin(0.15);
xframe->GetYaxis()->SetTitleOffset(1.4);
xframe->Draw();
c->cd(2);
gPad->SetLeftMargin(0.15);
xframe2->GetYaxis()->SetTitleOffset(1.4);
xframe2->Draw();
input_line_90:2:3: error: use of undeclared identifier 'xframe'
 (xframe->GetYaxis()->SetTitleOffset(1.3999999999999999))
  ^
Error in <HandleInterpreterException>: Error evaluating expression (xframe->GetYaxis()->SetTitleOffset(1.3999999999999999))
Execution of your code was aborted.

Draw all canvases

In [15]:
%jsroot on
gROOT->GetListOfCanvases()->Draw()