# rf105_funcbinding¶

'BASIC FUNCTIONALITY' RooFit tutorial macro #105 Demonstration of binding ROOT Math functions as RooFit functions and pdfs

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 Sunday, November 27, 2022 at 11:06 AM.

In [1]:
import ROOT

Welcome to JupyROOT 6.27/01


## Bind ROOT TMath::Erf C function¶

Bind one-dimensional ROOT.TMath.Erf function as ROOT.RooAbsReal function

In [2]:
x = ROOT.RooRealVar("x", "x", -3, 3)
erf = ROOT.RooFit.bindFunction("erf", ROOT.TMath.Erf, x)


Print erf definition

In [3]:
erf.Print()

RooCFunction1Binding<double,double>::erf[ function=TMath::Erf x=x ] = 0


Plot erf on frame

In [4]:
frame1 = x.frame(Title="TMath.Erf bound as ROOT.RooFit function")
erf.plotOn(frame1)

Out[4]:
<cppyy.gbl.RooPlot object at 0x8eaf770>

## Bind ROOT::Math::beta_pdf C function¶

Bind pdf ROOT.Math.Beta with three variables as ROOT.RooAbsPdf function

In [5]:
x2 = ROOT.RooRealVar("x2", "x2", 0, 0.999)
a = ROOT.RooRealVar("a", "a", 5, 0, 10)
b = ROOT.RooRealVar("b", "b", 2, 0, 10)
beta = ROOT.RooFit.bindPdf("beta", ROOT.Math.beta_pdf, x2, a, b)


Perf beta definition

In [6]:
beta.Print()

RooCFunction3PdfBinding<double,double,double,double>::beta[ function=ROOT::Math::beta_pdf x=x2 a=a b=b ] = 0.934689


Generate some events and fit

In [7]:
data = beta.generate({x2}, 10000)
beta.fitTo(data)

Out[7]:
<cppyy.gbl.RooFitResult object at 0x(nil)>
[#1] INFO:NumericIntegration -- RooRealIntegral::init(beta_Int[x2]) using numeric integrator RooIntegrator1D to calculate Int(x2)
[#1] INFO:NumericIntegration -- RooRealIntegral::init(beta_Int[x2]) using numeric integrator RooIntegrator1D to calculate Int(x2)
[#1] INFO:NumericIntegration -- RooRealIntegral::init(beta_Int[x2]) using numeric integrator RooIntegrator1D to calculate Int(x2)
[#1] INFO:Minimization -- RooAbsMinimizerFcn::setOptimizeConst: activating const optimization
**********
**    1 **SET PRINT           1
**********
**********
**********
PARAMETER DEFINITIONS:
NO.   NAME         VALUE      STEP SIZE      LIMITS
1 a            5.00000e+00  1.00000e+00    0.00000e+00  1.00000e+01
2 b            2.00000e+00  1.00000e+00    0.00000e+00  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=-4851.7 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  a            5.00000e+00   1.00000e+00   2.01358e-01  -5.86406e+01
2  b            2.00000e+00   1.00000e+00   2.57889e-01   3.98974e+02
ERR DEF= 0.5
MIGRAD WILL VERIFY CONVERGENCE AND ERROR MATRIX.
COVARIANCE MATRIX CALCULATED SUCCESSFULLY
FCN=-4851.9 FROM MIGRAD    STATUS=CONVERGED      39 CALLS          40 TOTAL
EDM=4.45661e-07    STRATEGY= 1      ERROR MATRIX ACCURATE
EXT PARAMETER                                   STEP         FIRST
NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE
1  a            4.99036e+00   7.12139e-02   3.69873e-04   8.65173e-02
2  b            1.98812e+00   2.63908e-02   1.71677e-04  -1.47761e-01
ERR DEF= 0.5
EXTERNAL ERROR MATRIX.    NDIM=  25    NPAR=  2    ERR DEF=0.5
5.072e-03  1.582e-03
1.582e-03  6.965e-04
PARAMETER  CORRELATION COEFFICIENTS
NO.  GLOBAL      1      2
1  0.84198   1.000  0.842
2  0.84198   0.842  1.000
**********
**    7 **SET ERR         0.5
**********
**********
**    8 **SET PRINT           1
**********
**********
**    9 **HESSE        1000
**********
COVARIANCE MATRIX CALCULATED SUCCESSFULLY
FCN=-4851.9 FROM HESSE     STATUS=OK             10 CALLS          50 TOTAL
EDM=4.46009e-07    STRATEGY= 1      ERROR MATRIX ACCURATE
EXT PARAMETER                                INTERNAL      INTERNAL
NO.   NAME      VALUE            ERROR       STEP SIZE       VALUE
1  a            4.99036e+00   7.12317e-02   7.39745e-05  -1.92762e-03
2  b            1.98812e+00   2.63974e-02   3.43355e-05  -6.46475e-01
ERR DEF= 0.5
EXTERNAL ERROR MATRIX.    NDIM=  25    NPAR=  2    ERR DEF=0.5
5.074e-03  1.583e-03
1.583e-03  6.968e-04
PARAMETER  CORRELATION COEFFICIENTS
NO.  GLOBAL      1      2
1  0.84207   1.000  0.842
2  0.84207   0.842  1.000
[#1] INFO:Minimization -- RooAbsMinimizerFcn::setOptimizeConst: deactivating const optimization


Plot data and pdf on frame

In [8]:
frame2 = x2.frame(Title="ROOT.Math.Beta bound as ROOT.RooFit pdf")
data.plotOn(frame2)
beta.plotOn(frame2)

Out[8]:
<cppyy.gbl.RooPlot object at 0x96c6d10>
[#1] INFO:NumericIntegration -- RooRealIntegral::init(beta_Int[x2]) using numeric integrator RooIntegrator1D to calculate Int(x2)


## Bind ROOT TF1 as RooFit function¶

Create a ROOT TF1 function

In [9]:
fa1 = ROOT.TF1("fa1", "sin(x)/x", 0, 10)


Create an observable

In [10]:
x3 = ROOT.RooRealVar("x3", "x3", 0.01, 20)


Create binding of TF1 object to above observable

In [11]:
rfa1 = ROOT.RooFit.bindFunction(fa1, x3)


Print rfa1 definition

In [12]:
rfa1.Print()

RooTFnBinding::fa1[ TFn={fa1=sin(x)/x} obs=(x3) ] = -0.0547936


Make plot frame in observable, TF1 binding function

In [13]:
frame3 = x3.frame(Title="TF1 bound as ROOT.RooFit function")
rfa1.plotOn(frame3)

c = ROOT.TCanvas("rf105_funcbinding", "rf105_funcbinding", 1200, 400)
c.Divide(3)
c.cd(1)
frame1.GetYaxis().SetTitleOffset(1.6)
frame1.Draw()
c.cd(2)
frame2.GetYaxis().SetTitleOffset(1.6)
frame2.Draw()
c.cd(3)
frame3.GetYaxis().SetTitleOffset(1.6)
frame3.Draw()

c.SaveAs("rf105_funcbinding.png")

Info in <TCanvas::Print>: png file rf105_funcbinding.png has been created


Draw all canvases

In [14]:
from ROOT import gROOT
gROOT.GetListOfCanvases().Draw()