Rf 2 1 0_Angularconv¶

Convolution in cyclical angular observables theta, and construction of p.d.f in terms of trasnformed angular coordinates, e.g. cos(theta), the convolution is performed in theta rather than cos(theta)

(require ROOT to be compiled with --enable-fftw3)

pdf(theta) = ROOT.T(theta) (x) gauss(theta) pdf(cosTheta) = ROOT.T(acos(cosTheta)) (x) gauss(acos(cosTheta))

Author: Wouter Verkerke (C version)
This notebook tutorial was automatically generated with ROOTBOOK-izer from the macro found in the ROOT repository on Monday, January 17, 2022 at 09:56 AM.

In [ ]:
import ROOT

Set up component pdfs¶

Define angle psi

In [ ]:
psi = ROOT.RooRealVar("psi", "psi", 0, 3.14159268)

Define physics p.d.f T(psi)

In [ ]:
Tpsi = ROOT.RooGenericPdf("Tpsi", "1+sin(2*@0)", [psi])

Define resolution R(psi)

In [ ]:
gbias = ROOT.RooRealVar("gbias", "gbias", 0.2, 0.0, 1)
greso = ROOT.RooRealVar("greso", "greso", 0.3, 0.1, 1.0)
Rpsi = ROOT.RooGaussian("Rpsi", "Rpsi", psi, gbias, greso)

Define cos(psi) and function psif that calculates psi from cos(psi)

In [ ]:
cpsi = ROOT.RooRealVar("cpsi", "cos(psi)", -1, 1)
psif = ROOT.RooFormulaVar("psif", "acos(cpsi)", [cpsi])

Define physics p.d.f. also as function of cos(psi): T(psif(cpsi)) = T(cpsi)

In [ ]:
Tcpsi = ROOT.RooGenericPdf("T", "1+sin(2*@0)", [psif])

Construct convolution pdf in psi¶

Define convoluted p.d.f. as function of psi: M=T(x)R = M(psi)

In [ ]:
Mpsi = ROOT.RooFFTConvPdf("Mf", "Mf", psi, Tpsi, Rpsi)

Set the buffer fraction to zero to obtain a ROOT.True cyclical convolution

In [ ]:
Mpsi.setBufferFraction(0)

Sample, fit and plot convoluted pdf (psi)¶

Generate some events in observable psi

In [ ]:
data_psi = Mpsi.generate({psi}, 10000)

Fit convoluted model as function of angle psi

In [ ]:
Mpsi.fitTo(data_psi)

Plot cos(psi) frame with Mf(cpsi)

In [ ]:
frame1 = psi.frame(Title="Cyclical convolution in angle psi")
data_psi.plotOn(frame1)
Mpsi.plotOn(frame1)

Overlay comparison to unsmeared physics p.d.f ROOT.T(psi)

In [ ]:
Tpsi.plotOn(frame1, LineColor="r")

Construct convolution pdf in cos(psi)¶

Define convoluted p.d.f. as function of cos(psi): M=T(x)R) = M(cpsi:

Need to give both observable psi here (for definition of convolution) and function psif here (for definition of observables, in cpsi)

In [ ]:
Mcpsi = ROOT.RooFFTConvPdf("Mf", "Mf", psif, psi, Tpsi, Rpsi)

Set the buffer fraction to zero to obtain a ROOT.True cyclical convolution

In [ ]:
Mcpsi.setBufferFraction(0)

Sample, fit and plot convoluted pdf (cospsi)¶

Generate some events

In [ ]:
data_cpsi = Mcpsi.generate({cpsi}, 10000)

set psi constant to exclude to be a parameter of the fit

In [ ]:
psi.setConstant(True)

Fit convoluted model as function of cos(psi)

In [ ]:
Mcpsi.fitTo(data_cpsi)

Plot cos(psi) frame with Mf(cpsi)

In [ ]:
frame2 = cpsi.frame(Title="Same convolution in psi, in cos(psi)")
data_cpsi.plotOn(frame2)
Mcpsi.plotOn(frame2)

Overlay comparison to unsmeared physics p.d.f ROOT.Tf(cpsi)

In [ ]:
Tcpsi.plotOn(frame2, LineColor="r")

Draw frame on canvas

In [ ]:
c = ROOT.TCanvas("rf210_angularconv", "rf210_angularconv", 800, 400)
c.Divide(2)
c.cd(1)
frame1.GetYaxis().SetTitleOffset(1.4)
frame1.Draw()
c.cd(2)