Rf 7 0 4_Amplitudefit

Special pdf's: using a pdf defined by a sum of real-valued amplitude components

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 Wednesday, January 19, 2022 at 10:35 AM.

In [ ]:
import ROOT

Setup 2D amplitude functions

Observables

In [ ]:
t = ROOT.RooRealVar("t", "time", -1.0, 15.0)
cosa = ROOT.RooRealVar("cosa", "cos(alpha)", -1.0, 1.0)

Use ROOT.RooTruthModel to obtain compiled implementation of sinh/cosh modulated decay functions

In [ ]:
tau = ROOT.RooRealVar("tau", "#tau", 1.5)
deltaGamma = ROOT.RooRealVar("deltaGamma", "deltaGamma", 0.3)
tm = ROOT.RooTruthModel("tm", "tm", t)
coshGBasis = ROOT.RooFormulaVar("coshGBasis", "exp([email protected]/ @1)*cosh(@0*@2/2)", [t, tau, deltaGamma])
sinhGBasis = ROOT.RooFormulaVar("sinhGBasis", "exp([email protected]/ @1)*sinh(@0*@2/2)", [t, tau, deltaGamma])
coshGConv = tm.convolution(coshGBasis, t)
sinhGConv = tm.convolution(sinhGBasis, t)

Construct polynomial amplitudes in cos(a)

In [ ]:
poly1 = ROOT.RooPolyVar("poly1", "poly1", cosa, [0.5, 0.2, 0.2], 0)
poly2 = ROOT.RooPolyVar("poly2", "poly2", cosa, [1.0, -0.2, 3.0], 0)

Construct 2D amplitude as uncorrelated product of amp(t)*amp(cosa)

In [ ]:
ampl1 = ROOT.RooProduct("ampl1", "amplitude 1", [poly1, coshGConv])
ampl2 = ROOT.RooProduct("ampl2", "amplitude 2", [poly2, sinhGConv])

Construct amplitude sum pdf

Amplitude strengths

In [ ]:
f1 = ROOT.RooRealVar("f1", "f1", 1, 0, 2)
f2 = ROOT.RooRealVar("f2", "f2", 0.5, 0, 2)

Construct pdf

In [ ]:
pdf = ROOT.RooRealSumPdf("pdf", "pdf", [ampl1, ampl2], [f1, f2])

Generate some toy data from pdf

In [ ]:
data = pdf.generate({t, cosa}, 10000)

Fit pdf to toy data with only amplitude strength floating

In [ ]:
pdf.fitTo(data)

Plot amplitude sum pdf

Make 2D plots of amplitudes

In [ ]:
hh_cos = ampl1.createHistogram("hh_cos", t, Binning=50, YVar=dict(var=cosa, Binning=50))
hh_sin = ampl2.createHistogram("hh_sin", t, Binning=50, YVar=dict(var=cosa, Binning=50))
hh_cos.SetLineColor(ROOT.kBlue)
hh_sin.SetLineColor(ROOT.kRed)

Make projection on t, data, and its components Note component projections may be larger than sum because amplitudes can be negative

In [ ]:
frame1 = t.frame()
data.plotOn(frame1)
pdf.plotOn(frame1)
pdf.plotOn(frame1, Components=ampl1, LineStyle="--")
pdf.plotOn(frame1, Components=ampl2, LineStyle="--", LineColor="r")

Make projection on cosa, data, and its components Note that components projection may be larger than sum because amplitudes can be negative

In [ ]:
frame2 = cosa.frame()
data.plotOn(frame2)
pdf.plotOn(frame2)
pdf.plotOn(frame2, Components=ampl1, LineStyle="--")
pdf.plotOn(frame2, Components=ampl2, LineStyle="--", LineColor="r")

c = ROOT.TCanvas("rf704_amplitudefit", "rf704_amplitudefit", 800, 800)
c.Divide(2, 2)
c.cd(1)
ROOT.gPad.SetLeftMargin(0.15)
frame1.GetYaxis().SetTitleOffset(1.4)
frame1.Draw()
c.cd(2)
ROOT.gPad.SetLeftMargin(0.15)
frame2.GetYaxis().SetTitleOffset(1.4)
frame2.Draw()
c.cd(3)
ROOT.gPad.SetLeftMargin(0.20)
hh_cos.GetZaxis().SetTitleOffset(2.3)
hh_cos.Draw("surf")
c.cd(4)
ROOT.gPad.SetLeftMargin(0.20)
hh_sin.GetZaxis().SetTitleOffset(2.3)
hh_sin.Draw("surf")

c.SaveAs("rf704_amplitudefit.png")

Draw all canvases

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