rf704_amplitudefit.py

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## \file
## \ingroup tutorial_roofit
## \notebook
## Special pdf's: using a pdf defined by a sum of real-valued amplitude components
##
## \macro_image
## \macro_code
## \macro_output
##
## \date February 2018
## \authors Clemens Lange, Wouter Verkerke (C++ version)
 
import ROOT
 
 
# Setup 2D amplitude functions
# -------------------------------------------------------
 
# Observables
t = ROOT.RooRealVar("t", "time", -1.0, 15.0)
cosa = ROOT.RooRealVar("cosa", "cos(alpha)", -1.0, 1.0)
 
tau = ROOT.RooRealVar("tau", "#tau", 1.5)
deltaGamma = ROOT.RooRealVar("deltaGamma", "deltaGamma", 0.3)
coshG = ROOT.RooFormulaVar("coshGBasis", "exp(-@0/ @1)*cosh(@0*@2/2)", [t, tau, deltaGamma])
sinhG = ROOT.RooFormulaVar("sinhGBasis", "exp(-@0/ @1)*sinh(@0*@2/2)", [t, tau, deltaGamma])
 
# Construct polynomial amplitudes in cos(a)
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)
ampl1 = ROOT.RooProduct("ampl1", "amplitude 1", [poly1, coshG])
ampl2 = ROOT.RooProduct("ampl2", "amplitude 2", [poly2, sinhG])
 
# Construct amplitude sum pdf
# -----------------------------------------------------
 
# Amplitude strengths
f1 = ROOT.RooRealVar("f1", "f1", 1, 0, 2)
f2 = ROOT.RooRealVar("f2", "f2", 0.5, 0, 2)
 
# Construct pdf
pdf = ROOT.RooRealSumPdf("pdf", "pdf", [ampl1, ampl2], [f1, f2])
 
# Generate some toy data from pdf
data = pdf.generate({t, cosa}, 10000)
 
# Fit pdf to toy data with only amplitude strength floating
pdf.fitTo(data, PrintLevel=-1)
 
# Plot amplitude sum pdf
# -------------------------------------------
 
# Make 2D plots of amplitudes
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
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
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")