rf306_condpereventerrors.py

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## \file
## \ingroup tutorial_roofit
## \notebook
## Multidimensional models: complete example with use of conditional p.d.f. with per-event errors
##
## \macro_code
##
## \date February 2018
## \author Clemens Lange, Wouter Verkerke (C++ version)
 
import ROOT
 
# B-physics pdf with per-event Gaussian resolution
# ----------------------------------------------------------------------------------------------
 
# Observables
dt = ROOT.RooRealVar("dt", "dt", -10, 10)
dterr = ROOT.RooRealVar("dterr", "per-event error on dt", 0.01, 10)
 
# Build a gaussian resolution model scaled by the per-error =
# gauss(dt,bias,sigma*dterr)
bias = ROOT.RooRealVar("bias", "bias", 0, -10, 10)
sigma = ROOT.RooRealVar(
    "sigma", "per-event error scale factor", 1, 0.1, 10)
gm = ROOT.RooGaussModel(
    "gm1", "gauss model scaled bt per-event error", dt, bias, sigma, dterr)
 
# Construct decay(dt) (x) gauss1(dt|dterr)
tau = ROOT.RooRealVar("tau", "tau", 1.548)
decay_gm = ROOT.RooDecay("decay_gm", "decay", dt,
                         tau, gm, ROOT.RooDecay.DoubleSided)
 
# Construct fake 'external' data with per-event error
# ------------------------------------------------------------------------------------------------------
 
# Use landau p.d.f to get somewhat realistic distribution with long tail
pdfDtErr = ROOT.RooLandau("pdfDtErr", "pdfDtErr", dterr, ROOT.RooFit.RooConst(
    1), ROOT.RooFit.RooConst(0.25))
expDataDterr = pdfDtErr.generate(ROOT.RooArgSet(dterr), 10000)
 
# Sample data from conditional decay_gm(dt|dterr)
# ---------------------------------------------------------------------------------------------
 
# Specify external dataset with dterr values to use decay_dm as
# conditional p.d.f.
data = decay_gm.generate(ROOT.RooArgSet(
    dt), ROOT.RooFit.ProtoData(expDataDterr))
 
# Fit conditional decay_dm(dt|dterr)
# ---------------------------------------------------------------------
 
# Specify dterr as conditional observable
decay_gm.fitTo(data, ROOT.RooFit.ConditionalObservables(
    ROOT.RooArgSet(dterr)))
 
# Plot conditional decay_dm(dt|dterr)
# ---------------------------------------------------------------------
 
# Make two-dimensional plot of conditional p.d.f in (dt,dterr)
hh_decay = decay_gm.createHistogram("hh_decay", dt, ROOT.RooFit.Binning(
    50), ROOT.RooFit.YVar(dterr, ROOT.RooFit.Binning(50)))
hh_decay.SetLineColor(ROOT.kBlue)
 
# Plot decay_gm(dt|dterr) at various values of dterr
frame = dt.frame(ROOT.RooFit.Title(
    "Slices of decay(dt|dterr) at various dterr"))
for ibin in range(0, 100, 20):
    dterr.setBin(ibin)
    decay_gm.plotOn(frame, ROOT.RooFit.Normalization(5.))
 
# Make projection of data an dt
frame2 = dt.frame(ROOT.RooFit.Title("Projection of decay(dt|dterr) on dt"))
data.plotOn(frame2)
 
# Make projection of decay(dt|dterr) on dt.
#
# Instead of integrating out dterr, a weighted average of curves
# at values dterr_i as given in the external dataset.
# (The kTRUE argument bins the data before projection to speed up the process)
decay_gm.plotOn(frame2, ROOT.RooFit.ProjWData(expDataDterr, ROOT.kTRUE))
 
# Draw all frames on canvas
c = ROOT.TCanvas("rf306_condpereventerrors",
                 "rf306_condperventerrors", 1200, 400)
c.Divide(3)
c.cd(1)
ROOT.gPad.SetLeftMargin(0.20)
hh_decay.GetZaxis().SetTitleOffset(2.5)
hh_decay.Draw("surf")
c.cd(2)
ROOT.gPad.SetLeftMargin(0.15)
frame.GetYaxis().SetTitleOffset(1.6)
frame.Draw()
c.cd(3)
ROOT.gPad.SetLeftMargin(0.15)
frame2.GetYaxis().SetTitleOffset(1.6)
frame2.Draw()
 
c.SaveAs("rf306_condpereventerrors.png")