doc/v622/rf202__extendedmlfit_8py.html

import ROOT


# Set up component pdfs

# ---------------------------------------


# Declare observable x

x = ROOT.RooRealVar("x", "x", 0, 10)


# Create two Gaussian PDFs g1(x,mean1,sigma) anf g2(x,mean2,sigma) and

# their parameters

mean = ROOT.RooRealVar("mean", "mean of gaussians", 5)

sigma1 = ROOT.RooRealVar("sigma1", "width of gaussians", 0.5)

sigma2 = ROOT.RooRealVar("sigma2", "width of gaussians", 1)


sig1 = ROOT.RooGaussian("sig1", "Signal component 1", x, mean, sigma1)

sig2 = ROOT.RooGaussian("sig2", "Signal component 2", x, mean, sigma2)


# Build Chebychev polynomial p.d.f.

a0 = ROOT.RooRealVar("a0", "a0", 0.5, 0., 1.)

a1 = ROOT.RooRealVar("a1", "a1", -0.2, 0., 1.)

bkg = ROOT.RooChebychev("bkg", "Background", x, ROOT.RooArgList(a0, a1))


# Sum the signal components into a composite signal p.d.f.

sig1frac = ROOT.RooRealVar(

    "sig1frac", "fraction of component 1 in signal", 0.8, 0., 1.)

sig = ROOT.RooAddPdf(

    "sig", "Signal", ROOT.RooArgList(sig1, sig2), ROOT.RooArgList(sig1frac))


# Method 1 - Construct extended composite model

# -------------------------------------------------------------------


# Sum the composite signal and background into an extended pdf

# nsig*sig+nbkg*bkg

nsig = ROOT.RooRealVar("nsig", "number of signal events", 500, 0., 10000)

nbkg = ROOT.RooRealVar(

    "nbkg", "number of background events", 500, 0, 10000)

model = ROOT.RooAddPdf(

    "model",

    "(g1+g2)+a",

    ROOT.RooArgList(

        bkg,

        sig),

    ROOT.RooArgList(

        nbkg,

        nsig))


# Sample, fit and plot extended model

# ---------------------------------------------------------------------


# Generate a data sample of expected number events in x from model

# = model.expectedEvents() = nsig+nbkg

data = model.generate(ROOT.RooArgSet(x))


# Fit model to data, ML term automatically included

model.fitTo(data)


# Plot data and PDF overlaid, expected number of events for p.d.f projection normalization

# rather than observed number of events (==data.numEntries())

xframe = x.frame(ROOT.RooFit.Title("extended ML fit example"))

data.plotOn(xframe)

model.plotOn(xframe, ROOT.RooFit.Normalization(

    1.0, ROOT.RooAbsReal.RelativeExpected))


# Overlay the background component of model with a dashed line

ras_bkg = ROOT.RooArgSet(bkg)

model.plotOn(

    xframe, ROOT.RooFit.Components(ras_bkg), ROOT.RooFit.LineStyle(

        ROOT.kDashed), ROOT.RooFit.Normalization(

            1.0, ROOT.RooAbsReal.RelativeExpected))


# Overlay the background+sig2 components of model with a dotted line

ras_bkg_sig2 = ROOT.RooArgSet(bkg, sig2)

model.plotOn(

    xframe, ROOT.RooFit.Components(ras_bkg_sig2), ROOT.RooFit.LineStyle(

        ROOT.kDotted), ROOT.RooFit.Normalization(

            1.0, ROOT.RooAbsReal.RelativeExpected))


# Print structure of composite p.d.f.

model.Print("t")


# Method 2 - Construct extended components first

# ---------------------------------------------------------------------


# Associated nsig/nbkg as expected number of events with sig/bkg

esig = ROOT.RooExtendPdf("esig", "extended signal p.d.f", sig, nsig)

ebkg = ROOT.RooExtendPdf("ebkg", "extended background p.d.f", bkg, nbkg)


# Sum extended components without coefs

# -------------------------------------------------------------------------


# Construct sum of two extended p.d.f. (no coefficients required)

model2 = ROOT.RooAddPdf("model2", "(g1+g2)+a", ROOT.RooArgList(ebkg, esig))


# Draw the frame on the canvas

c = ROOT.TCanvas("rf202_extendedmlfit", "rf202_extendedmlfit", 600, 600)

ROOT.gPad.SetLeftMargin(0.15)

xframe.GetYaxis().SetTitleOffset(1.4)

xframe.Draw()


c.SaveAs("rf202_extendedmlfit.png")