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rf603_multicpu.py File Reference

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namespace  rf603_multicpu
 

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Likelihood and minimization: setting up a multi-core parallelized unbinned maximum likelihood fit

import ROOT
# Create 3D pdf and data
# -------------------------------------------
# Create observables
x = ROOT.RooRealVar("x", "x", -5, 5)
y = ROOT.RooRealVar("y", "y", -5, 5)
z = ROOT.RooRealVar("z", "z", -5, 5)
# Create signal pdf gauss(x)*gauss(y)*gauss(z)
gx = ROOT.RooGaussian("gx", "gx", x, ROOT.RooFit.RooConst(0), ROOT.RooFit.RooConst(1))
gy = ROOT.RooGaussian("gy", "gy", y, ROOT.RooFit.RooConst(0), ROOT.RooFit.RooConst(1))
gz = ROOT.RooGaussian("gz", "gz", z, ROOT.RooFit.RooConst(0), ROOT.RooFit.RooConst(1))
sig = ROOT.RooProdPdf("sig", "sig", [gx, gy, gz])
# Create background pdf poly(x)*poly(y)*poly(z)
px = ROOT.RooPolynomial("px", "px", x, [-0.1, 0.004])
py = ROOT.RooPolynomial("py", "py", y, [0.1, -0.004])
pz = ROOT.RooPolynomial("pz", "pz", z)
bkg = ROOT.RooProdPdf("bkg", "bkg", [px, py, pz])
# Create composite pdf sig+bkg
fsig = ROOT.RooRealVar("fsig", "signal fraction", 0.1, 0.0, 1.0)
model = ROOT.RooAddPdf("model", "model", [sig, bkg], [fsig])
# Generate large dataset
data = model.generate({x, y, z}, 200000)
# Parallel fitting
# -------------------------------
# In parallel mode the likelihood calculation is split in N pieces,
# that are calculated in parallel and added a posteriori before passing
# it back to MINUIT.
# Use four processes and time results both in wall time and CPU time
model.fitTo(data, NumCPU=4, Timer=True)
# Parallel MC projections
# ----------------------------------------------
# Construct signal, likelihood projection on (y,z) observables and
# likelihood ratio
sigyz = sig.createProjection({x})
totyz = model.createProjection({x})
llratio_func = ROOT.RooFormulaVar("llratio", "log10(@0)-log10(@1)", [sigyz, totyz])
# Calculate likelihood ratio for each event, subset of events with high
# signal likelihood
data.addColumn(llratio_func)
dataSel = data.reduce(Cut="llratio>0.7")
# Make plot frame and plot data
frame = x.frame(Title="Projection on X with LLratio(y,z)>0.7", Bins=40)
dataSel.plotOn(frame)
# Perform parallel projection using MC integration of pdf using given input dataSet.
# In self mode the data-weighted average of the pdf is calculated by splitting the
# input dataset in N equal pieces and calculating in parallel the weighted average
# one each subset. The N results of those calculations are then weighted into the
# final result
# Use four processes
model.plotOn(frame, ProjWData=dataSel, NumCPU=4)
c = ROOT.TCanvas("rf603_multicpu", "rf603_multicpu", 600, 600)
ROOT.gPad.SetLeftMargin(0.15)
frame.GetYaxis().SetTitleOffset(1.6)
frame.Draw()
c.SaveAs("rf603_multicpu.png")
Date
February 2018
Authors
Clemens Lange, Wouter Verkerke (C++ version)

Definition in file rf603_multicpu.py.