rf303_conditional.py

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## \file
## \ingroup tutorial_roofit
## \notebook
## 'MULTIDIMENSIONAL MODELS' RooFit tutorial macro #303
## Use of tailored p.d.f as conditional p.d.fs.s
##
## pdf = gauss(x,f(y),sx | y ) with f(y) = a0 + a1*y
##
## \macro_image
## \macro_code
## \macro_output
##
## \date February 2018
## \authors Clemens Lange, Wouter Verkerke (C version)
 
import ROOT
 
 
def makeFakeDataXY():
 
    trnd = ROOT.TRandom3()
 
    x = ROOT.RooRealVar("x", "x", -10, 10)
    y = ROOT.RooRealVar("y", "y", -10, 10)
    coord = {x, y}
 
    d = ROOT.RooDataSet("d", "d", coord)
 
    for i in range(10000):
        tmpy = trnd.Gaus(0, 10)
        tmpx = trnd.Gaus(0.5 * tmpy, 1)
        if (abs(tmpy) < 10) and (abs(tmpx) < 10):
            x.setVal(tmpx)
            y.setVal(tmpy)
            d.add(coord)
 
    return d
 
 
# Set up composed model gauss(x, m(y), s)
# -----------------------------------------------------------------------
 
# Create observables
x = ROOT.RooRealVar("x", "x", -10, 10)
y = ROOT.RooRealVar("y", "y", -10, 10)
 
# Create function f(y) = a0 + a1*y
a0 = ROOT.RooRealVar("a0", "a0", -0.5, -5, 5)
a1 = ROOT.RooRealVar("a1", "a1", -0.5, -1, 1)
fy = ROOT.RooPolyVar("fy", "fy", y, [a0, a1])
 
# Creat gauss(x,f(y),s)
sigma = ROOT.RooRealVar("sigma", "width of gaussian", 0.5, 0.1, 2.0)
model = ROOT.RooGaussian("model", "Gaussian with shifting mean", x, fy, sigma)
 
# Obtain fake external experimental dataset with values for x and y
expDataXY = makeFakeDataXY()
 
# Generate data from conditional p.d.f. model(x|y)
# ---------------------------------------------------------------------------------------------
 
# Make subset of experimental data with only y values
expDataY = expDataXY.reduce({y})
 
# Generate 10000 events in x obtained from _conditional_ model(x|y) with y
# values taken from experimental data
data = model.generate({x}, ProtoData=expDataY)
data.Print()
 
# Fit conditional p.d.f model(x|y) to data
# ---------------------------------------------------------------------------------------------
 
model.fitTo(expDataXY, ConditionalObservables={y}, PrintLevel=-1)
 
# Project conditional p.d.f on x and y dimensions
# ---------------------------------------------------------------------------------------------
 
# Plot x distribution of data and projection of model x = 1/Ndata
# sum(data(y_i)) model(x;y_i)
xframe = x.frame()
expDataXY.plotOn(xframe)
model.plotOn(xframe, ProjWData=expDataY)
 
# Speed up (and approximate) projection by using binned clone of data for
# projection
binnedDataY = expDataY.binnedClone()
model.plotOn(xframe, ProjWData=binnedDataY, LineColor="c", LineStyle=":")
 
# Show effect of projection with too coarse binning
(expDataY.get().find("y")).setBins(5)
binnedDataY2 = expDataY.binnedClone()
model.plotOn(xframe, ProjWData=binnedDataY2, LineColor="r")
 
# Make canvas and draw ROOT.RooPlots
c = ROOT.TCanvas("rf303_conditional", "rf303_conditional", 600, 460)
ROOT.gPad.SetLeftMargin(0.15)
xframe.GetYaxis().SetTitleOffset(1.2)
xframe.Draw()
 
c.SaveAs("rf303_conditional.png")