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@kreczko
Last active Aug 29, 2015
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RooSimultaneous
#####################################
#
# 'ORGANIZATION AND SIMULTANEOUS FITS' RooFit tutorial macro #501
#
# Using simultaneous p.d.f.s to describe simultaneous fits to multiple
# datasets
#
#
#
# 07/2008 - Wouter Verkerke
#
####################################/
# ifndef __CINT__
# include "RooGlobalFunc.h"
# endif
# include "RooRealVar.h"
# include "RooDataSet.h"
# include "RooGaussian.h"
# include "RooConstVar.h"
# include "RooChebychev.h"
# include "RooAddPdf.h"
# include "RooSimultaneous.h"
# include "RooCategory.h"
# include "TCanvas.h"
# include "TAxis.h"
# include "RooPlot.h"
from ROOT import RooFit, RooRealVar, RooGaussian, RooChebychev, RooAddPdf, \
RooArgList, RooArgSet, RooDataSet, RooCategory, RooPlot, TCanvas, gPad, \
RooSimultaneous, kDashed
def rf501_simultaneouspdf():
# C r e a t e m o d e l f o r p h y s i c s s a m p l e
# -------------------------------------------------------------
# Create observables
x = RooRealVar( "x", "x", -8, 8 )
# Construct signal pdf
mean = RooRealVar( "mean", "mean", 0, -8, 8 )
sigma = RooRealVar( "sigma", "sigma", 0.3, 0.1, 10 )
gx = RooGaussian( "gx", "gx", x, mean, sigma )
# Construct background pdf
a0 = RooRealVar( "a0", "a0", -0.1, -1, 1 )
a1 = RooRealVar( "a1", "a1", 0.004, -1, 1 )
px = RooChebychev( "px", "px", x, RooArgList( a0, a1 ) )
# Construct composite pdf
f = RooRealVar( "f", "f", 0.2, 0., 1. )
model = RooAddPdf( "model", "model", RooArgList( gx, px ), RooArgList( f ) )
# C r e a t e m o d e l f o r c o n t r o l s a m p l e
# --------------------------------------------------------------
# Construct signal pdf.
# NOTE that sigma is shared with the signal sample model
mean_ctl = RooRealVar( "mean_ctl", "mean_ctl", -3, -8, 8 )
gx_ctl = RooGaussian( "gx_ctl", "gx_ctl", x, mean_ctl, sigma )
# Construct the background pdf
a0_ctl = RooRealVar( "a0_ctl", "a0_ctl", -0.1, -1, 1 )
a1_ctl = RooRealVar( "a1_ctl", "a1_ctl", 0.5, -0.1, 1 )
px_ctl = RooChebychev( "px_ctl", "px_ctl", x, RooArgList( a0_ctl, a1_ctl ) )
# Construct the composite model
f_ctl = RooRealVar( "f_ctl", "f_ctl", 0.5, 0., 1. )
model_ctl = RooAddPdf( "model_ctl", "model_ctl", RooArgList( gx_ctl, px_ctl ),
RooArgList( f_ctl ) )
# G e n e r a t e e v e n t s f o r b o t h s a m p l e s
# ---------------------------------------------------------------
# Generate 1000 events in x and y from model
data = model.generate( RooArgSet( x ), 100 )
data_ctl = model_ctl.generate( RooArgSet( x ), 2000 )
# C r e a t e i n d e x c a t e g o r y a n d j o i n s a m p l e s
# ---------------------------------------------------------------------------
# Define category to distinguish physics and control samples events
sample = RooCategory( "sample", "sample" )
sample.defineType( "physics" )
sample.defineType( "control" )
# Construct combined dataset in (x,sample)
combData = RooDataSet( "combData", "combined data", RooArgSet(x), RooFit.Index( sample ),
RooFit.Import( "physics", data ),
RooFit.Import( "control", data_ctl ) )
# C o n s t r u c t a s i m u l t a n e o u s p d f i n ( x , s a m p l e )
# -----------------------------------------------------------------------------------
# Construct a simultaneous pdf using category sample as index
simPdf = RooSimultaneous( "simPdf", "simultaneous pdf", sample )
# Associate model with the physics state and model_ctl with the control state
simPdf.addPdf( model, "physics" )
simPdf.addPdf( model_ctl, "control" )
# P e r f o r m a s i m u l t a n e o u s f i t
# ---------------------------------------------------
# Perform simultaneous fit of model to data and model_ctl to data_ctl
simPdf.fitTo( combData )
# P l o t m o d e l s l i c e s o n d a t a s l i c e s
# ----------------------------------------------------------------
# Make a frame for the physics sample
frame1 = x.frame( RooFit.Bins( 30 ), RooFit.Title( "Physics sample" ) )
# Plot all data tagged as physics sample
combData.plotOn( frame1, RooFit.Cut( "sample==sample::physics" ) )
# Plot "physics" slice of simultaneous pdf.
# NBL You _must_ project the sample index category with data using ProjWData
# as a RooSimultaneous makes no prediction on the shape in the index category
# and can thus not be integrated
simPdf.plotOn( frame1, RooFit.Slice( sample, "physics" ),
RooFit.ProjWData( RooArgSet(sample), combData ) )
simPdf.plotOn( frame1, RooFit.Slice( sample, "physics" ),
RooFit.Components( "px" ),
RooFit.ProjWData( RooArgSet(sample), combData ),
RooFit.LineStyle( kDashed ) )
# The same plot for the control sample slice
frame2 = x.frame( RooFit.Bins( 30 ), RooFit.Title( "Control sample" ) )
combData.plotOn( frame2, RooFit.Cut( "sample==sample::control" ) )
simPdf.plotOn( frame2, RooFit.Slice( sample, "control" ),
RooFit.ProjWData( RooArgSet(sample), combData ) )
simPdf.plotOn( frame2, RooFit.Slice( sample, "control" ),
RooFit.Components( "px_ctl" ),
RooFit.ProjWData( RooArgSet(sample), combData ),
RooFit.LineStyle( kDashed ) )
c = TCanvas( "rf501_simultaneouspdf", "rf403_simultaneouspdf", 800, 400 )
c.Divide( 2 )
c.cd( 1 )
gPad.SetLeftMargin( 0.15 )
frame1.GetYaxis().SetTitleOffset( 1.4 )
frame1.Draw()
c.cd( 2 )
gPad.SetLeftMargin( 0.15 )
frame2.GetYaxis().SetTitleOffset( 1.4 )
frame2.Draw()
raw_input()
if __name__ == '__main__':
rf501_simultaneouspdf()
#####################################
#
# 'ORGANIZATION AND SIMULTANEOUS FITS' RooFit tutorial macro #501
#
# Using simultaneous p.d.f.s to describe simultaneous fits to multiple
# datasets
#
#
#
# 07/2008 - Wouter Verkerke
#
####################################/
# ifndef __CINT__
# include "RooGlobalFunc.h"
# endif
# include "RooRealVar.h"
# include "RooDataSet.h"
# include "RooGaussian.h"
# include "RooConstVar.h"
# include "RooChebychev.h"
# include "RooAddPdf.h"
# include "RooSimultaneous.h"
# include "RooCategory.h"
# include "TCanvas.h"
# include "TAxis.h"
# include "RooPlot.h"
from ROOT import RooFit, RooRealVar, RooGaussian, RooChebychev, RooAddPdf, \
RooArgList, RooArgSet, RooDataSet, RooCategory, RooPlot, TCanvas, gPad, \
RooSimultaneous, kDashed, RooDataHist
import numpy as np
from rootpy.plotting import Hist
def get_data():
N_bkg1_obs = 1000
N_signal_obs = 200
mu1, mu2, sigma1, sigma2 = 100, 140, 15, 5
x1_obs = mu1 + sigma1 * np.random.randn( N_bkg1_obs )
x2_obs = mu2 + sigma2 * np.random.randn( N_signal_obs )
h1 = Hist( 100, 40, 200, title = 'data' )
# fill the histograms with our distributions
map( h1.Fill, x1_obs )
map( h1.Fill, x2_obs )
return h1
def rf501_simultaneouspdf():
real_data = get_data()
# C r e a t e m o d e l f o r p h y s i c s s a m p l e
# -------------------------------------------------------------
# Create observables
x = RooRealVar( "x", "x", 40, 200 )
# Construct signal pdf
mean = RooRealVar( "mean", "mean", 140, 40, 200 )
sigma = RooRealVar( "sigma", "sigma", 5, 0.1, 10 )
gx = RooGaussian( "gx", "gx", x, mean, sigma )
# Construct background pdf
mean_bkg = RooRealVar( "mean_bkg", "mean_bkg", 100, 40, 200 )
sigma_bkg = RooRealVar( "sigma_bkg", "sigma_bkg", 15, 0.1, 20 )
px = RooGaussian( "px", "px", x, mean_bkg, sigma_bkg )
# Construct composite pdf
f = RooRealVar( "f", "f", 0.2, 0., 20. )
model = RooAddPdf( "model", "model", RooArgList( gx, px ), RooArgList( f ) )
# C r e a t e m o d e l f o r c o n t r o l s a m p l e
# --------------------------------------------------------------
# Construct signal pdf.
# NOTE that sigma is shared with the signal sample model
mean_ctl = RooRealVar( "mean_ctl", "mean_ctl", 140, 40, 200 )
gx_ctl = RooGaussian( "gx_ctl", "gx_ctl", x, mean_ctl, sigma )
# Construct the background pdf
mean_bkg_ctl = RooRealVar( "mean_bkg_ctl", "mean_bkg_ctl", 100, 40, 200 )
sigma_bkg_ctl = RooRealVar( "sigma_bkg_ctl", "sigma_bkg_ctl", 15, 0.1, 20 )
px_ctl = RooGaussian( "px_ctl", "px_ctl", x, mean_bkg_ctl, sigma_bkg_ctl )
# Construct the composite model
f_ctl = RooRealVar( "f_ctl", "f_ctl", 0.5, 0., 20. )
model_ctl = RooAddPdf( "model_ctl", "model_ctl", RooArgList( gx_ctl, px_ctl ),
RooArgList( f_ctl ) )
# G e n e r a t e e v e n t s f o r b o t h s a m p l e s
# ---------------------------------------------------------------
# Generate 1000 events in x and y from model
data = model.generate( RooArgSet( x ), 100 )
# real_data.Draw()
data = RooDataHist( 'real_data', 'real_data', RooArgList( x ), real_data )
frame0 = x.frame( RooFit.Bins( 30 ), RooFit.Title( "Physics sample test" ) )
data.plotOn( frame0)
c = TCanvas( "rf501_simultaneouspdf_test", "rf403_simultaneouspdf_test", 800, 400 )
c.cd()
gPad.SetLeftMargin( 0.15 )
frame0.GetYaxis().SetTitleOffset( 1.4 )
frame0.Draw()
data_ctl = model_ctl.generate( RooArgSet( x ), 12000 )
# C r e a t e i n d e x c a t e g o r y a n d j o i n s a m p l e s
# ---------------------------------------------------------------------------
# Define category to distinguish physics and control samples events
sample = RooCategory( "sample", "sample" )
sample.defineType( "physics" )
sample.defineType( "control" )
# Construct combined dataset in (x,sample)
combData = RooDataSet( "combData", "combined data", RooArgSet( x ), RooFit.Index( sample ),
RooFit.Import( "physics", data ),
RooFit.Import( "control", data_ctl ) )
# C o n s t r u c t a s i m u l t a n e o u s p d f i n ( x , s a m p l e )
# -----------------------------------------------------------------------------------
# Construct a simultaneous pdf using category sample as index
simPdf = RooSimultaneous( "simPdf", "simultaneous pdf", sample )
# Associate model with the physics state and model_ctl with the control state
simPdf.addPdf( model, "physics" )
simPdf.addPdf( model_ctl, "control" )
# P e r f o r m a s i m u l t a n e o u s f i t
# ---------------------------------------------------
# Perform simultaneous fit of model to data and model_ctl to data_ctl
simPdf.fitTo( combData )
# P l o t m o d e l s l i c e s o n d a t a s l i c e s
# ----------------------------------------------------------------
# Make a frame for the physics sample
frame1 = x.frame( RooFit.Bins( 30 ), RooFit.Title( "Physics sample" ) )
# Plot all data tagged as physics sample
combData.plotOn( frame1, RooFit.Cut( "sample==sample::physics" ) )
# Plot "physics" slice of simultaneous pdf.
# NBL You _must_ project the sample index category with data using ProjWData
# as a RooSimultaneous makes no prediction on the shape in the index category
# and can thus not be integrated
simPdf.plotOn( frame1, RooFit.Slice( sample, "physics" ),
RooFit.ProjWData( RooArgSet( sample ), combData ) )
simPdf.plotOn( frame1, RooFit.Slice( sample, "physics" ),
RooFit.Components( "px" ),
RooFit.ProjWData( RooArgSet( sample ), combData ),
RooFit.LineStyle( kDashed ) )
# The same plot for the control sample slice
frame2 = x.frame( RooFit.Bins( 30 ), RooFit.Title( "Control sample" ) )
combData.plotOn( frame2, RooFit.Cut( "sample==sample::control" ) )
simPdf.plotOn( frame2, RooFit.Slice( sample, "control" ),
RooFit.ProjWData( RooArgSet( sample ), combData ) )
simPdf.plotOn( frame2, RooFit.Slice( sample, "control" ),
RooFit.Components( "px_ctl" ),
RooFit.ProjWData( RooArgSet( sample ), combData ),
RooFit.LineStyle( kDashed ) )
c = TCanvas( "rf501_simultaneouspdf", "rf403_simultaneouspdf", 800, 400 )
c.Divide( 2 )
c.cd( 1 )
gPad.SetLeftMargin( 0.15 )
frame1.GetYaxis().SetTitleOffset( 1.4 )
frame1.Draw()
c.cd( 2 )
gPad.SetLeftMargin( 0.15 )
frame2.GetYaxis().SetTitleOffset( 1.4 )
frame2.Draw()
raw_input()
if __name__ == '__main__':
rf501_simultaneouspdf()
# please fill in with multi-dimensional fit of all differential cross section measurement variables
# THANKS!
import numpy as np
from rootpy.plotting import Hist
from ROOT import RooFit, RooRealVar, RooDataHist, RooArgList, RooHistPdf, \
RooArgSet, RooAddPdf, RooMsgService, RooProdPdf, RooGaussian, RooLinkedList, \
RooCategory, RooSimultaneous, RooDataSet
from copy import deepcopy
def main ():
N_bkg1 = 9000
N_signal = 1000
N_bkg1_obs = 10000
N_signal_obs = 2000
N_data = N_bkg1_obs + N_signal_obs
mu1, mu2, sigma1, sigma2 = 100, 140, 15, 5
x1 = mu1 + sigma1 * np.random.randn( N_bkg1 )
x2 = mu2 + sigma2 * np.random.randn( N_signal )
x1_obs = mu1 + sigma1 * np.random.randn( N_bkg1_obs )
x2_obs = mu2 + sigma2 * np.random.randn( N_signal_obs )
h1 = Hist( 100, 40, 200, title = 'Background' )
h2 = h1.Clone( title = 'Signal' )
h3 = h1.Clone( title = 'Data' )
h3.markersize = 1.2
# fill the histograms with our distributions
map( h1.Fill, x1 )
map( h2.Fill, x2 )
map( h3.Fill, x1_obs )
map( h3.Fill, x2_obs )
histograms_1 = {'signal': h2,
'bkg1': h1,
'data': h3}
histograms_2 = {'signal': h2,
'bkg1': h1,
'data': h3}
# roofit_histograms contains RooDataHist
# model = RooAddPdf
model1, roofit_histograms_1 = get_roofit_model( histograms_1, fit_boundaries = ( 40, 200 ), name = 'm1' )
model2, roofit_histograms_2 = get_roofit_model( histograms_2, fit_boundaries = ( 40, 200 ), name = 'm2' )
sample = RooCategory( 'sample', 'sample' )
sample.defineType( 'm1' )
sample.defineType( 'm2' )
combined_data = deepcopy( roofit_histograms_1['data'] )
combined_data.add( roofit_histograms_2['data'] )
sim_pdf = RooSimultaneous( "simPdf", "simultaneous pdf", sample )
sim_pdf.addPdf( model1, 'm1' )
sim_pdf.addPdf( model2, 'm2' )
sim_pdf.fitTo( combined_data )
def get_roofit_model( histograms, fit_boundaries, name = 'model' ):
data_label = 'data'
samples = sorted( histograms.keys() )
samples.remove( data_label )
roofit_histograms = {}
roofit_pdfs = {}
roofit_variables = {}
variables = RooArgList()
variable_set = RooArgSet()
fit_variable = RooRealVar( "fit_variable", "fit_variable", fit_boundaries[0], fit_boundaries[1] )
variables.add( fit_variable )
variable_set.add( fit_variable )
roofit_histograms[data_label] = RooDataHist( data_label,
data_label,
variables,
histograms[data_label] )
pdf_arglist = RooArgList()
variable_arglist = RooArgList()
N_total = histograms[data_label].Integral() * 2
N_min = 0
for sample in samples:
roofit_histogram = RooDataHist( sample, sample, variables, histograms[sample] )
roofit_histograms[sample] = roofit_histogram
roofit_pdf = RooHistPdf ( 'pdf' + sample, 'pdf' + sample, variable_set, roofit_histogram, 0 )
roofit_pdfs[sample] = roofit_pdf
roofit_variable = RooRealVar( sample, "number of " + sample + " events", histograms[sample].Integral(), N_min, N_total, "event" )
roofit_variables[sample] = roofit_variable
pdf_arglist.add( roofit_pdf )
variable_arglist.add( roofit_variable )
model = RooAddPdf( name, name, pdf_arglist, variable_arglist )
return model, roofit_histograms
if __name__ == '__main__':
main()
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kreczko commented May 20, 2014

The corrected version is:

#####################################
#
# 'ORGANIZATION AND SIMULTANEOUS FITS' RooFit tutorial macro #501
# 
# Using simultaneous p.d.f.s to describe simultaneous fits to multiple
# datasets
#
#
#
#07/2008 - Wouter Verkerke 
# 
####################################/
from ROOT import RooFit, RooRealVar, RooGaussian, RooChebychev, RooAddPdf, \
RooArgList, RooArgSet, RooDataSet, RooCategory, RooPlot, TCanvas, gPad, \
RooSimultaneous, kDashed, RooDataHist

import numpy as np
from rootpy.plotting import Hist
import rootpy.stl as stl
MapStrRootPtr = stl.map(stl.string, "TH1*")
StrHist = stl.pair(stl.string, "TH1*")

def get_data():
    N_bkg1_ctl = 10000
    N_signal_ctl = 2000
    N_bkg1_obs = 1000
    N_signal_obs = 200
    mu1, mu2, sigma1, sigma2 = 100, 140, 15, 5
    x1_ctl = mu1 + sigma1 * np.random.randn( N_bkg1_ctl )
    x2_ctl = mu2 + sigma2 * np.random.randn( N_signal_ctl )
    x1_obs = mu1 + sigma1 * np.random.randn( N_bkg1_obs )
    x2_obs = mu2 + sigma2 * np.random.randn( N_signal_obs )

    h1 = Hist( 100, 40, 200, title = 'data' )
    h2 = Hist( 100, 40, 200, title = 'data_ctl' )

    # fill the histograms with our distributions
    map( h1.Fill, x1_obs )
    map( h1.Fill, x2_obs )
    map( h2.Fill, x1_ctl )
    map( h2.Fill, x2_ctl )

    return h1, h2

def rf501_simultaneouspdf():
    # C r e a t e   m o d e l   f o r   p h y s i c s   s a m p l e
    # -------------------------------------------------------------

    # Create observables
    x = RooRealVar( "x", "x", 40, 200 ) 

    # Construct signal pdf
    mean = RooRealVar( "mean", "mean", 140, 40, 200 ) 
    sigma = RooRealVar( "sigma", "sigma", 5, 0.1, 10 ) 
    gx = RooGaussian( "gx", "gx", x, mean, sigma ) 

    # Construct background pdf
    mean_bkg = RooRealVar( "mean_bkg", "mean_bkg", 100, 40, 200 ) 
    sigma_bkg = RooRealVar( "sigma_bkg", "sigma_bkg", 15, 0.1, 20 ) 
    px = RooGaussian( "px", "px", x, mean_bkg, sigma_bkg ) 

    # Construct composite pdf
    f = RooRealVar( "f", "f", 0.2, 0., 20. ) 
    model = RooAddPdf( "model", "model", RooArgList( gx, px ), RooArgList( f ) ) 



    # C r e a t e   m o d e l   f o r   c o n t r o l   s a m p l e
    # --------------------------------------------------------------

    # Construct signal pdf. 
    # NOTE that sigma is shared with the signal sample model
    mean_ctl = RooRealVar( "mean_ctl", "mean_ctl", 140, 40, 200 ) 
    gx_ctl = RooGaussian( "gx_ctl", "gx_ctl", x, mean_ctl, sigma ) 

    # Construct the background pdf
    mean_bkg_ctl = RooRealVar( "mean_bkg_ctl", "mean_bkg_ctl", 100, 40, 200 ) 
    sigma_bkg_ctl = RooRealVar( "sigma_bkg_ctl", "sigma_bkg_ctl", 15, 0.1, 20 ) 
    px_ctl = RooGaussian( "px_ctl", "px_ctl", x, mean_bkg_ctl, sigma_bkg_ctl ) 

    # Construct the composite model
    f_ctl = RooRealVar( "f_ctl", "f_ctl", 0.5, 0., 20. ) 
    model_ctl = RooAddPdf( "model_ctl", "model_ctl", RooArgList( gx_ctl, px_ctl ),
                           RooArgList( f_ctl ) ) 



    # G e t   e v e n t s   f o r   b o t h   s a m p l e s 
    # ---------------------------------------------------------------
    real_data, real_data_ctl = get_data()
    input_hists = MapStrRootPtr()
    input_hists.insert(StrHist("physics", real_data))
    input_hists.insert(StrHist("control", real_data_ctl ))

    # C r e a t e   i n d e x   c a t e g o r y   a n d   j o i n   s a m p l e s 
    # ---------------------------------------------------------------------------
    # Define category to distinguish physics and control samples events
    sample = RooCategory( "sample", "sample" ) 
    sample.defineType( "physics" ) 
    sample.defineType( "control" ) 

    # Construct combined dataset in (x,sample)
    combData = RooDataHist("combData", "combined data", RooArgList( x ), sample ,
                           input_hists)


    # C o n s t r u c t   a   s i m u l t a n e o u s   p d f   i n   ( x , s a m p l e )
    # -----------------------------------------------------------------------------------

    # Construct a simultaneous pdf using category sample as index
    simPdf = RooSimultaneous( "simPdf", "simultaneous pdf", sample ) 

    # Associate model with the physics state and model_ctl with the control state
    simPdf.addPdf( model, "physics" ) 
    simPdf.addPdf( model_ctl, "control" ) 



    # P e r f o r m   a   s i m u l t a n e o u s   f i t
    # ---------------------------------------------------

    # Perform simultaneous fit of model to data and model_ctl to data_ctl
    simPdf.fitTo( combData ) 



    # P l o t   m o d e l   s l i c e s   o n   d a t a    s l i c e s 
    # ----------------------------------------------------------------

    # Make a frame for the physics sample
    frame1 = x.frame( RooFit.Bins( 30 ), RooFit.Title( "Physics sample" ) ) 

    # Plot all data tagged as physics sample
    combData.plotOn( frame1, RooFit.Cut( "sample==sample::physics" ) ) 

    # Plot "physics" slice of simultaneous pdf. 
    # NBL You _must_ project the sample index category with data using ProjWData 
    # as a RooSimultaneous makes no prediction on the shape in the index category 
    # and can thus not be integrated
    simPdf.plotOn( frame1, RooFit.Slice( sample, "physics" ),
                   RooFit.ProjWData( RooArgSet( sample ), combData ) ) 
    simPdf.plotOn( frame1, RooFit.Slice( sample, "physics" ),
                   RooFit.Components( "px" ),
                   RooFit.ProjWData( RooArgSet( sample ), combData ),
                   RooFit.LineStyle( kDashed ) ) 

    # The same plot for the control sample slice
    frame2 = x.frame( RooFit.Bins( 30 ), RooFit.Title( "Control sample" ) ) 
    combData.plotOn( frame2, RooFit.Cut( "sample==sample::control" ) ) 
    simPdf.plotOn( frame2, RooFit.Slice( sample, "control" ),
                  RooFit.ProjWData( RooArgSet( sample ), combData ) ) 
    simPdf.plotOn( frame2, RooFit.Slice( sample, "control" ),
                  RooFit.Components( "px_ctl" ),
                  RooFit.ProjWData( RooArgSet( sample ), combData ),
                  RooFit.LineStyle( kDashed ) ) 



    c = TCanvas( "rf501_simultaneouspdf", "rf403_simultaneouspdf", 800, 400 ) 
    c.Divide( 2 ) 
    c.cd( 1 )
    gPad.SetLeftMargin( 0.15 )
    frame1.GetYaxis().SetTitleOffset( 1.4 )
    frame1.Draw() 
    c.cd( 2 )
    gPad.SetLeftMargin( 0.15 )
    frame2.GetYaxis().SetTitleOffset( 1.4 )
    frame2.Draw() 
    raw_input()

if __name__ == '__main__':
    rf501_simultaneouspdf()

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