def generate_testfiles():
h = TH1D("gaussian_hist", "Gaussian histgram", 100, -3, 3)
h.FillRandom("gaus", 1000)
file = TFile(
os.path.dirname(__file__) + ('/../testfiles/root_testfiles.root'),
'RECREATE')
file.cd()
h.Write()
x = RooRealVar("D0_M", "m(K_{S}^{0}K^{+}K^{-})", 1860, 1800, 1930,
"\\mathrm{MeV}/c^{2}")
x.setBins(130)
m1 = RooRealVar("m1", "mean 1", 1864, 1860, 1870)
s1 = RooRealVar("s1", "sigma 1", 2, 0, 5)
g1 = RooGaussian("g1", "Gaussian 1", x, m1, s1)
m2 = RooRealVar("m2", "mean 2", 1864, 1860, 1870)
s2 = RooRealVar("s2", "sigma 2", 4, 0, 5)
g2 = RooGaussian("g2", "Gaussian 2", x, m2, s2)
f1 = RooRealVar("f", "f", 0.5, 0, 1)
m = RooAddPdf("model", "model", RooArgList(g1, g2), f1)
data = m.generate(x, 1e6)
x.Write("x")
m.Write("model")
data.Write("data")
file.Close()
return
def rooFit203():
print ">>> setup model..."
x = RooRealVar("x", "x", -10, 10)
mean = RooRealVar("mean", "mean of gaussian", 0, -10, 10)
gauss = RooGaussian("gauss", "gaussian PDF", x, mean, RooConst(1))
# Construct px = 1 (flat in x)
px = RooPolynomial("px", "px", x)
# Construct model = f*gx + (1-f)px
f = RooRealVar("f", "f", 0., 1.)
model = RooAddPdf("model", "model", RooArgList(gauss, px), RooArgList(f))
data = model.generate(RooArgSet(x), 10000) # RooDataSet
print ">>> fit to full data range..."
result_full = model.fitTo(data, Save(kTRUE)) # RooFitResult
print "\n>>> fit \"signal\" range..."
# Define "signal" range in x as [-3,3]
x.setRange("signal", -3, 3)
result_sig = model.fitTo(data, Save(kTRUE),
Range("signal")) # RooFitResult
print "\n>>> plot and print results..."
# Make plot frame in x and add data and fitted model
frame1 = x.frame(Title("Fitting a sub range")) # RooPlot
data.plotOn(frame1, Name("data"))
model.plotOn(frame1, Range("Full"), LineColor(kBlue),
Name("model")) # Add shape in full ranged dashed
model.plotOn(frame1, LineStyle(kDashed), LineColor(kRed),
Name("model2")) # By default only fitted range is shown
print "\n>>> result of fit on all data:"
result_full.Print()
print "\n>>> result of fit in in signal region (note increased error on signal fraction):"
result_sig.Print()
print ">>> draw on canvas..."
canvas = TCanvas("canvas", "canvas", 100, 100, 800, 600)
legend = TLegend(0.2, 0.85, 0.4, 0.65)
legend.SetTextSize(0.032)
legend.SetBorderSize(0)
legend.SetFillStyle(0)
gPad.SetLeftMargin(0.14)
gPad.SetRightMargin(0.02)
frame1.GetYaxis().SetLabelOffset(0.008)
frame1.GetYaxis().SetTitleOffset(1.4)
frame1.GetYaxis().SetTitleSize(0.045)
frame1.GetXaxis().SetTitleSize(0.045)
frame1.Draw()
legend.AddEntry("data", "data", 'LEP')
legend.AddEntry("model", "fit (full range)", 'L')
legend.AddEntry("model2", "fit (signal range)", 'L')
legend.Draw()
canvas.SaveAs("rooFit203.png")
def test_correlated_values():
try:
import uncertainties
except ImportError:
raise SkipTest("uncertainties package is not installed")
from rootpy.stats.correlated_values import correlated_values
# construct pdf and toy data following example at
# http://root.cern.ch/drupal/content/roofit
# --- Observable ---
mes = RooRealVar("mes", "m_{ES} (GeV)", 5.20, 5.30)
# --- Parameters ---
sigmean = RooRealVar("sigmean", "B^{#pm} mass", 5.28, 5.20, 5.30)
sigwidth = RooRealVar("sigwidth", "B^{#pm} width", 0.0027, 0.001, 1.)
# --- Build Gaussian PDF ---
signal = RooGaussian("signal", "signal PDF", mes, sigmean, sigwidth)
# --- Build Argus background PDF ---
argpar = RooRealVar("argpar", "argus shape parameter", -20.0, -100., -1.)
background = RooArgusBG("background", "Argus PDF",
mes, RooFit.RooConst(5.291), argpar)
# --- Construct signal+background PDF ---
nsig = RooRealVar("nsig", "#signal events", 200, 0., 10000)
nbkg = RooRealVar("nbkg", "#background events", 800, 0., 10000)
model = RooAddPdf("model", "g+a",
RooArgList(signal,background),
RooArgList(nsig,nbkg))
# --- Generate a toyMC sample from composite PDF ---
data = model.generate(RooArgSet(mes), 2000)
# --- Perform extended ML fit of composite PDF to toy data ---
fitresult = model.fitTo(data, RooFit.Save(), RooFit.PrintLevel(-1))
nsig, nbkg = correlated_values(["nsig", "nbkg"], fitresult)
# Arbitrary math expression according to what the `uncertainties`
# package supports, automatically computes correct error propagation
sum_value = nsig + nbkg
value, error = sum_value.nominal_value, sum_value.std_dev
workspace = Workspace(name='workspace')
# import the data
assert_false(workspace(data))
with TemporaryFile():
workspace.Write()
def test_correlated_values():
try:
import uncertainties
except ImportError:
raise SkipTest("uncertainties package is not installed")
from rootpy.stats.correlated_values import correlated_values
# construct pdf and toy data following example at
# http://root.cern.ch/drupal/content/roofit
# --- Observable ---
mes = RooRealVar("mes", "m_{ES} (GeV)", 5.20, 5.30)
# --- Parameters ---
sigmean = RooRealVar("sigmean", "B^{#pm} mass", 5.28, 5.20, 5.30)
sigwidth = RooRealVar("sigwidth", "B^{#pm} width", 0.0027, 0.001, 1.)
# --- Build Gaussian PDF ---
signal = RooGaussian("signal", "signal PDF", mes, sigmean, sigwidth)
# --- Build Argus background PDF ---
argpar = RooRealVar("argpar", "argus shape parameter", -20.0, -100., -1.)
background = RooArgusBG("background", "Argus PDF",
mes, RooFit.RooConst(5.291), argpar)
# --- Construct signal+background PDF ---
nsig = RooRealVar("nsig", "#signal events", 200, 0., 10000)
nbkg = RooRealVar("nbkg", "#background events", 800, 0., 10000)
model = RooAddPdf("model", "g+a",
RooArgList(signal,background),
RooArgList(nsig,nbkg))
# --- Generate a toyMC sample from composite PDF ---
data = model.generate(RooArgSet(mes), 2000)
# --- Perform extended ML fit of composite PDF to toy data ---
fitresult = model.fitTo(data, RooFit.Save(), RooFit.PrintLevel(-1))
nsig, nbkg = correlated_values(["nsig", "nbkg"], fitresult)
# Arbitrary math expression according to what the `uncertainties`
# package supports, automatically computes correct error propagation
sum_value = nsig + nbkg
value, error = sum_value.nominal_value, sum_value.std_dev
workspace = Workspace(name='workspace')
# import the data
assert_false(workspace(data))
with TemporaryFile():
workspace.Write()
def toy_run(nevents):
lower = -1
upper = 1
# create observables
obs = RooRealVar("obs", "obs1", lower, upper)
# create parameters
mean1 = RooRealVar("mean1", "mean of gaussian", 0, -1, 1)
sigma1 = RooRealVar("sigma1", "sigma of gaussian", 0.1, -1, 1)
gauss1 = RooGaussian("gauss1", "gaussian PDF", obs, mean1, sigma1)
mean2 = RooRealVar("mean2", "mean of gaussian", 0.5, -1, 1)
sigma2 = RooRealVar("sigma2", "sigma of gaussian", 0.2, -1, 1)
gauss2 = RooGaussian("gauss2", "gaussian PDF", obs, mean2, sigma2)
frac = RooRealVar("frac", "Fraction of a gauss", 0.5, 0, 1)
arg_list = RooArgList(
gauss1,
gauss2,
gauss2,
gauss2,
gauss2,
# gauss2,
gauss2,
gauss2,
gauss1)
arg_list.addOwned(gauss2)
pdf = RooAddPdf(
"sum_pdf",
"sum of pdfs",
arg_list,
RooArgList(
frac,
frac,
frac,
# frac,
# frac,
frac,
frac,
frac,
frac,
frac))
# obs, pdf = build_pdf()
timer = zfit_benchmark.timer.Timer(f"Toys {nevents}")
with timer:
data = pdf.generate(RooArgSet(obs), nevents)
pdf.fitTo(data)
# mgr.generateAndFit(n_toys, nevents)
return float(timer.elapsed)
def test_plottable():
# construct pdf and toy data following example at
# http://root.cern.ch/drupal/content/roofit
# Observable
mes = RooRealVar("mes", "m_{ES} (GeV)", 5.20, 5.30)
# Parameters
sigmean = RooRealVar("sigmean", "B^{#pm} mass", 5.28, 5.20, 5.30)
sigwidth = RooRealVar("sigwidth", "B^{#pm} width", 0.0027, 0.001, 1.)
# Build Gaussian PDF
signal = RooGaussian("signal", "signal PDF", mes, sigmean, sigwidth)
# Build Argus background PDF
argpar = RooRealVar("argpar", "argus shape parameter", -20.0, -100., -1.)
background = RooArgusBG("background", "Argus PDF",
mes, RooFit.RooConst(5.291), argpar)
# Construct signal+background PDF
nsig = RooRealVar("nsig", "#signal events", 200, 0., 10000)
nbkg = RooRealVar("nbkg", "#background events", 800, 0., 10000)
model = RooAddPdf("model", "g+a",
RooArgList(signal, background),
RooArgList(nsig, nbkg))
# Generate a toyMC sample from composite PDF
data = model.generate(RooArgSet(mes), 2000)
# Perform extended ML fit of composite PDF to toy data
fitresult = model.fitTo(data, RooFit.Save(), RooFit.PrintLevel(-1))
# Plot toy data and composite PDF overlaid
mesframe = asrootpy(mes.frame())
data.plotOn(mesframe)
model.plotOn(mesframe)
for obj in mesframe.objects:
assert_true(obj)
for curve in mesframe.curves:
assert_true(curve)
for hist in mesframe.data_hists:
assert_true(hist)
assert_true(mesframe.plotvar)
with TemporaryFile():
mesframe.Write()
def test_plottable():
# construct pdf and toy data following example at
# http://root.cern.ch/drupal/content/roofit
# Observable
mes = RooRealVar("mes", "m_{ES} (GeV)", 5.20, 5.30)
# Parameters
sigmean = RooRealVar("sigmean", "B^{#pm} mass", 5.28, 5.20, 5.30)
sigwidth = RooRealVar("sigwidth", "B^{#pm} width", 0.0027, 0.001, 1.)
# Build Gaussian PDF
signal = RooGaussian("signal", "signal PDF", mes, sigmean, sigwidth)
# Build Argus background PDF
argpar = RooRealVar("argpar", "argus shape parameter", -20.0, -100., -1.)
background = RooArgusBG("background", "Argus PDF",
mes, RooFit.RooConst(5.291), argpar)
# Construct signal+background PDF
nsig = RooRealVar("nsig", "#signal events", 200, 0., 10000)
nbkg = RooRealVar("nbkg", "#background events", 800, 0., 10000)
model = RooAddPdf("model", "g+a",
RooArgList(signal, background),
RooArgList(nsig, nbkg))
# Generate a toyMC sample from composite PDF
data = model.generate(RooArgSet(mes), 2000)
# Perform extended ML fit of composite PDF to toy data
fitresult = model.fitTo(data, RooFit.Save(), RooFit.PrintLevel(-1))
# Plot toy data and composite PDF overlaid
mesframe = asrootpy(mes.frame())
data.plotOn(mesframe)
model.plotOn(mesframe)
for obj in mesframe.objects:
assert_true(obj)
for curve in mesframe.curves:
assert_true(curve)
for hist in mesframe.data_hists:
assert_true(hist)
assert_true(mesframe.plotvar)
with TemporaryFile():
mesframe.Write()
def rooFit502():
print ">>> setup model components..."
x = RooRealVar("x", "x", 0, 10)
mean = RooRealVar("mean", "mean of gaussians", 5, 0, 10)
sigma1 = RooRealVar("sigma1", "width of gaussians", 0.5)
sigma2 = RooRealVar("sigma2", "width of gaussians", 1)
sig1 = RooGaussian("sig1", "Signal component 1", x, mean, sigma1)
sig2 = RooGaussian("sig2", "Signal component 2", x, mean, sigma2)
a0 = RooRealVar("a0", "a0", 0.5, 0., 1.)
a1 = RooRealVar("a1", "a1", -0.2, 0., 1.)
bkg = RooChebychev("bkg", "Background", x, RooArgList(a0, a1))
print ">>> sum model components..."
sig1frac = RooRealVar("sig1frac", "fraction of component 1 in signal", 0.8,
0., 1.)
sig = RooAddPdf("sig", "Signal", RooArgList(sig1, sig2),
RooArgList(sig1frac))
bkgfrac = RooRealVar("bkgfrac", "fraction of background", 0.5, 0., 1.)
model = RooAddPdf("model", "g1+g2+a", RooArgList(bkg, sig),
RooArgList(bkgfrac))
print ">>> generate data..."
data = model.generate(RooArgSet(x), 1000) # RooDataSet
print ">>> create workspace, import data and model..."
workspace = RooWorkspace("workspace", "workspace") # empty RooWorkspace
getattr(workspace, 'import')(model) # import model and all its components
getattr(workspace, 'import')(data) # import data
#workspace.import(model) # causes synthax error in python
#workspace.import(data) # causes synthax error in python
print "\n>>> print workspace contents:"
workspace.Print()
print "\n>>> save workspace in file..."
workspace.writeToFile("rooFit502_workspace.root")
print ">>> save workspace in memory (gDirectory)..."
gDirectory.Add(workspace)
def rooFit602():
print ">>> setup model..."
x = RooRealVar("x","x",0,10)
mean = RooRealVar("mean","mean of gaussian",5)
sigma1 = RooRealVar("sigma1","width of gaussian",0.5)
sigma2 = RooRealVar("sigma2","width of gaussian",1)
sig1 = RooGaussian("sig1","Signal component 1",x,mean,sigma1)
sig2 = RooGaussian("sig2","Signal component 2",x,mean,sigma2)
a0 = RooRealVar("a0","a0",0.5,0.,1.)
a1 = RooRealVar("a1","a1",-0.2,0.,1.)
bkg = RooChebychev("bkg","Background",x,RooArgSet(a0,a1))
sig1frac = RooRealVar("sig1frac","fraction of component 1 in signal",0.8,0.,1.)
sig = RooAddPdf("sig","Signal",RooArgList(sig1,sig2),sig1frac)
bkgfrac = RooRealVar("bkgfrac","fraction of background",0.5,0.,1.)
model = RooAddPdf("model","g1+g2+a",RooArgList(bkg,sig),bkgfrac)
print ">>> create binned dataset..."
data = model.generate(RooArgSet(x),10000) # RooDataSet
hist = data.binnedClone() # RooDataHist
# Construct a chi^2 of the data and the model.
# When a p.d.f. is used in a chi^2 fit, the probability density scaled
# by the number of events in the dataset to obtain the fit function
# If model is an extended p.d.f, the expected number events is used
# instead of the observed number of events.
model.chi2FitTo(hist)
# NB: It is also possible to fit a RooAbsReal function to a RooDataHist
# using chi2FitTo().
# Note that entries with zero bins are _not_ allowed
# for a proper chi^2 calculation and will give error
# messages
data_small = date.reduce(EventRange(1,100)) # RooDataSet
hist_small = data_small.binnedClone() # RooDataHist
chi2_lowstat("chi2_lowstat","chi2",model,hist_small)
print ">>> chi2_lowstat.getVal() = %s" % chi2_lowstat.getVal()
def rooFit601():
print ">>> setup pdf and likelihood..."
x = RooRealVar("x", "x", -20, 20)
mean = RooRealVar("mean", "mean of g1 and g2", 0)
sigma1 = RooRealVar("sigma1", "width of g1", 3)
sigma2 = RooRealVar("sigma2", "width of g2", 4, 3.0,
6.0) # intentional strong correlations
gauss1 = RooGaussian("gauss1", "gauss1", x, mean, sigma1)
gauss2 = RooGaussian("gauss2", "gauss2", x, mean, sigma2)
frac = RooRealVar("frac", "frac", 0.5, 0.0, 1.0)
model = RooAddPdf("model", "model", RooArgList(gauss1, gauss2),
RooArgList(frac))
print ">>> generate to data..."
data = model.generate(RooArgSet(x), 1000) # RooDataSet
print ">>> construct unbinned likelihood of model wrt data..."
nll = model.createNLL(data) # RooAbsReal
print ">>> interactive minimization and error analysis with MINUIT interface object..."
minuit = RooMinuit(nll)
print ">>> set avtive verbosity for logging of MINUIT parameter space stepping..."
minuit.setVerbose(kTRUE)
print ">>> call MIGRAD to minimize the likelihood..."
minuit.migrad()
print "\n>>> parameter values and error estimates that are back propagated from MINUIT:"
model.getParameters(RooArgSet(x)).Print("s")
print "\n>>> disable verbose logging..."
minuit.setVerbose(kFALSE)
print ">>> run HESSE to calculate errors from d2L/dp2..."
minuit.hesse()
print ">>> value of and error on sigma2 (back propagated from MINUIT):"
sigma2.Print()
print "\n>>> run MINOS on sigma2 parameter only..."
minuit.minos(RooArgSet(sigma2))
print "\n>>> value of and error on sigma2 (back propagated from MINUIT after running MINOS):"
sigma2.Print()
print "\n>>> saving results, contour plots..."
# Save a snapshot of the fit result. This object contains the initial
# fit parameters, the final fit parameters, the complete correlation
# matrix, the EDM, the minimized FCN , the last MINUIT status code and
# the number of times the RooFit function object has indicated evaluation
# problems (e.g. zero probabilities during likelihood evaluation)
result = minuit.save() # RooFitResult
# Make contour plot of mx vs sx at 1,2,3 sigma
frame1 = minuit.contour(frac, sigma2, 1, 2, 3) # RooPlot
frame1.SetTitle("RooMinuit contour plot")
# Print the fit result snapshot
result.Print("v")
print "\n>>> change value of \"mean\" parameter..."
mean.setVal(0.3)
# Rerun MIGRAD,HESSE
print ">>> rerun MIGRAD, HESSE..."
minuit.migrad()
minuit.hesse()
print ">>> value on and error of frac:"
frac.Print()
print "\n>>> fix value of \"sigma\" parameter (setConstant)..."
sigma2.setConstant(kTRUE)
print ">>> rerun MIGRAD, HESSE..."
minuit.migrad()
minuit.hesse()
frac.Print()
pdf_combine1 = RooAddPdf("pdf_combine1"," gauss4 + gauss5 ", RooArgList(gauss4 , gauss5 ), RooArgList( frac_combine1 ))
#pdf_combine1.plotOn(xframe3,RooFit.LineColor(RooFit.kBlue))
gauss4.plotOn(xframe3, RooFit.Normalization( frac_combine1.getVal() ,RooAbsReal.Relative),RooFit.LineColor(RooFit.kOrange))
gauss5.plotOn(xframe3, RooFit.Normalization( 1-frac_combine1.getVal() ,RooAbsReal.Relative),RooFit.LineColor(RooFit.kCyan))
pdf_combine1.plotOn(xframe3, RooFit.Normalization(1.0,RooAbsReal.Relative) ,RooFit.LineColor(RooFit.kBlue))
# -------------------------------------------
# 4. use combine PDF to generate MC
xframe4 = x.frame(RooFit.Title("4. use combine PDF to generate MC"))
data2 = pdf_combine1.generate(RooArgSet(x),500)
#pdf_combine1.plotOn(xframe4, RooFit.Normalization(500, RooAbsReal.NumEvent) , RooFit.LineColor(RooFit.kOrange))
data2.plotOn(xframe4)
pdf_combine1.plotOn(xframe4,RooFit.LineColor(RooFit.kBlue))
# -------------------------------------------
# 5. use combine PDF to fit the toy MC
xframe5 = x.frame(RooFit.Title("5. use combine PDF to fit the toy MC"))
# gauss 6
mean6 = RooRealVar("mean6","mean of gaussian",-1,-10,10)
sigma6 = RooRealVar("sigma6","width of gaussian",4,0.1,10)
gauss6 = RooGaussian("gauss6","gaussian PDF",x,mean6,sigma6)
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()
sigmean = RooRealVar("sigmean", "B^{#pm} mass", 5.28, 5.20, 5.30)
sigwidth = RooRealVar("sigwidth", "B^{#pm} width", 0.0027, 0.001, 1.)
# --- Build Gaussian PDF ---
signal = RooGaussian("signal", "signal PDF", mes, sigmean, sigwidth)
argpar = RooRealVar("argpar", "argus shape parameter", -20.0, -100., -1.)
background = RooArgusBG("background", "Argus PDF", mes, RooFit.RooConst(5.291), argpar)
# --- Construct signal+background PDF ---
nsig = RooRealVar("nsig", "#signal events", 200, 0., 10000)
nbkg = RooRealVar("nbkg", "#background events", 800, 0., 10000)
model = RooAddPdf("model", "g+a", RooArgList(signal, background), RooArgList(nsig, nbkg))
# --- Generate a toyMC sample from composite PDF ---
data = model.generate(RooArgSet(mes), 2000)
# --- Perform extended ML fit of composite PDF to toy data ---
model.fitTo(data)
# --- Plot toy data and composite PDF overlaid ---
mesframe = mes.frame()
data.plotOn(mesframe)
model.plotOn(mesframe)
model.plotOn(mesframe, RooFit.Components('background'), RooFit.LineStyle(kDashed))
mesframe.Draw()
print 'nsig:',nsig.getValV(), '+-', nsig.getError()
print 'nbkg:', nbkg.getValV(), '+-', nbkg.getError()
print 'mes:', mes.getValV(), '+-', mes.getError()
def rooFit501():
print ">>> setup model for physics sample..."
x = RooRealVar("x", "x", -8, 8)
mean = RooRealVar("mean", "mean", 0, -8, 8)
sigma = RooRealVar("sigma", "sigma", 0.3, 0.1, 10)
gauss = RooGaussian("gx", "gx", x, mean, sigma)
a0 = RooRealVar("a0", "a0", -0.1, -1, 1)
a1 = RooRealVar("a1", "a1", 0.004, -1, 1)
px = RooChebychev("px", "px", x, RooArgList(a0, a1))
f = RooRealVar("f", "f", 0.2, 0., 1.)
model = RooAddPdf("model", "model", RooArgList(gauss, px), RooArgList(f))
print ">>> setup model for control sample..."
# NOTE: sigma is shared with the signal sample model
mean_ctrl = RooRealVar("mean_ctrl", "mean_ctrl", -3, -8, 8)
gauss_ctrl = RooGaussian("gauss_ctrl", "gauss_ctrl", x, mean_ctrl, sigma)
a0_ctrl = RooRealVar("a0_ctrl", "a0_ctrl", -0.1, -1, 1)
a1_ctrl = RooRealVar("a1_ctrl", "a1_ctrl", 0.5, -0.1, 1)
px_ctrl = RooChebychev("px_ctrl", "px_ctrl", x,
RooArgList(a0_ctrl, a1_ctrl))
f_ctrl = RooRealVar("f_ctrl", "f_ctrl", 0.5, 0., 1.)
model_ctrl = RooAddPdf("model_ctrl", "model_ctrl",
RooArgList(gauss_ctrl, px_ctrl), RooArgList(f_ctrl))
print ">>> generate events for both samples..."
data = model.generate(RooArgSet(x), 100) # RooDataSet
data_ctrl = model_ctrl.generate(RooArgSet(x), 2000) # RooDataSet
print ">>> create index category and join samples..."
# Define category to distinguish physics and control samples events
sample = RooCategory("sample", "sample")
sample.defineType("physics")
sample.defineType("control")
print ">>> construct combined dataset in (x,sample)..."
combData = RooDataSet("combData", "combined data", RooArgSet(x),
Index(sample), Import("physics", data),
Import("control", data_ctrl))
print ">>> construct a simultaneous pdf in (x,sample)..."
# Construct a simultaneous pdf using category sample as index
simPdf = RooSimultaneous("simPdf", "simultaneous pdf", sample)
# Associate model with the physics state and model_ctrl with the control state
simPdf.addPdf(model, "physics")
simPdf.addPdf(model_ctrl, "control")
print ">>> perform a simultaneous fit..."
# Perform simultaneous fit of model to data and model_ctrl to data_ctrl
simPdf.fitTo(combData)
print "\n>>> plot model slices on data slices..."
frame1 = x.frame(Bins(30), Title("Physics sample")) # RooPlot
combData.plotOn(frame1, 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, Slice(sample, "physics"),
ProjWData(RooArgSet(sample), combData))
simPdf.plotOn(frame1, Slice(sample, "physics"), Components("px"),
ProjWData(RooArgSet(sample), combData), LineStyle(kDashed))
print "\n>>> plot control sample slices..."
frame2 = x.frame(Bins(30), Title("Control sample")) # RooPlot
combData.plotOn(frame2, Cut("sample==sample::control"))
simPdf.plotOn(frame2, Slice(sample, "control"),
ProjWData(RooArgSet(sample), combData))
simPdf.plotOn(frame2, Slice(sample, "control"), Components("px_ctrl"),
ProjWData(RooArgSet(sample), combData), LineStyle(kDashed))
print "\n>>> draw on canvas..."
canvas = TCanvas("canvas", "canvas", 100, 100, 1400, 600)
canvas.Divide(2)
canvas.cd(1)
gPad.SetLeftMargin(0.15)
gPad.SetRightMargin(0.02)
frame1.GetYaxis().SetLabelOffset(0.008)
frame1.GetYaxis().SetTitleOffset(1.6)
frame1.GetYaxis().SetTitleSize(0.045)
frame1.GetXaxis().SetTitleSize(0.045)
frame1.Draw()
canvas.cd(2)
gPad.SetLeftMargin(0.15)
gPad.SetRightMargin(0.02)
frame2.GetYaxis().SetLabelOffset(0.008)
frame2.GetYaxis().SetTitleOffset(1.6)
frame2.GetYaxis().SetTitleSize(0.045)
frame2.GetXaxis().SetTitleSize(0.045)
frame2.Draw()
canvas.SaveAs("rooFit501.png")
def rooFit204():
print ">>> setup model signal components: gaussians..."
x = RooRealVar("x","x",0,10)
mean = RooRealVar("mean","mean of gaussian",5)
sigma1 = RooRealVar("sigma1","width of gaussians",0.5)
sigma2 = RooRealVar("sigma2","width of gaussians",1)
sig1 = RooGaussian("sig1","Signal component 1",x,mean,sigma1)
sig2 = RooGaussian("sig2","Signal component 2",x,mean,sigma2)
sig1frac = RooRealVar("sig1frac","fraction of component 1 in signal",0.8,0.,1.)
sig = RooAddPdf("sig","Signal",RooArgList(sig1,sig2),RooArgList(sig1frac))
print ">>> setup model background components: Chebychev polynomial..."
a0 = RooRealVar("a0","a0",0.5,0.,1.)
a1 = RooRealVar("a1","a1",-0.2,0.,1.)
bkg = RooChebychev("bkg","Background",x,RooArgList(a0,a1))
print ">>> construct extended components with specified range..."
# Define signal range in which events counts are to be defined
x.setRange("signalRange",5,6)
# Associated nsig/nbkg as expected number of events with sig/bkg _in_the_range_ "signalRange"
nsig = RooRealVar("nsig","number of signal events in signalRange", 500,0.,10000)
nbkg = RooRealVar("nbkg","number of background events in signalRange",500,0,10000)
esig = RooExtendPdf("esig","extended signal pdf", sig,nsig,"signalRange")
ebkg = RooExtendPdf("ebkg","extended background pdf",bkg,nbkg,"signalRange")
print ">>> sum extended components..."
# Construct sum of two extended p.d.f. (no coefficients required)
model = RooAddPdf("model","(g1+g2)+a",RooArgList(ebkg,esig))
print ">>> sample data, fit model..."
data = model.generate(RooArgSet(x),1000) # RooDataSet
result = model.fitTo(data,Extended(kTRUE),Save()) # RooFitResult
print "\n>>> fit result:"
result.Print()
print "\n>>> plot everything..."
frame1 = x.frame(Title("Fitting a sub range")) # RooPlot
data.plotOn(frame1,Binning(50),Name("data"))
model.plotOn(frame1,LineColor(kBlue),Name("model"))
argset1 = RooArgSet(bkg)
model.plotOn(frame1,Components(argset1),LineStyle(kDashed),LineColor(kBlue),Name("bkg"),Normalization(1.0,RooAbsReal.RelativeExpected))
#model.plotOn(frame1,Components(argset1),LineStyle(kDashed),LineColor(kRed),Name("bkg2"))
print ">>> draw on canvas..."
canvas = TCanvas("canvas","canvas",100,100,800,600)
legend = TLegend(0.2,0.85,0.4,0.7)
legend.SetTextSize(0.032)
legend.SetBorderSize(0)
legend.SetFillStyle(0)
gPad.SetLeftMargin(0.14); gPad.SetRightMargin(0.02)
frame1.GetYaxis().SetLabelOffset(0.008)
frame1.GetYaxis().SetTitleOffset(1.4)
frame1.GetYaxis().SetTitleSize(0.045)
frame1.GetXaxis().SetTitleSize(0.045)
frame1.Draw()
legend.AddEntry("data", "data", 'LEP')
legend.AddEntry("model", "fit", 'L')
legend.AddEntry("bkg", "background only",'L')
#legend.AddEntry("bkg2", "background only (no extended norm)",'L')
legend.Draw()
canvas.SaveAs("rooFit204.png")
class BaseFitter(object):
def __init__(self, histos, uncertainty):
self._histos = histos
self._uncertainty = uncertainty
self._make_underlying_model()
self._make_dataset()
self._make_fit_model()
self._fit()
def _make_underlying_model(self):
self.pdfs = {}
self.yields = {} # yields are plain floats
self.ryields = {} # keep track of roofit objects for memory management
h = self._histos[0]
nbins = h.GetXaxis().GetNbins()
xmin = h.GetXaxis().GetXmin()
xmax = h.GetXaxis().GetXmax()
self.xvar = RooRealVar("x", "x", xmin, xmax)
self.xvar.setBins(nbins)
self.pdfs = {}
self.hists = []
pdfs = RooArgList()
yields = RooArgList()
for histo in self._histos:
if histo.Integral() == 0:
continue
compname = histo.GetName()
hist = RooDataHist(compname, compname, RooArgList(self.xvar),
histo)
SetOwnership(hist, False)
# self.hists.append(hist)
pdf = RooHistPdf(compname, compname, RooArgSet(self.xvar), hist)
self.pdfs[compname] = pdf
# self.pdfs[compname].Print()
pdfs.add(pdf)
nevts = histo.Integral()
uncertainty = self._uncertainty
nmin = min(0, nevts * (1 - uncertainty))
nmax = nevts * (1 + uncertainty)
theyield = RooRealVar('n{}'.format(compname),
'n{}'.format(compname), nevts, nmin, nmax)
self.ryields[compname] = theyield
self.yields[compname] = nevts
yields.add(theyield)
self.underlying_model = RooAddPdf('model', 'model', pdfs, yields)
def _make_fit_model(self):
pass
def _make_dataset(self):
nevents = sum(self.yields.values())
self.data = self.underlying_model.generate(RooArgSet(self.xvar),
nevents)
def _fit(self):
self.tresult = self.underlying_model.fitTo(self.data,
RooFit.Extended(),
RooFit.Save(),
RooFit.PrintEvalErrors(-1))
def print_result(self, comps):
print 'input background uncertainty:', self._uncertainty
self.tresult.Print()
signal_percent_unc = None
for comp in comps:
yzh = self.ryields[comp]
zh_val = yzh.getVal()
zh_err = yzh.getError()
percent_unc = zh_err / zh_val * 100.
if signal_percent_unc is None:
signal_percent_unc = percent_unc
print '{} yield = {:8.2f}'.format(comp, zh_val)
print '{} uncert = {:8.2f}%'.format(comp, percent_unc)
print '{} abs uncert = {:8.2f}'.format(comp, zh_err)
return percent_unc
def draw_pdfs(self):
self.pframe = self.xvar.frame()
for pdf in self.pdfs.values():
pdf.plotOn(self.pframe)
self.pframe.Draw()
def draw_data(self):
self.mframe = self.xvar.frame()
self.data.plotOn(self.mframe)
self.underlying_model.plotOn(self.mframe)
for icomp, compname in enumerate(self.pdfs):
self.underlying_model.plotOn(self.mframe,
RooFit.Components(compname),
RooFit.LineColor(icomp + 1))
self.mframe.Draw()
gPad.Modified()
gPad.Update()
frac_combine4 = RooRealVar("frac_combine4", "fraction of gauss4 wrt gauss5", 0.7, 0., 1.)
pdf_combine4 = RooAddPdf("pdf_combine4"," gauss12 + gauss13 ", RooArgList(gauss12 , gauss13 ), RooArgList( frac_combine4 ))
#pdf_combine1.plotOn(xframe3,RooFit.LineColor(RooFit.kBlue))
#gauss12.plotOn(xframe8, RooFit.Normalization( frac_combine4.getVal() ,RooAbsReal.Relative),RooFit.LineColor(RooFit.kOrange))
#gauss13.plotOn(xframe8, RooFit.Normalization( 1-frac_combine4.getVal() ,RooAbsReal.Relative),RooFit.LineColor(RooFit.kCyan))
#pdf_combine2.plotOn(xframe8, RooFit.Normalization(1.0,RooAbsReal.Relative) ,RooFit.LineColor(RooFit.kBlue))
# generate toy MC
n_generate = 5000
data4 = pdf_combine4.generate(RooArgSet(x), n_generate )
data4_SB = RooDataSet("data4_SB", "data4 SB", RooArgSet(x), RooFit.Import( data4 ), RooFit.Cut("x<-2||x>4") )
# set range
x.setRange("signal_region",-2 ,4 )
x.setRange("left_side_band_region",-10 ,-2 )
x.setRange("right_side_band_region",4 ,10 )
# use gauss 13 to generate toy MC and cut right SB
data_gauss13 = gauss13.generate(RooArgSet(x), n_generate*(1-frac_combine4.getVal() ) )
#data_gauss13.plotOn(xframe8,RooFit.LineColor(RooFit.kGreen))
data_gauss13_right_SB = RooDataSet("data_gauss13_right_SB", "data_gauss13_right_SB", RooArgSet(x), RooFit.Import( data_gauss13 ), RooFit.Cut("x>4") )
from ROOT import RooRealVar, RooGaussian, RooChebychev, RooAddPdf, RooArgList, RooArgSet, RooFit
x = RooRealVar("x", "x", -1, 1)
# Use RooGaussian in the generation
mean = RooRealVar("mean", "mean of gaussian", 0, -1, 1)
sigma = RooRealVar("sigma", "sigma of gaussian", 0.1, -1, 1)
sig = RooGaussian("gauss", "gaussian PDF", x, mean, sigma)
# Background
a0 = RooRealVar("a0", "a0", 0.5, 0., 1.)
a1 = RooRealVar("a1", "a1", -0.2, 0., 1.)
bkg = RooChebychev("bkg", "Background", x, RooArgList(a0, a1))
bkgfrac = RooRealVar("bkgfrac", "fraction of background", 0.5, 0., 1.)
model = RooAddPdf("model", "g+a", RooArgList(bkg, sig), RooArgList(bkgfrac))
data = model.generate(RooArgSet(x), 10000)
model.fitTo(data)
vybgd = RooRealVar("nbgd", 'nbgd', ybgd, 0, 100000)
model = RooAddPdf("model", "model", RooArgList(sig, bgd),
RooArgList(vysig, vybgd))
#model = RooAddPdf("model", "model", RooArgList(sig),
# RooArgList(vysig))
c2 = TCanvas()
mframe = x.frame()
model.plotOn(mframe)
mframe.Draw()
######### data generation, parametrized
data = model.generate(RooArgSet(x), ndata)
######### fit, parametrized
result = model.fitTo(data, RooFit.Extended(), RooFit.Save())
cf_p = TCanvas('cf_p', 'fit, parametrized')
cf_p_frame = x.frame()
data.plotOn(cf_p_frame)
model.plotOn(cf_p_frame)
cf_p_frame.Draw()
######### model definition, template
# --- Build Gaussian PDF ---
signal = RooGaussian("signal", "signal PDF", mes, sigmean, sigwidth)
argpar = RooRealVar("argpar", "argus shape parameter", -20.0, -100., -1.)
background = RooArgusBG("background", "Argus PDF", mes, RooFit.RooConst(5.291),
argpar)
# --- Construct signal+background PDF ---
nsig = RooRealVar("nsig", "#signal events", 200, 0., 10000)
nbkg = RooRealVar("nbkg", "#background events", 800, 0., 10000)
model = RooAddPdf("model", "g+a", RooArgList(signal, background),
RooArgList(nsig, nbkg))
# --- Generate a toyMC sample from composite PDF ---
data = model.generate(RooArgSet(mes), 2000)
# --- Perform extended ML fit of composite PDF to toy data ---
model.fitTo(data)
# --- Plot toy data and composite PDF overlaid ---
mesframe = mes.frame()
data.plotOn(mesframe)
model.plotOn(mesframe)
model.plotOn(mesframe, RooFit.Components('background'),
RooFit.LineStyle(kDashed))
mesframe.Draw()
print 'nsig:', nsig.getValV(), '+-', nsig.getError()
print 'nbkg:', nbkg.getValV(), '+-', nbkg.getError()
def rooFit205():
print ">>> setup model signal components: gaussians..."
x = RooRealVar("x", "x", 0, 10)
mean = RooRealVar("mean", "mean of gaussians", 5)
sigma1 = RooRealVar("sigma1", "width of gaussians", 0.5)
sigma2 = RooRealVar("sigma2", "width of gaussians", 1)
sig1 = RooGaussian("sig1", "Signal component 1", x, mean, sigma1)
sig2 = RooGaussian("sig2", "Signal component 2", x, mean, sigma2)
sig1frac = RooRealVar("sig1frac", "fraction of component 1 in signal", 0.8,
0., 1.)
sig = RooAddPdf("sig", "Signal", RooArgList(sig1, sig2),
RooArgList(sig1frac))
print ">>> setup model background components: Chebychev polynomial plus exponential..."
a0 = RooRealVar("a0", "a0", 0.5, 0., 1.)
a1 = RooRealVar("a1", "a1", -0.2, 0., 1.)
bkg1 = RooChebychev("bkg1", "Background 1", x, RooArgList(a0, a1))
alpha = RooRealVar("alpha", "alpha", -1)
bkg2 = RooExponential("bkg2", "Background 2", x, alpha)
bkg1frac = RooRealVar("bkg1frac", "fraction of component 1 in background",
0.2, 0., 1.)
bkg = RooAddPdf("bkg", "Signal", RooArgList(bkg1, bkg2),
RooArgList(bkg1frac))
print ">>> sum signal and background component..."
bkgfrac = RooRealVar("bkgfrac", "fraction of background", 0.5, 0., 1.)
model = RooAddPdf("model", "g1+g2+a", RooArgList(bkg, sig),
RooArgList(bkgfrac))
print ">>> setup basic plot with data and full pdf..."
data = model.generate(RooArgSet(x), 1000) # RooDataSet
frame1 = x.frame(
Title("Component plotting of pdf=(sig1+sig2)+(bkg1+bkg2)")) # RooPlot
data.plotOn(frame1, Name("data"))
model.plotOn(frame1, Name("model"))
print ">>> clone frame for reuse..."
frame2 = frame1.Clone("frame2") # RooPlot
frame2.SetTitle("Get components with regular expressions")
print ">>> make omponent by object reference..."
# Plot multiple background components specified by object reference
# Note that specified components may occur at any level in object tree
# (e.g bkg is component of 'model' and 'sig2' is component 'sig')
argset1 = RooArgSet(bkg)
argset2 = RooArgSet(bkg2)
argset3 = RooArgSet(bkg, sig2)
model.plotOn(frame1, Components(argset1), LineColor(kRed), Name("bkgs1"))
model.plotOn(frame1, Components(argset2), LineStyle(kDashed),
LineColor(kRed), Name("bkg2"))
model.plotOn(frame1, Components(argset3), LineStyle(kDotted),
Name("bkgssig21"))
print "\n>>> make component by name / regular expressions..."
model.plotOn(frame2, Components("bkg"), LineColor(kAzure - 4),
Name("bkgs2")) # by name
model.plotOn(frame2, Components("bkg1,sig2"), LineColor(kAzure - 4),
LineStyle(kDotted), Name("bkg1sig22")) # by name
model.plotOn(frame2, Components("sig*"), LineColor(kAzure - 4),
LineStyle(kDashed), Name("sigs2")) # with regexp (wildcard *)
model.plotOn(frame2, Components("bkg1,sig*"), LineColor(kYellow),
LineStyle(kDashed),
Name("bkg1sigs2")) # with regexp (,) #Invisible()
print "\n>>> draw pfds and fits on canvas..."
canvas = TCanvas("canvas", "canvas", 100, 100, 1400, 600)
legend1 = TLegend(0.22, 0.85, 0.4, 0.65)
legend2 = TLegend(0.22, 0.85, 0.4, 0.65)
for legend in [legend1, legend2]:
legend.SetTextSize(0.032)
legend.SetBorderSize(0)
legend.SetFillStyle(0)
canvas.Divide(2)
canvas.cd(1)
gPad.SetLeftMargin(0.15)
gPad.SetRightMargin(0.02)
frame1.GetYaxis().SetLabelOffset(0.008)
frame1.GetYaxis().SetTitleOffset(1.6)
frame1.GetYaxis().SetTitleSize(0.045)
frame1.GetXaxis().SetTitleSize(0.045)
frame1.Draw()
legend1.AddEntry("data", "data", 'LEP')
legend1.AddEntry("model", "model", 'L')
legend1.AddEntry("bkgs1", "bkg", 'L')
legend1.AddEntry("bkg2", "bkg2", 'L')
legend1.AddEntry("bkgssig21", "bkg,sig2", 'L')
legend1.Draw()
canvas.cd(2)
gPad.SetLeftMargin(0.15)
gPad.SetRightMargin(0.02)
frame2.GetYaxis().SetLabelOffset(0.008)
frame2.GetYaxis().SetTitleOffset(1.6)
frame2.GetYaxis().SetTitleSize(0.045)
frame2.GetXaxis().SetTitleSize(0.045)
frame2.Draw()
legend2.AddEntry("data", "data", 'LEP')
legend2.AddEntry("model", "model", 'L')
legend2.AddEntry("bkgs2", "\"bkg\"", 'L')
legend2.AddEntry("bkg1sig22", "\"bkg1,sig2\"", 'L')
legend2.AddEntry("sigs2", "\"sig*\"", 'L')
legend2.AddEntry("bkg1sigs2", "\"bkg1,sig*\"", 'L')
legend2.Draw()
canvas.SaveAs("rooFit205.png")
def rooFit206():
print ">>> setup model signal components: gaussians..."
x = RooRealVar("x", "x", 0, 10)
mean = RooRealVar("mean", "mean of gaussians", 5)
sigma1 = RooRealVar("sigma1", "width of gaussians", 0.5)
sigma2 = RooRealVar("sigma2", "width of gaussians", 1)
sig1 = RooGaussian("sig1", "Signal component 1", x, mean, sigma1)
sig2 = RooGaussian("sig2", "Signal component 2", x, mean, sigma2)
sig1frac = RooRealVar("sig1frac", "fraction of component 1 in signal", 0.8,
0., 1.)
sig = RooAddPdf("sig", "Signal", RooArgList(sig1, sig2),
RooArgList(sig1frac))
print ">>> setup model background components: Chebychev polynomial plus exponential..."
a0 = RooRealVar("a0", "a0", 0.5, 0., 1.)
a1 = RooRealVar("a1", "a1", -0.2, 0., 1.)
bkg1 = RooChebychev("bkg1", "Background 1", x, RooArgList(a0, a1))
alpha = RooRealVar("alpha", "alpha", -1)
bkg2 = RooExponential("bkg2", "Background 2", x, alpha)
bkg1frac = RooRealVar("bkg1frac", "fraction of component 1 in background",
0.2, 0., 1.)
bkg = RooAddPdf("bkg", "Signal", RooArgList(bkg1, bkg2),
RooArgList(bkg1frac))
print ">>> sum signal and background component..."
bkgfrac = RooRealVar("bkgfrac", "fraction of background", 0.5, 0., 1.)
model = RooAddPdf("model", "g1+g2+a", RooArgList(bkg, sig),
RooArgList(bkgfrac))
print ">>> composite tree in ASCII:"
model.Print("t")
print "\n>>> write to txt file"
model.printCompactTree("", "rooFit206_asciitree.txt")
print ">>> draw composite tree graphically..."
# Print GraphViz DOT file with representation of tree
model.graphVizTree("rooFit206_model.dot")
# Make graphic output file with one of the GraphViz tools
# (freely available from www.graphviz.org)
#
# 'Top-to-bottom graph'
# unix> dot -Tgif -o rooFit206_model_dot.gif rooFit206_model.dot
#
# 'Spring-model graph'
# unix> fdp -Tgif -o rooFit206_model_fdp.gif rooFit206_model.dot
print ">>> plot everything..."
data = model.generate(RooArgSet(x), 1000) # RooDataSet
frame1 = x.frame(
Title("Component plotting of pdf=(sig1+sig2)+(bkg1+bkg2)")) # RooPlot
data.plotOn(frame1, Name("data"), Binning(40))
model.plotOn(frame1, Name("model"))
argset1 = RooArgSet(bkg)
argset2 = RooArgSet(bkg2)
argset3 = RooArgSet(bkg, sig2)
model.plotOn(frame1, Components(argset1), LineColor(kRed), Name("bkg"))
model.plotOn(frame1, Components(argset2), LineStyle(kDashed),
LineColor(kRed), Name("bkg2"))
model.plotOn(frame1, Components(argset3), LineStyle(kDotted),
Name("bkgsig2"))
print "\n>>> draw pfds and fits on canvas..."
canvas = TCanvas("canvas", "canvas", 100, 100, 800, 600)
legend = TLegend(0.22, 0.85, 0.4, 0.65)
legend.SetTextSize(0.032)
legend.SetBorderSize(0)
legend.SetFillStyle(0)
gPad.SetLeftMargin(0.15)
gPad.SetRightMargin(0.02)
frame1.GetYaxis().SetLabelOffset(0.008)
frame1.GetYaxis().SetTitleOffset(1.6)
frame1.GetYaxis().SetTitleSize(0.045)
frame1.GetXaxis().SetTitleSize(0.045)
frame1.Draw()
legend.AddEntry("data", "data", 'LEP')
legend.AddEntry("model", "model", 'L')
legend.AddEntry("bkg", "bkg", 'L')
legend.AddEntry("bkg2", "bkg2", 'L')
legend.AddEntry("bkgsig2", "bkg,sig2", 'L')
legend.Draw()
canvas.SaveAs("rooFit206.png")
def rooFit201():
print ">>> setup model component: gaussian signals and Chebychev polynomial background..."
x = RooRealVar("x","x",0,11)
mean = RooRealVar("mean","mean of gaussians",5)
sigma1 = RooRealVar("sigma1","width of gaussians",0.5)
sigma2 = RooRealVar("sigma2","width of gaussians",1)
sig1 = RooGaussian("sig1","Signal component 1",x,mean,sigma1)
sig2 = RooGaussian("sig2","Signal component 2",x,mean,sigma2)
a0 = RooRealVar("a0","a0",0.5,0.,1.)
a1 = RooRealVar("a1","a1",-0.2,0.,1.)
bkg = RooChebychev("bkg","Background",x,RooArgList(a0,a1))
print ">>>\n>>> METHOD 1 - Two RooAddPdfs"
print ">>> add signal components..."
# Sum the signal components into a composite signal p.d.f.
sig1frac = RooRealVar("sig1frac","fraction of component 1 in signal",0.8,0.,1.)
sig = RooAddPdf("sig","Signal",RooArgList(sig1,sig2),RooArgList(sig1frac))
print ">>> add signal and background..."
# Sum the composite signal and background
bkgfrac = RooRealVar("bkgfrac","fraction of background",0.5,0.,1.)
model = RooAddPdf("model","g1+g2+a",RooArgList(bkg,sig),RooArgList(bkgfrac))
print ">>> sample, fit and plot model..."
data = model.generate(RooArgSet(x),1000) # RooDataSet
model.fitTo(data)
frame1 = x.frame(Title("Example of composite pdf=(sig1+sig2)+bkg")) # RooPlot
data.plotOn(frame1,Binning(50),Name("data"))
model.plotOn(frame1,Name("model"))
# Overlay the background component of model with a dashed line
argset1 = RooArgSet(bkg)
model.plotOn(frame1,Components(argset1),LineWidth(2),Name("bkg")) #,LineStyle(kDashed)
# Overlay the background+sig2 components of model with a dotted line
argset2 = RooArgSet(bkg,sig2)
model.plotOn(frame1,Components(argset2),LineWidth(2),LineStyle(kDashed),LineColor(kAzure-4),Name("bkgsig2")) #,LineStyle(kDotted)
print "\n>>> structure of composite pdf:"
model.Print("t") # "tree" mode
print "\n>>> parameters:"
params = model.getVariables() # RooArgSet
params.Print("v")
params.Print()
print "\n>>> params.find(\"...\").getVal():"
print ">>> sigma1 = %.2f" % params.find("sigma1").getVal()
print ">>> sigma2 = %.2f" % params.find("sigma2").getVal()
print ">>> bkgfrac = %5.2f" % params.find("bkgfrac").getVal()
print ">>> sig1frac = %5.2f" % params.find("sig1frac").getVal()
print ">>>\n>>> components:"
comps = model.getComponents() # RooArgSet
sig = comps.find("sig") # RooAbsArg
sigVars = sig.getVariables() # RooArgSet
sigVars.Print()
print ">>>\n>>> METHOD 2 - One RooAddPdf with recursive fractions"
# Construct sum of models on one go using recursive fraction interpretations
# model2 = bkg + (sig1 + sig2)
model2 = RooAddPdf("model","g1+g2+a",RooArgList(bkg,sig1,sig2),RooArgList(bkgfrac,sig1frac),kTRUE)
# NB: Each coefficient is interpreted as the fraction of the
# left-hand component of the i-th recursive sum, i.e.
# sum4 = A + ( B + ( C + D ) )
# with fraction fA, fB and fC expands to
# sum4 = fA*A + (1-fA)*(fB*B + (1-fB)*(fC*C + (1-fC)*D))
print ">>> plot recursive addition model..."
argset3 = RooArgSet(bkg,sig2)
model2.plotOn(frame1,LineColor(kRed),LineStyle(kDashDotted),LineWidth(3),Name("model2"))
model2.plotOn(frame1,Components(argset3),LineColor(kMagenta),LineStyle(kDashDotted),LineWidth(3),Name("bkgsig22"))
model2.Print("t")
print ">>> draw pdfs and fits on canvas..."
canvas = TCanvas("canvas","canvas",100,100,800,600)
legend = TLegend(0.57,0.87,0.95,0.65)
legend.SetTextSize(0.030)
legend.SetBorderSize(0)
legend.SetFillStyle(0)
gPad.SetLeftMargin(0.14); gPad.SetRightMargin(0.02)
frame1.GetYaxis().SetLabelOffset(0.008)
frame1.GetYaxis().SetTitleOffset(1.4)
frame1.GetYaxis().SetTitleSize(0.045)
frame1.GetXaxis().SetTitleSize(0.045)
frame1.Draw()
legend.AddEntry("data", "data", 'LEP')
legend.AddEntry("model", "composite model", 'L')
legend.AddEntry("model2", "composite model (method 2)", 'L')
legend.AddEntry("bkg", "background only", 'L')
legend.AddEntry("bkgsig2", "background + signal 2", 'L')
legend.AddEntry("bkgsig22","background + signal 2 (method 2)",'L')
legend.Draw()
canvas.SaveAs("rooFit201.png")
def rooFit202():
print ">>> setup model component: gaussian signals and Chebychev polynomial background..."
x = RooRealVar("x", "x", 0, 10)
mean = RooRealVar("mean", "mean of gaussian", 5)
sigma1 = RooRealVar("sigma1", "width of gaussian", 0.5)
sigma2 = RooRealVar("sigma2", "width of gaussian", 1.0)
sig1 = RooGaussian("sig1", "Signal component 1", x, mean, sigma1)
sig2 = RooGaussian("sig2", "Signal component 2", x, mean, sigma2)
a0 = RooRealVar("a0", "a0", 0.5, 0., 1.)
a1 = RooRealVar("a1", "a1", -0.2, 0., 1.)
bkg = RooChebychev("bkg", "Background", x, RooArgList(a0, a1))
# Sum the signal components into a composite signal p.d.f.
sig1frac = RooRealVar("sig1frac", "fraction of component 1 in signal", 0.8,
0., 1.)
sig = RooAddPdf("sig", "Signal", RooArgList(sig1, sig2),
RooArgList(sig1frac))
print ">>>\n>>> METHOD 1"
print ">>> construct extended composite model..."
# Sum the composite signal and background into an extended pdf nsig*sig+nbkg*bkg
nsig = RooRealVar("nsig", "number of signal events", 500, 0., 10000)
nbkg = RooRealVar("nbkg", "number of background events", 500, 0, 10000)
model = RooAddPdf("model", "(g1+g2)+a", RooArgList(bkg, sig),
RooArgList(nbkg, nsig))
print ">>> sample, fit and plot extended model...\n"
# Generate a data sample of expected number events in x from model
# nsig + nbkg = model.expectedEvents()
# NOTE: since the model predicts a specific number events, one can
# omit the requested number of events to be generated
# Introduce Poisson fluctuation with Extended(kTRUE)
data = model.generate(RooArgSet(x), Extended(kTRUE)) # RooDataSet
# Fit model to data, extended ML term automatically included
# NOTE: Composite extended pdfs can only be successfully fit if the extended likelihood
# term -log(Poisson(Nobs,Nexp)) is included in the minimization because they have
# one extra degree of freedom in their parameterization that is constrained by
# this extended term. If a pdf is capable of calculating an extended term (i.e.
# any extended RooAddPdf), the extended term is AUTOMATICALLY included in the
# likelihood calculation. Override this behaviour with Extended():
# Extended(kTRUE) ADD extended likelihood term
# Extended(kFALSE) DO NOT ADD extended likelihood
#model.fitTo(data,Extended(kTRUE))
model.fitTo(data)
print "\n>>> plot data, model and model components..."
# Plot data and PDF overlaid, use expected number of events for pdf projection
# normalization, rather than observed number of events, data.numEntries()
frame1 = x.frame(Title("extended ML fit example")) # RooPlot
data.plotOn(frame1, Binning(30), Name("data"))
model.plotOn(frame1, Normalization(1.0, RooAbsReal.RelativeExpected),
Name("model"))
# Overlay the background components of model
# NOTE: By default, the pdf is normalized to event count of the last dataset added
# to the plot frame. Use "RelativeExpected" to normalize to the expected
# event count of the pdf instead
argset1 = RooArgSet(bkg)
argset2 = RooArgSet(sig1)
argset3 = RooArgSet(sig2)
argset4 = RooArgSet(bkg, sig2)
model.plotOn(frame1, Components(argset1), LineStyle(kDashed),
LineColor(kBlue),
Normalization(1.0, RooAbsReal.RelativeExpected), Name("bkg"))
#model.plotOn(frame1,Components(argset1),LineStyle(kDashed),LineColor(kBlue), Name("bkg2"))
model.plotOn(frame1, Components(argset2), LineStyle(kDotted),
LineColor(kMagenta),
Normalization(1.0, RooAbsReal.RelativeExpected), Name("sig1"))
model.plotOn(frame1, Components(argset3), LineStyle(kDotted),
LineColor(kPink),
Normalization(1.0, RooAbsReal.RelativeExpected), Name("sig2"))
model.plotOn(frame1, Components(argset4), LineStyle(kDashed),
LineColor(kAzure - 4),
Normalization(1.0, RooAbsReal.RelativeExpected),
Name("bkgsig2"))
print "\n>>> structure of composite pdf:"
model.Print("t") # "tree" mode
print "\n>>> parameters:"
params = model.getVariables() # RooArgSet
params.Print("v")
params.Print()
print "\n>>> params.find(\"...\").getVal():"
print ">>> sigma1 = %.2f" % params.find("sigma1").getVal()
print ">>> sigma2 = %.2f" % params.find("sigma2").getVal()
print ">>> nsig = %6.2f, sig1frac = %5.2f" % (
params.find("nsig").getVal(), params.find("sig1frac").getVal())
print ">>> nbkg = %6.2f" % params.find("nbkg").getVal()
print ">>>\n>>> components:"
comps = model.getComponents() # RooArgSet
sig = comps.find("sig") # RooAbsArg
sigVars = sig.getVariables() # RooArgSet
sigVars.Print()
print ">>>\n>>> METHOD 2"
print ">>> construct extended components first..."
# Associated nsig/nbkg as expected number of events with sig/bkg
nsig = RooRealVar("nsig", "number of signal events", 500, 0., 10000)
nbkg = RooRealVar("nbkg", "number of background events", 500, 0, 10000)
esig = RooExtendPdf("esig", "extended signal pdf", sig, nsig)
ebkg = RooExtendPdf("ebkg", "extended background pdf", bkg, nbkg)
print ">>> sum extended components without coefficients..."
# Construct sum of two extended p.d.f. (no coefficients required)
model2 = RooAddPdf("model2", "(g1+g2)+a", RooArgList(ebkg, esig))
# METHOD 2 is functionally completely equivalent to METHOD 1.
# Its advantage is that the yield parameter is associated to the shape pdf
# directly, while in METHOD 1 the association is made after constructing
# a RooAddPdf. Also, class RooExtendPdf offers extra functionality to
# interpret event counts in a different range.
print ">>> plot model..."
model2.plotOn(frame1, LineStyle(kDashed), LineColor(kRed),
Normalization(1.0, RooAbsReal.RelativeExpected),
Name("model2"))
print ">>> draw on canvas..."
canvas = TCanvas("canvas", "canvas", 100, 100, 800, 600)
legend = TLegend(0.2, 0.85, 0.4, 0.65)
legend.SetTextSize(0.032)
legend.SetBorderSize(0)
legend.SetFillStyle(0)
gPad.SetLeftMargin(0.14)
gPad.SetRightMargin(0.02)
frame1.GetYaxis().SetLabelOffset(0.008)
frame1.GetYaxis().SetTitleOffset(1.4)
frame1.GetYaxis().SetTitleSize(0.045)
frame1.GetXaxis().SetTitleSize(0.045)
frame1.Draw()
legend.AddEntry("data", "data", 'LEP')
legend.AddEntry("model", "composite model", 'L')
legend.AddEntry("model2", "composite model (method 2)", 'L')
legend.AddEntry("bkg", "background only", 'L')
#legend.AddEntry("bkg2", "background only (no extended norm)", 'L')
legend.AddEntry("sig1", "signal 1", 'L')
legend.AddEntry("sig2", "signal 2", 'L')
legend.AddEntry("bkgsig2", "background + signal 2", 'L')
legend.Draw()
canvas.SaveAs("rooFit202.png")
class BaseFitter(object):
def __init__(self, plot):
assert (isinstance(plot, DataMCPlot))
self.plot = plot
self._make_underlying_model()
self._make_dataset()
self._make_fit_model()
self._fit()
def _make_underlying_model(self):
self.pdfs = {}
self.yields = {} # yields are plain floats
self.ryields = {} # keep track of roofit objects for memory management
nbins, xmin, xmax = self.plot.histos[0].GetBinning()
self.xvar = RooRealVar("x", "x", xmin, xmax)
self.xvar.setBins(nbins)
self.pdfs = {}
self.hists = []
pdfs = RooArgList()
yields = RooArgList()
for compname, comp in self.plot.histosDict.iteritems():
print compname
assert (isinstance(comp, Histogram))
hist = RooDataHist(compname, compname, RooArgList(self.xvar),
comp.weighted)
SetOwnership(hist, False)
# self.hists.append(hist)
pdf = RooHistPdf(compname, compname, RooArgSet(self.xvar), hist)
self.pdfs[compname] = pdf
self.pdfs[compname].Print()
pdfs.add(pdf)
nevts = comp.Integral(xmin=xmin, xmax=xmax)
theyield = RooRealVar('n{}'.format(compname),
'n{}'.format(compname), nevts, 0, 50000)
self.ryields[compname] = theyield
self.yields[compname] = nevts
yields.add(theyield)
self.underlying_model = RooAddPdf('model', 'model', pdfs, yields)
def _make_fit_model(self):
pass
def _make_dataset(self):
nevents = sum(self.yields.values())
self.data = self.underlying_model.generate(RooArgSet(self.xvar),
nevents)
def _fit(self):
self.tresult = self.underlying_model.fitTo(self.data,
RooFit.Extended(),
RooFit.Save())
self.tresult.Print()
def draw_pdfs(self):
self.pframe = self.xvar.frame()
for pdf in self.pdfs.values():
pdf.plotOn(self.pframe)
self.pframe.Draw()
def draw_data(self):
self.canvas_data = TCanvas()
self.mframe = self.xvar.frame()
self.data.plotOn(self.mframe)
self.underlying_model.plotOn(self.mframe)
for icomp, compname in enumerate(self.pdfs):
self.underlying_model.plotOn(self.mframe,
RooFit.Components(compname),
RooFit.LineColor(icomp + 1))
self.mframe.Draw()
class BaseFitter(object):
def __init__(self, plot):
assert (isinstance(plot, DataMCPlot))
self.plot = plot
self._make_underlying_model()
self._make_dataset()
self._make_fit_model()
self._fit()
def _make_underlying_model(self):
self.pdfs = {}
self.yields = {} # yields are plain floats
self.ryields = {} # keep track of roofit objects for memory management
nbins, xmin, xmax = self.plot.histos[0].GetBinning()
self.xvar = RooRealVar("x", "x", xmin, xmax)
self.xvar.setBins(nbins)
self.pdfs = {}
self.hists = []
pdfs = RooArgList()
yields = RooArgList()
for compname, comp in self.plot.histosDict.iteritems():
if comp.weighted.Integral() == 0:
continue
assert (isinstance(comp, Histogram))
hist = RooDataHist(compname, compname, RooArgList(self.xvar),
comp.weighted)
SetOwnership(hist, False)
# self.hists.append(hist)
pdf = RooHistPdf(compname, compname, RooArgSet(self.xvar), hist)
self.pdfs[compname] = pdf
# self.pdfs[compname].Print()
pdfs.add(pdf)
nevts = comp.Integral(xmin=xmin, xmax=xmax)
nmin = min(0, nevts * (1 - comp.uncertainty))
nmax = nevts * (1 + comp.uncertainty)
theyield = RooRealVar('n{}'.format(compname),
'n{}'.format(compname), nevts, nmin, nmax)
self.ryields[compname] = theyield
self.yields[compname] = nevts
yields.add(theyield)
self.underlying_model = RooAddPdf('model', 'model', pdfs, yields)
def _make_fit_model(self):
pass
def _make_dataset(self):
nevents = sum(self.yields.values())
self.data = self.underlying_model.generate(RooArgSet(self.xvar),
nevents)
def _fit(self):
self.tresult = self.underlying_model.fitTo(self.data,
RooFit.Extended(),
RooFit.Save(),
RooFit.PrintEvalErrors(-1))
def print_result(self):
self.tresult.Print()
yzh = self.ryields['ZH']
zh_val = yzh.getVal()
zh_err = yzh.getError()
percent_unc = zh_err / zh_val * 100.
print 'ZH yield = {:8.2f}'.format(zh_val)
print 'ZH uncert = {:8.2f}%'.format(percent_unc)
return percent_unc
def draw_pdfs(self):
self.pframe = self.xvar.frame()
for pdf in self.pdfs.values():
pdf.plotOn(self.pframe)
self.pframe.Draw()
def draw_data(self):
self.mframe = self.xvar.frame()
self.data.plotOn(self.mframe)
self.underlying_model.plotOn(self.mframe)
for icomp, compname in enumerate(self.pdfs):
self.underlying_model.plotOn(self.mframe,
RooFit.Components(compname),
RooFit.LineColor(icomp + 1))
self.mframe.Draw()
def fillWorkspace(workspace):
print ">>> setup model components..."
x = RooRealVar("x", "x", 0, 10)
mean = RooRealVar("mean", "mean of gaussians", 5, 0, 10)
sigma1 = RooRealVar("sigma1", "width of gaussians", 0.5)
sigma2 = RooRealVar("sigma2", "width of gaussians", 1)
sig1 = RooGaussian("sig1", "Signal component 1", x, mean, sigma1)
sig2 = RooGaussian("sig2", "Signal component 2", x, mean, sigma2)
a0 = RooRealVar("a0", "a0", 0.5, 0., 1.)
a1 = RooRealVar("a1", "a1", -0.2, 0., 1.)
bkg = RooChebychev("bkg", "Background", x, RooArgList(a0, a1))
print ">>> sum model components..."
sig1frac = RooRealVar("sig1frac", "fraction of component 1 in signal", 0.8,
0., 1.)
sig = RooAddPdf("sig", "Signal", RooArgList(sig1, sig2),
RooArgList(sig1frac))
bkgfrac = RooRealVar("bkgfrac", "fraction of background", 0.5, 0., 1.)
model = RooAddPdf("model", "g1+g2+a", RooArgList(bkg, sig),
RooArgList(bkgfrac))
print ">>> import model into workspace..."
getattr(workspace, 'import')(model) # import model and all its components
#workspace.import(model) # causes synthax error in python
print "\n>>> encode definition of parameters and observables in workspace..."
# Define named sets "parameters" and "observables", which list which variables should
# be considered parameters and observables by the users convention
#
# Variables appearing in sets _must_ live in the workspace already, or the autoImport
# flag of defineSet must be set to import them on the fly. Named sets contain only
# references to the original variables, therefore the value of observables in named
# sets already reflect their 'current' value
params = model.getParameters(RooArgSet(x)) # RooArgSet
workspace.defineSet("parameters", RooArgSet(params))
workspace.defineSet("observables", RooArgSet(x))
# Encode reference value for parameters in workspace:
# Define a parameter 'snapshot' in the pdf
# Unlike a named set, a parameter snapshot stores an independent set of values for
# a given set of variables in the workspace. The values can be stored and reloaded
# into the workspace variable objects using the loadSnapshot() and saveSnapshot()
# methods. A snapshot saves the value of each variable, any errors that are stored
# with it as well as the 'Constant' flag that is used in fits to determine if a
# parameter is kept fixed or not.
print ">>> generate and fit data..."
# Do a dummy fit to a (supposedly) reference dataset here and store the results
# of that fit into a snapshot
refData = model.generate(RooArgSet(x), 10000) # RooDataSet
model.fitTo(refData, PrintLevel(-1))
print "\n>>> save fit results into a snapshot in the workspace..."
# The kTRUE flag imports the values of the objects in (*params) into the workspace
# If not set, the present values of the workspace parameters objects are stored
workspace.saveSnapshot("reference_fit", params, kTRUE)
print ">>> make another fit with the signal component forced to zero..."
bkgfrac.setVal(1)
bkgfrac.setConstant(kTRUE)
bkgfrac.removeError()
model.fitTo(refData, PrintLevel(-1))
print "\n>>> save new fit parameters in different snapshot..."
workspace.saveSnapshot("reference_fit_bkgonly", params, kTRUE)
