doc/v620/rf610__visualerror_8py.html

import ROOT


# Setup example fit

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


# Create sum of two Gaussians p.d.f. with factory

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


m = ROOT.RooRealVar("m", "m", 0, -10, 10)

s = ROOT.RooRealVar("s", "s", 2, 1, 50)

sig = ROOT.RooGaussian("sig", "sig", x, m, s)


m2 = ROOT.RooRealVar("m2", "m2", -1, -10, 10)

s2 = ROOT.RooRealVar("s2", "s2", 6, 1, 50)

bkg = ROOT.RooGaussian("bkg", "bkg", x, m2, s2)


fsig = ROOT.RooRealVar("fsig", "fsig", 0.33, 0, 1)

model = ROOT.RooAddPdf("model", "model", ROOT.RooArgList(

    sig, bkg), ROOT.RooArgList(fsig))


# Create binned dataset

x.setBins(25)

d = model.generateBinned(ROOT.RooArgSet(x), 1000)


# Perform fit and save fit result

r = model.fitTo(d, ROOT.RooFit.Save())


# Visualize fit error

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


# Make plot frame

frame = x.frame(ROOT.RooFit.Bins(40), ROOT.RooFit.Title(

    "P.d.f with visualized 1-sigma error band"))

d.plotOn(frame)


# Visualize 1-sigma error encoded in fit result 'r' as orange band using linear error propagation

# ROOT.This results in an error band that is by construction symmetric

#

# The linear error is calculated as

# error(x) = Z* F_a(x) * Corr(a,a') F_a'(x)

#

# where     F_a(x) = [ f(x,a+da) - f(x,a-da) ] / 2,

#

#         with f(x) = the plotted curve

#              'da' = error taken from the fit result

#        Corr(a,a') = the correlation matrix from the fit result

#                Z = requested significance 'Z sigma band'

#

# The linear method is fast (required 2*N evaluations of the curve, N is the number of parameters),

# but may not be accurate in the presence of strong correlations (~>0.9) and at Z>2 due to linear and

# Gaussian approximations made

#

model.plotOn(frame, ROOT.RooFit.VisualizeError(

    r, 1), ROOT.RooFit.FillColor(ROOT.kOrange))


# Calculate error using sampling method and visualize as dashed red line.

#

# In self method a number of curves is calculated with variations of the parameter values, sampled

# from a multi-variate Gaussian p.d.f. that is constructed from the fit results covariance matrix.

# The error(x) is determined by calculating a central interval that capture N% of the variations

# for each valye of x, N% is controlled by Z (i.e. Z=1 gives N=68%). The number of sampling curves

# is chosen to be such that at least 100 curves are expected to be outside the N% interval, is minimally

# 100 (e.g. Z=1.Ncurve=356, Z=2.Ncurve=2156)) Intervals from the sampling method can be asymmetric,

# and may perform better in the presence of strong correlations, may take

# (much) longer to calculate

model.plotOn(

    frame,

    ROOT.RooFit.VisualizeError(

        r,

        1,

        ROOT.kFALSE),

    ROOT.RooFit.DrawOption("L"),

    ROOT.RooFit.LineWidth(2),

    ROOT.RooFit.LineColor(

        ROOT.kRed))


# Perform the same type of error visualization on the background component only.

# The VisualizeError() option can generally applied to _any_ kind of

# plot (components, asymmetries, etc..)

model.plotOn(

    frame, ROOT.RooFit.VisualizeError(

        r, 1), ROOT.RooFit.FillColor(

            ROOT.kOrange), ROOT.RooFit.Components("bkg"))

model.plotOn(

    frame,

    ROOT.RooFit.VisualizeError(

        r,

        1,

        ROOT.kFALSE),

    ROOT.RooFit.DrawOption("L"),

    ROOT.RooFit.LineWidth(2),

    ROOT.RooFit.LineColor(

        ROOT.kRed),

    ROOT.RooFit.Components("bkg"),

    ROOT.RooFit.LineStyle(

        ROOT.kDashed))


# Overlay central value

model.plotOn(frame)

model.plotOn(frame, ROOT.RooFit.Components("bkg"),

             ROOT.RooFit.LineStyle(ROOT.kDashed))

d.plotOn(frame)

frame.SetMinimum(0)


# Visualize partial fit error

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


# Make plot frame

frame2 = x.frame(ROOT.RooFit.Bins(40), ROOT.RooFit.Title(

    "Visualization of 2-sigma partial error from (m,m2)"))


# Visualize partial error. For partial error visualization the covariance matrix is first reduced as follows

#        ___                   -1

# Vred = V22  = V11 - V12 * V22   * V21

#

# Where V11,V12,V21, represent a block decomposition of the covariance matrix into observables that

# are propagated (labeled by index '1') and that are not propagated (labeled by index '2'), V22bar

# is the Shur complement of V22, as shown above

#

# (Note that Vred is _not_ a simple sub-matrix of V)


# Propagate partial error due to shape parameters (m,m2) using linear and

# sampling method

model.plotOn(frame2, ROOT.RooFit.VisualizeError(

    r, ROOT.RooArgSet(m, m2), 2), ROOT.RooFit.FillColor(ROOT.kCyan))

model.plotOn(frame2, ROOT.RooFit.Components("bkg"), ROOT.RooFit.VisualizeError(

    r, ROOT.RooArgSet(m, m2), 2), ROOT.RooFit.FillColor(ROOT.kCyan))


model.plotOn(frame2)

model.plotOn(frame2, ROOT.RooFit.Components("bkg"),

             ROOT.RooFit.LineStyle(ROOT.kDashed))

frame2.SetMinimum(0)


# Make plot frame

frame3 = x.frame(ROOT.RooFit.Bins(40), ROOT.RooFit.Title(

    "Visualization of 2-sigma partial error from (s,s2)"))


# Propagate partial error due to yield parameter using linear and sampling

# method

model.plotOn(frame3, ROOT.RooFit.VisualizeError(

    r, ROOT.RooArgSet(s, s2), 2), ROOT.RooFit.FillColor(ROOT.kGreen))

model.plotOn(frame3, ROOT.RooFit.Components("bkg"), ROOT.RooFit.VisualizeError(

    r, ROOT.RooArgSet(s, s2), 2), ROOT.RooFit.FillColor(ROOT.kGreen))


model.plotOn(frame3)

model.plotOn(frame3, ROOT.RooFit.Components("bkg"),

             ROOT.RooFit.LineStyle(ROOT.kDashed))

frame3.SetMinimum(0)


# Make plot frame

frame4 = x.frame(ROOT.RooFit.Bins(40), ROOT.RooFit.Title(

    "Visualization of 2-sigma partial error from fsig"))


# Propagate partial error due to yield parameter using linear and sampling

# method

model.plotOn(frame4, ROOT.RooFit.VisualizeError(

    r, ROOT.RooArgSet(fsig), 2), ROOT.RooFit.FillColor(ROOT.kMagenta))

model.plotOn(frame4, ROOT.RooFit.Components("bkg"), ROOT.RooFit.VisualizeError(

    r, ROOT.RooArgSet(fsig), 2), ROOT.RooFit.FillColor(ROOT.kMagenta))


model.plotOn(frame4)

model.plotOn(frame4, ROOT.RooFit.Components("bkg"),

             ROOT.RooFit.LineStyle(ROOT.kDashed))

frame4.SetMinimum(0)


c = ROOT.TCanvas("rf610_visualerror", "rf610_visualerror", 800, 800)

c.Divide(2, 2)

c.cd(1)

ROOT.gPad.SetLeftMargin(0.15)

frame.GetYaxis().SetTitleOffset(1.4)

frame.Draw()

c.cd(2)

ROOT.gPad.SetLeftMargin(0.15)

frame2.GetYaxis().SetTitleOffset(1.6)

frame2.Draw()

c.cd(3)

ROOT.gPad.SetLeftMargin(0.15)

frame3.GetYaxis().SetTitleOffset(1.6)

frame3.Draw()

c.cd(4)

ROOT.gPad.SetLeftMargin(0.15)

frame4.GetYaxis().SetTitleOffset(1.6)

frame4.Draw()


c.SaveAs("rf610_visualerror.png")