rf612_recoverFromInvalidParameters.py

## \ingroup tutorial_roofit_main

## \notebook

## Likelihood and minimization: Recover from regions where the function is not defined.

##

## We demonstrate improved recovery from disallowed parameters. For this, we use a polynomial PDF of the form

## \f[

## \mathrm{Pol2} = \mathcal{N} \left( c + a_1 \cdot x + a_2 \cdot x^2 + 0.01 \cdot x^3 \right),

## \f]

## where \f$ \mathcal{N} \f$ is a normalisation factor. Unless the parameters are chosen carefully,

## this function can be negative, and hence, it cannot be used as a PDF. In this case, RooFit passes

## an error to the minimiser, which might try to recover.

##

## \macro_code

## \macro_output

##

## \date June 2021

## \author Harshal Shende, Stephan Hageboeck (C++ version)

import ROOT

# Create a fit model:

# The polynomial is notoriously unstable, because it can quickly go negative.

# Since PDFs need to be positive, one often ends up with an unstable fit model.

x = ROOT.RooRealVar("x", "x", -15, 15)

a1 = ROOT.RooRealVar("a1", "a1", -0.5, -10.0, 20.0)

a2 = ROOT.RooRealVar("a2", "a2", 0.2, -10.0, 20.0)

a3 = ROOT.RooRealVar("a3", "a3", 0.01)

pdf = ROOT.RooPolynomial("pol3", "c + a1 * x + a2 * x*x + 0.01 * x*x*x", x, [a1, a2, a3])

# Create toy data with all-positive coefficients:

data = pdf.generate(x, 10000)

# For plotting.

# We create pointers to the plotted objects. We want these objects to leak out of the function,

# so we can still see them after it returns.

c = ROOT.TCanvas()

frame = x.frame()

data.plotOn(frame, Name="data")

# Plotting a PDF with disallowed parameters doesn't work. We would get a lot of error messages.

# Therefore, we disable plotting messages in RooFit's message streams:

ROOT.RooMsgService.instance().getStream(0).removeTopic(ROOT.RooFit.Plotting)

ROOT.RooMsgService.instance().getStream(1).removeTopic(ROOT.RooFit.Plotting)

# RooFit before ROOT 6.24

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

# Before 6.24, RooFit wasn't able to recover from invalid parameters. The minimiser just errs around

# the starting values of the parameters without finding any improvement.

# Set up the parameters such that the PDF would come out negative. The PDF is now undefined.

a1.setVal(10.0)

a2.setVal(-1.0)

# Perform a fit:

fitWithoutRecovery = pdf.fitTo(

data,

Save=True,

RecoverFromUndefinedRegions=0.0, # This is how RooFit behaved prior to ROOT 6.24

PrintEvalErrors=-1, # We are expecting a lot of evaluation errors. -1 switches off printing.

PrintLevel=-1,

)

pdf.plotOn(frame, LineColor="r", Name="noRecovery")

# RooFit since ROOT 6.24

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

# The minimiser gets information about the "badness" of the violation of the function definition. It uses this

# to find its way out of the disallowed parameter regions.

print("\n\n\n-------------- Starting second fit ---------------\n\n")

# Reset the parameters such that the PDF is again undefined.

a1.setVal(10.0)

a2.setVal(-1.0)

# Fit again, but pass recovery information to the minimiser:

fitWithRecovery = pdf.fitTo(

data,

Save=True,

RecoverFromUndefinedRegions=1.0, # The magnitude of the recovery information can be chosen here.

# Higher values mean more aggressive recovery.

PrintEvalErrors=-1, # We are still expecting a few evaluation errors.

PrintLevel=0,

)

pdf.plotOn(frame, LineColor="b", Name="recovery")

# Collect results and plot.

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

# We print the two fit results, and plot the fitted curves.

# The curve of the fit without recovery cannot be plotted, because the PDF is undefined if a2 < 0.

fitWithoutRecovery.Print()

print(

"Without recovery, the fitter encountered {}".format(fitWithoutRecovery.numInvalidNLL())

+ " invalid function values. The parameters are unchanged.\n"

)

fitWithRecovery.Print()

print(

"With recovery, the fitter encountered {}".format(fitWithoutRecovery.numInvalidNLL())

+ " invalid function values, but the parameters are fitted.\n"

)

legend = ROOT.TLegend(0.5, 0.7, 0.9, 0.9)

legend.SetBorderSize(0)

legend.SetFillStyle(0)

legend.AddEntry("data", "Data", "P")

legend.AddEntry("noRecovery", "Without recovery (cannot be plotted)", "L")

legend.AddEntry("recovery", "With recovery", "L")

frame.Draw()

legend.Draw()

c.Draw()

c.SaveAs("rf612_recoverFromInvalidParameters.png")