We demonstrate improved recovery from disallowed parameters. For this, we use a polynomial PDF of the form
\[
\mathrm{Pol2} = \mathcal{N} \left( c + a_1 \cdot x + a_2 \cdot x^2 + 0.01 \cdot x^3 \right),
\]
where \( \mathcal{N} \) 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.
[#1] INFO:Fitting -- RooAbsPdf::fitTo(pol3_over_pol3_Int[x]) fixing normalization set for coefficient determination to observables in data
[#1] INFO:Fitting -- using CPU computation library compiled with -mavx512
[#1] INFO:Fitting -- RooAddition::defaultErrorLevel(nll_pol3_over_pol3_Int[x]_pol3Data) Summation contains a RooNLLVar, using its error level
[#1] INFO:Minimization -- RooAbsMinimizerFcn::setOptimizeConst: activating const optimization
[#0] ERROR:Minimization -- RooMinimizer: all function calls during minimization gave invalid NLL values!
[#0] ERROR:Minimization -- RooMinimizer::calculateHessErrors() Error when calculating Hessian
[#0] ERROR:Minimization -- RooMinimizer: all function calls during minimization gave invalid NLL values!
[#1] INFO:Minimization -- RooAbsMinimizerFcn::setOptimizeConst: deactivating const optimization
[#0] ERROR:Eval -- RooAbsReal::logEvalError(pol3) evaluation error,
origin : RooPolynomial::pol3[ x=x coefList=(a1,a2,a3) ]
message : p.d.f normalization integral is zero or negative: -2220.000000
server values: x=x=0, coefList=(a1 = 10 +/- 0,a2 = -1 +/- 0,a3 = 0.01)
-------------- Starting second fit ---------------
[#1] INFO:Fitting -- RooAbsPdf::fitTo(pol3_over_pol3_Int[x]) fixing normalization set for coefficient determination to observables in data
[#1] INFO:Fitting -- RooAddition::defaultErrorLevel(nll_pol3_over_pol3_Int[x]_pol3Data) Summation contains a RooNLLVar, using its error level
[#1] INFO:Minimization -- RooAbsMinimizerFcn::setOptimizeConst: activating const optimization
Minuit2Minimizer: Minimize with max-calls 1000 convergence for edm < 1 strategy 1
Minuit2Minimizer : Valid minimum - status = 0
FVAL = -1002.22625939860154
Edm = 1.70291335762746681e-07
Nfcn = 245
a1 = -0.49816 +/- 0.0227243 (limited)
a2 = 0.198318 +/- 0.00564929 (limited)
[#1] INFO:Minimization -- RooAbsMinimizerFcn::setOptimizeConst: deactivating const optimization
RooFitResult: minimized FCN value: 0, estimated distance to minimum: 0
covariance matrix quality: Not calculated at all
Status : MINIMIZE=-1 HESSE=302
Floating Parameter FinalValue +/- Error
-------------------- --------------------------
a1 1.0000e+01 +/- 0.00e+00
a2 -1.0000e+00 +/- 0.00e+00
Without recovery, the fitter encountered 23 invalid function values. The parameters are unchanged.
RooFitResult: minimized FCN value: 29650.9, estimated distance to minimum: 1.70451e-07
covariance matrix quality: Full, accurate covariance matrix
Status : MINIMIZE=0 HESSE=0
Floating Parameter FinalValue +/- Error
-------------------- --------------------------
a1 -4.9816e-01 +/- 2.27e-02
a2 1.9832e-01 +/- 5.65e-03
With recovery, the fitter encountered 23 invalid function values, but the parameters are fitted.