{
"cells": [
{
"cell_type": "markdown",
"id": "799c83ca",
"metadata": {},
"source": [
"# rf612_recoverFromInvalidParameters\n",
"Likelihood and minimization: Recover from regions where the function is not defined.\n",
"\n",
"We demonstrate improved recovery from disallowed parameters. For this, we use a polynomial PDF of the form\n",
" \\mathrm{Pol2} = \\mathcal{N} \\left( c + a_1 \\cdot x + a_2 \\cdot x^2 + 0.01 \\cdot x^3 \\right),\n",
"where \\f$ \\mathcal{N} \\f$ is a normalisation factor. Unless the parameters are chosen carefully,\n",
"this function can be negative, and hence, it cannot be used as a PDF. In this case, RooFit passes\n",
"an error to the minimiser, which might try to recover.\n",
"\n",
"\n",
"\n",
"\n",
"**Author:** Harshal Shende, Stephan Hageboeck (C++ version) \n",
"This notebook tutorial was automatically generated with ROOTBOOK-izer from the macro found in the ROOT repository on Tuesday, May 19, 2026 at 08:33 PM."
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "9b5d90e1",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:33:40.599075Z",
"iopub.status.busy": "2026-05-19T20:33:40.598961Z",
"iopub.status.idle": "2026-05-19T20:33:41.540273Z",
"shell.execute_reply": "2026-05-19T20:33:41.539466Z"
}
},
"outputs": [],
"source": [
"import ROOT"
]
},
{
"cell_type": "markdown",
"id": "958b3d7e",
"metadata": {},
"source": [
"Create a fit model:\n",
"The polynomial is notoriously unstable, because it can quickly go negative.\n",
"Since PDFs need to be positive, one often ends up with an unstable fit model."
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "9e9b85bb",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:33:41.542423Z",
"iopub.status.busy": "2026-05-19T20:33:41.542292Z",
"iopub.status.idle": "2026-05-19T20:33:41.797201Z",
"shell.execute_reply": "2026-05-19T20:33:41.796465Z"
}
},
"outputs": [],
"source": [
"x = ROOT.RooRealVar(\"x\", \"x\", -15, 15)\n",
"a1 = ROOT.RooRealVar(\"a1\", \"a1\", -0.5, -10.0, 20.0)\n",
"a2 = ROOT.RooRealVar(\"a2\", \"a2\", 0.2, -10.0, 20.0)\n",
"a3 = ROOT.RooRealVar(\"a3\", \"a3\", 0.01)\n",
"pdf = ROOT.RooPolynomial(\"pol3\", \"c + a1 * x + a2 * x*x + 0.01 * x*x*x\", x, [a1, a2, a3])"
]
},
{
"cell_type": "markdown",
"id": "a0a443a8",
"metadata": {},
"source": [
"Create toy data with all-positive coefficients:"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "be8e738f",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:33:41.799319Z",
"iopub.status.busy": "2026-05-19T20:33:41.799194Z",
"iopub.status.idle": "2026-05-19T20:33:41.945381Z",
"shell.execute_reply": "2026-05-19T20:33:41.944652Z"
}
},
"outputs": [],
"source": [
"data = pdf.generate(x, 10000)"
]
},
{
"cell_type": "markdown",
"id": "34757ae0",
"metadata": {},
"source": [
"For plotting.\n",
"We create pointers to the plotted objects. We want these objects to leak out of the function,\n",
"so we can still see them after it returns."
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "2fed161b",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:33:41.947395Z",
"iopub.status.busy": "2026-05-19T20:33:41.947267Z",
"iopub.status.idle": "2026-05-19T20:33:42.119199Z",
"shell.execute_reply": "2026-05-19T20:33:42.118392Z"
}
},
"outputs": [
{
"data": {
"text/plain": [
""
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"c = ROOT.TCanvas()\n",
"frame = x.frame()\n",
"data.plotOn(frame, Name=\"data\")"
]
},
{
"cell_type": "markdown",
"id": "a6a330ac",
"metadata": {},
"source": [
"Plotting a PDF with disallowed parameters doesn't work. We would get a lot of error messages.\n",
"Therefore, we disable plotting messages in RooFit's message streams:"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "b4efaaa5",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:33:42.121002Z",
"iopub.status.busy": "2026-05-19T20:33:42.120873Z",
"iopub.status.idle": "2026-05-19T20:33:42.247732Z",
"shell.execute_reply": "2026-05-19T20:33:42.246924Z"
}
},
"outputs": [],
"source": [
"ROOT.RooMsgService.instance().getStream(0).removeTopic(ROOT.RooFit.Plotting)\n",
"ROOT.RooMsgService.instance().getStream(1).removeTopic(ROOT.RooFit.Plotting)"
]
},
{
"cell_type": "markdown",
"id": "a9362b2d",
"metadata": {},
"source": [
"RooFit before ROOT 6.24\n",
"--------------------------------\n",
"Before 6.24, RooFit wasn't able to recover from invalid parameters. The minimiser just errs around\n",
"the starting values of the parameters without finding any improvement."
]
},
{
"cell_type": "markdown",
"id": "15bb9184",
"metadata": {},
"source": [
"Set up the parameters such that the PDF would come out negative. The PDF is now undefined."
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "2e2aea80",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:33:42.249570Z",
"iopub.status.busy": "2026-05-19T20:33:42.249449Z",
"iopub.status.idle": "2026-05-19T20:33:42.357378Z",
"shell.execute_reply": "2026-05-19T20:33:42.356698Z"
}
},
"outputs": [],
"source": [
"a1.setVal(10.0)\n",
"a2.setVal(-1.0)"
]
},
{
"cell_type": "markdown",
"id": "f6c9e71d",
"metadata": {},
"source": [
"Perform a fit:"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "6c4a1531",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:33:42.359537Z",
"iopub.status.busy": "2026-05-19T20:33:42.359407Z",
"iopub.status.idle": "2026-05-19T20:33:42.589557Z",
"shell.execute_reply": "2026-05-19T20:33:42.588900Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[#1] INFO:Fitting -- RooAbsPdf::fitTo(pol3_over_pol3_Int[x]) fixing normalization set for coefficient determination to observables in data\n",
"[#1] INFO:Fitting -- using generic CPU library compiled with no vectorizations\n",
"[#1] INFO:Fitting -- Creation of NLL object took 738.062 μs\n",
"[#1] INFO:Fitting -- RooAddition::defaultErrorLevel(nll_pol3_over_pol3_Int[x]_pol3Data) Summation contains a RooNLLVar, using its error level\n",
"[#1] INFO:Minimization -- [fitFCN] No discrete parameters, performing continuous minimization only\n",
"[#0] ERROR:Minimization -- RooMinimizer: all function calls during minimization gave invalid NLL values!\n",
"[#0] ERROR:Minimization -- RooMinimizer::calculateHessErrors() Error when calculating Hessian\n",
"[#0] ERROR:Minimization -- RooMinimizer: all function calls during minimization gave invalid NLL values!\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"[#0] ERROR:Eval -- RooAbsReal::logEvalError(pol3) evaluation error, \n",
" origin : RooPolynomial::pol3[ x=x coefList=(a1,a2,a3) ]\n",
" message : p.d.f normalization integral is zero or negative: -2220.000000\n",
" server values: x=x=0, coefList=(a1 = 10 +/- 0,a2 = -1 +/- 0,a3 = 0.01)\n"
]
},
{
"data": {
"text/plain": [
""
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"fitWithoutRecovery = pdf.fitTo(\n",
" data,\n",
" Save=True,\n",
" RecoverFromUndefinedRegions=0.0, # This is how RooFit behaved prior to ROOT 6.24\n",
" PrintEvalErrors=-1, # We are expecting a lot of evaluation errors. -1 switches off printing.\n",
" PrintLevel=-1,\n",
")\n",
"\n",
"pdf.plotOn(frame, LineColor=\"r\", Name=\"noRecovery\")"
]
},
{
"cell_type": "markdown",
"id": "5eab3368",
"metadata": {},
"source": [
"RooFit since ROOT 6.24\n",
"--------------------------------\n",
"The minimiser gets information about the \"badness\" of the violation of the function definition. It uses this\n",
"to find its way out of the disallowed parameter regions."
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "5bdc7d36",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:33:42.591731Z",
"iopub.status.busy": "2026-05-19T20:33:42.591585Z",
"iopub.status.idle": "2026-05-19T20:33:42.694971Z",
"shell.execute_reply": "2026-05-19T20:33:42.694339Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"\n",
"\n",
"-------------- Starting second fit ---------------\n",
"\n",
"\n"
]
}
],
"source": [
"print(\"\\n\\n\\n-------------- Starting second fit ---------------\\n\\n\")"
]
},
{
"cell_type": "markdown",
"id": "f6c623a8",
"metadata": {},
"source": [
"Reset the parameters such that the PDF is again undefined."
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "f7aab350",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:33:42.696762Z",
"iopub.status.busy": "2026-05-19T20:33:42.696637Z",
"iopub.status.idle": "2026-05-19T20:33:42.799922Z",
"shell.execute_reply": "2026-05-19T20:33:42.799381Z"
}
},
"outputs": [],
"source": [
"a1.setVal(10.0)\n",
"a2.setVal(-1.0)"
]
},
{
"cell_type": "markdown",
"id": "c90052eb",
"metadata": {},
"source": [
"Fit again, but pass recovery information to the minimiser:"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "7fce52a9",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:33:42.802028Z",
"iopub.status.busy": "2026-05-19T20:33:42.801907Z",
"iopub.status.idle": "2026-05-19T20:33:42.937963Z",
"shell.execute_reply": "2026-05-19T20:33:42.937370Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[#1] INFO:Fitting -- RooAbsPdf::fitTo(pol3_over_pol3_Int[x]) fixing normalization set for coefficient determination to observables in data\n",
"[#1] INFO:Fitting -- Creation of NLL object took 190.681 μs\n",
"[#1] INFO:Fitting -- RooAddition::defaultErrorLevel(nll_pol3_over_pol3_Int[x]_pol3Data) Summation contains a RooNLLVar, using its error level\n",
"[#1] INFO:Minimization -- [fitFCN] No discrete parameters, performing continuous minimization only\n",
"Minuit2Minimizer: Minimize with max-calls 1000 convergence for edm < 1 strategy 1\n",
"Minuit2Minimizer : Valid minimum - status = 0\n",
"FVAL = -1002.22625947982669\n",
"Edm = 8.90543439440185486e-08\n",
"Nfcn = 245\n",
"a1\t = -0.498159\t +/- 0.0227243\t(limited)\n",
"a2\t = 0.198318\t +/- 0.00564924\t(limited)\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"Warning in : MnPosDef non-positive diagonal element in covariance matrix[ 0 ] = -13.133\n",
"Warning in : MnPosDef Added to diagonal of Error matrix a value 13.633\n",
"Warning in : DavidonErrorUpdator delgam < 0 : first derivatives increasing along search line (details in info log)\n",
"Warning in : VariableMetricBuilder Matrix not pos.def, gdel = 67.8685 > 0\n",
"Warning in : MnPosDef non-positive diagonal element in covariance matrix[ 0 ] = -0.000525791\n",
"Warning in : MnPosDef non-positive diagonal element in covariance matrix[ 1 ] = -0.00482974\n",
"Warning in : MnPosDef Added to diagonal of Error matrix a value 0.50483\n",
"Warning in : VariableMetricBuilder gdel = -51905.4\n",
"Warning in : DavidonErrorUpdator delgam < 0 : first derivatives increasing along search line (details in info log)\n",
"Warning in : VariableMetricBuilder Matrix not pos.def, gdel = 56.5625 > 0\n",
"Warning in : MnPosDef non-positive diagonal element in covariance matrix[ 1 ] = -0.00239309\n",
"Warning in : MnPosDef Added to diagonal of Error matrix a value 0.502393\n",
"Warning in : VariableMetricBuilder gdel = -15405\n",
"Warning in : DavidonErrorUpdator delgam < 0 : first derivatives increasing along search line (details in info log)\n",
"Warning in : VariableMetricBuilder Matrix not pos.def, gdel = 3573.83 > 0\n",
"Warning in : MnPosDef non-positive diagonal element in covariance matrix[ 0 ] = -1.28848e-05\n",
"Warning in : MnPosDef non-positive diagonal element in covariance matrix[ 1 ] = -2.85489e-05\n",
"Warning in : MnPosDef Added to diagonal of Error matrix a value 0.500029\n",
"Warning in : VariableMetricBuilder gdel = -5.37564e+07\n"
]
},
{
"data": {
"text/plain": [
""
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"fitWithRecovery = pdf.fitTo(\n",
" data,\n",
" Save=True,\n",
" RecoverFromUndefinedRegions=1.0, # The magnitude of the recovery information can be chosen here.\n",
" # Higher values mean more aggressive recovery.\n",
" PrintEvalErrors=-1, # We are still expecting a few evaluation errors.\n",
" PrintLevel=0,\n",
")\n",
"\n",
"pdf.plotOn(frame, LineColor=\"b\", Name=\"recovery\")"
]
},
{
"cell_type": "markdown",
"id": "299bcd40",
"metadata": {},
"source": [
"Collect results and plot.\n",
"--------------------------------\n",
"We print the two fit results, and plot the fitted curves.\n",
"The curve of the fit without recovery cannot be plotted, because the PDF is undefined if a2 < 0."
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "7f41c53f",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:33:42.939783Z",
"iopub.status.busy": "2026-05-19T20:33:42.939655Z",
"iopub.status.idle": "2026-05-19T20:33:43.205935Z",
"shell.execute_reply": "2026-05-19T20:33:43.205475Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Without recovery, the fitter encountered 23 invalid function values. The parameters are unchanged.\n",
"\n",
"With recovery, the fitter encountered 23 invalid function values, but the parameters are fitted.\n",
"\n",
"\n",
" RooFitResult: minimized FCN value: 0, estimated distance to minimum: 0\n",
" covariance matrix quality: Not calculated at all\n",
" Status : MINIMIZE=-1 HESSE=302 \n",
"\n",
" Floating Parameter FinalValue +/- Error \n",
" -------------------- --------------------------\n",
" a1 1.0000e+01 +/- 0.00e+00\n",
" a2 -1.0000e+00 +/- 0.00e+00\n",
"\n",
"\n",
" RooFitResult: minimized FCN value: 29650.9, estimated distance to minimum: 8.92102e-08\n",
" covariance matrix quality: Full, accurate covariance matrix\n",
" Status : MINIMIZE=0 HESSE=0 \n",
"\n",
" Floating Parameter FinalValue +/- Error \n",
" -------------------- --------------------------\n",
" a1 -4.9816e-01 +/- 2.27e-02\n",
" a2 1.9832e-01 +/- 5.65e-03\n",
"\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"Info in : png file rf612_recoverFromInvalidParameters.png has been created\n"
]
},
{
"data": {
"text/html": [
"\n",
"\n",
"\n",
"
\n",
"\n",
"\n",
"\n"
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fitWithoutRecovery.Print()\n",
"print(\n",
" \"Without recovery, the fitter encountered {}\".format(fitWithoutRecovery.numInvalidNLL())\n",
" + \" invalid function values. The parameters are unchanged.\\n\"\n",
")\n",
"\n",
"fitWithRecovery.Print()\n",
"print(\n",
" \"With recovery, the fitter encountered {}\".format(fitWithoutRecovery.numInvalidNLL())\n",
" + \" invalid function values, but the parameters are fitted.\\n\"\n",
")\n",
"\n",
"legend = ROOT.TLegend(0.5, 0.7, 0.9, 0.9)\n",
"legend.SetBorderSize(0)\n",
"legend.SetFillStyle(0)\n",
"legend.AddEntry(\"data\", \"Data\", \"P\")\n",
"legend.AddEntry(\"noRecovery\", \"Without recovery (cannot be plotted)\", \"L\")\n",
"legend.AddEntry(\"recovery\", \"With recovery\", \"L\")\n",
"frame.Draw()\n",
"legend.Draw()\n",
"c.Draw()\n",
"\n",
"c.SaveAs(\"rf612_recoverFromInvalidParameters.png\")"
]
},
{
"cell_type": "markdown",
"id": "593914a0",
"metadata": {},
"source": [
"Draw all canvases "
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "1cb9d312",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:33:43.207459Z",
"iopub.status.busy": "2026-05-19T20:33:43.207344Z",
"iopub.status.idle": "2026-05-19T20:33:43.322185Z",
"shell.execute_reply": "2026-05-19T20:33:43.321784Z"
}
},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"\n",
"
\n",
"\n",
"\n",
"\n"
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from ROOT import gROOT \n",
"gROOT.GetListOfCanvases().Draw()"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.12.12"
}
},
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}