{
"cells": [
{
"cell_type": "markdown",
"id": "dfbedf1d",
"metadata": {},
"source": [
"# rf314_paramfitrange\n",
"Multidimensional models: working with parameterized ranges in a fit.\n",
"This an example of a fit with an acceptance that changes per-event\n",
"\n",
"`pdf = exp(-t/tau)` with `t[tmin,5]`\n",
"\n",
"where `t` and `tmin` are both observables in the dataset\n",
"\n",
"\n",
"\n",
"\n",
"**Author:** Clemens Lange, Wouter Verkerke (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 08:31 PM."
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "fb125a9d",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:31:16.796989Z",
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"shell.execute_reply": "2026-05-19T20:31:17.745993Z"
}
},
"outputs": [],
"source": [
"import ROOT"
]
},
{
"cell_type": "markdown",
"id": "9e1e9e1a",
"metadata": {},
"source": [
"Define observables and decay pdf\n",
"---------------------------------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "9526c5db",
"metadata": {},
"source": [
"Declare observables"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "fa209daa",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:31:17.754182Z",
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"shell.execute_reply": "2026-05-19T20:31:17.928854Z"
}
},
"outputs": [],
"source": [
"t = ROOT.RooRealVar(\"t\", \"t\", 0, 5)\n",
"tmin = ROOT.RooRealVar(\"tmin\", \"tmin\", 0, 0, 5)"
]
},
{
"cell_type": "markdown",
"id": "82aef061",
"metadata": {},
"source": [
"Make parameterized range in t : [tmin,5]"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "f2404ae4",
"metadata": {
"collapsed": false,
"execution": {
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"shell.execute_reply": "2026-05-19T20:31:18.053576Z"
}
},
"outputs": [],
"source": [
"t.setRange(tmin, ROOT.RooFit.RooConst(t.getMax()))"
]
},
{
"cell_type": "markdown",
"id": "0f9149c6",
"metadata": {},
"source": [
"Make pdf"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "99bbe3fd",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:31:18.058502Z",
"iopub.status.busy": "2026-05-19T20:31:18.058359Z",
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"shell.execute_reply": "2026-05-19T20:31:18.179556Z"
}
},
"outputs": [],
"source": [
"tau = ROOT.RooRealVar(\"tau\", \"tau\", -1.54, -10, -0.1)\n",
"model = ROOT.RooExponential(\"model\", \"model\", t, tau)"
]
},
{
"cell_type": "markdown",
"id": "120352c4",
"metadata": {},
"source": [
"Create input data\n",
"------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "cfc0ad99",
"metadata": {},
"source": [
"Generate complete dataset without acceptance cuts (for reference)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "16832ba3",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:31:18.182323Z",
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"shell.execute_reply": "2026-05-19T20:31:18.332760Z"
}
},
"outputs": [],
"source": [
"dall = model.generate({t}, 10000)"
]
},
{
"cell_type": "markdown",
"id": "f372e6d8",
"metadata": {},
"source": [
"Generate a (fake) prototype dataset for acceptance limit values"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "de59a4db",
"metadata": {
"collapsed": false,
"execution": {
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"shell.execute_reply": "2026-05-19T20:31:18.454162Z"
}
},
"outputs": [],
"source": [
"tmp = ROOT.RooGaussian(\"gmin\", \"gmin\", tmin, 0.0, 0.5).generate({tmin}, 5000)"
]
},
{
"cell_type": "markdown",
"id": "3ee3eae7",
"metadata": {},
"source": [
"Generate dataset with t values that observe (t>tmin)"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "0d90d731",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:31:18.456926Z",
"iopub.status.busy": "2026-05-19T20:31:18.456804Z",
"iopub.status.idle": "2026-05-19T20:31:18.586345Z",
"shell.execute_reply": "2026-05-19T20:31:18.585708Z"
}
},
"outputs": [],
"source": [
"dacc = model.generate({t}, ProtoData=tmp)"
]
},
{
"cell_type": "markdown",
"id": "20030120",
"metadata": {},
"source": [
"Fit pdf to data in acceptance region\n",
"-----------------------------------------------------------------------"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "787f8b1c",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:31:18.588428Z",
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"shell.execute_reply": "2026-05-19T20:31:18.772647Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[#1] INFO:Fitting -- RooAbsPdf::fitTo(model_over_model_Int[t]) 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 751.474 μs\n",
"[#1] INFO:Fitting -- RooAddition::defaultErrorLevel(nll_model_over_model_Int[t]_modelData) Summation contains a RooNLLVar, using its error level\n",
"[#1] INFO:Minimization -- [fitFCN] No discrete parameters, performing continuous minimization only\n"
]
}
],
"source": [
"r = model.fitTo(dacc, Save=True, PrintLevel=-1)"
]
},
{
"cell_type": "markdown",
"id": "2a8e4bcd",
"metadata": {},
"source": [
"Plot fitted pdf on full and accepted data\n",
"---------------------------------------------------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "7469fb37",
"metadata": {},
"source": [
"Make plot frame, datasets and overlay model"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "26466bf6",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:31:18.775338Z",
"iopub.status.busy": "2026-05-19T20:31:18.775210Z",
"iopub.status.idle": "2026-05-19T20:31:18.961823Z",
"shell.execute_reply": "2026-05-19T20:31:18.961217Z"
}
},
"outputs": [
{
"data": {
"text/plain": [
""
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"[#1] INFO:Plotting -- RooPlot::updateFitRangeNorm: New event count of 5000 will supersede previous event count of 10000 for normalization of PDF projections\n"
]
}
],
"source": [
"frame = t.frame(Title=\"Fit to data with per-event acceptance\")\n",
"dall.plotOn(frame, MarkerColor=\"r\", LineColor=\"r\")\n",
"model.plotOn(frame)\n",
"dacc.plotOn(frame)"
]
},
{
"cell_type": "markdown",
"id": "3b3f8071",
"metadata": {},
"source": [
"Print fit results to demonstrate absence of bias"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "f6e636e6",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:31:18.963546Z",
"iopub.status.busy": "2026-05-19T20:31:18.963426Z",
"iopub.status.idle": "2026-05-19T20:31:19.205523Z",
"shell.execute_reply": "2026-05-19T20:31:19.204439Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
" RooFitResult: minimized FCN value: 2823.97, estimated distance to minimum: 3.17108e-08\n",
" covariance matrix quality: Full, accurate covariance matrix\n",
" Status : MINIMIZE=0 HESSE=0 \n",
"\n",
" Floating Parameter InitialValue FinalValue +/- Error GblCorr.\n",
" -------------------- ------------ -------------------------- --------\n",
" tau -1.5400e+00 -1.5335e+00 +/- 2.22e-02 \n",
"\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"Info in : png file rf314_paramranges.png has been created\n"
]
}
],
"source": [
"r.Print(\"v\")\n",
"\n",
"c = ROOT.TCanvas(\"rf314_paramranges\", \"rf314_paramranges\", 600, 600)\n",
"ROOT.gPad.SetLeftMargin(0.15)\n",
"frame.GetYaxis().SetTitleOffset(1.6)\n",
"frame.Draw()\n",
"\n",
"c.SaveAs(\"rf314_paramranges.png\")"
]
},
{
"cell_type": "markdown",
"id": "9ff83f6a",
"metadata": {},
"source": [
"Draw all canvases "
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "ed13af2a",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:31:19.207075Z",
"iopub.status.busy": "2026-05-19T20:31:19.206940Z",
"iopub.status.idle": "2026-05-19T20:31:19.388752Z",
"shell.execute_reply": "2026-05-19T20:31:19.388152Z"
}
},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"\n",
"
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"\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",
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"nbconvert_exporter": "python",
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