{
"cells": [
{
"cell_type": "markdown",
"id": "920dc66e",
"metadata": {},
"source": [
"# rf208_convolution\n",
"'ADDITION AND CONVOLUTION' RooFit tutorial macro #208\n",
"One-dimensional numeric convolution\n",
"(require ROOT to be compiled with --enable-fftw3)\n",
"\n",
"pdf = landau(t) (x) gauss(t)\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 08:30 PM."
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "d47cc015",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:07.417409Z",
"iopub.status.busy": "2026-05-19T20:30:07.417291Z",
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"shell.execute_reply": "2026-05-19T20:30:08.384586Z"
}
},
"outputs": [],
"source": [
"import ROOT"
]
},
{
"cell_type": "markdown",
"id": "e131f095",
"metadata": {},
"source": [
"Set up component pdfs\n",
"---------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "ee50b928",
"metadata": {},
"source": [
"Construct observable"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "e6b37953",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:08.387954Z",
"iopub.status.busy": "2026-05-19T20:30:08.387820Z",
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"shell.execute_reply": "2026-05-19T20:30:08.547572Z"
}
},
"outputs": [],
"source": [
"t = ROOT.RooRealVar(\"t\", \"t\", -10, 30)"
]
},
{
"cell_type": "markdown",
"id": "05666d7b",
"metadata": {},
"source": [
"Construct landau(t,ml,sl)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "d8f274e5",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:08.550429Z",
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"shell.execute_reply": "2026-05-19T20:30:08.676261Z"
}
},
"outputs": [],
"source": [
"ml = ROOT.RooRealVar(\"ml\", \"mean landau\", 5.0, -20, 20)\n",
"sl = ROOT.RooRealVar(\"sl\", \"sigma landau\", 1, 0.1, 10)\n",
"landau = ROOT.RooLandau(\"lx\", \"lx\", t, ml, sl)"
]
},
{
"cell_type": "markdown",
"id": "de4517a6",
"metadata": {},
"source": [
"Construct gauss(t,mg,sg)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "d2779cd6",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:08.678711Z",
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"shell.execute_reply": "2026-05-19T20:30:08.793113Z"
}
},
"outputs": [],
"source": [
"mg = ROOT.RooRealVar(\"mg\", \"mg\", 0)\n",
"sg = ROOT.RooRealVar(\"sg\", \"sg\", 2, 0.1, 10)\n",
"gauss = ROOT.RooGaussian(\"gauss\", \"gauss\", t, mg, sg)"
]
},
{
"cell_type": "markdown",
"id": "b75b0b42",
"metadata": {},
"source": [
"Construct convolution pdf\n",
"---------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "6e9fff45",
"metadata": {},
"source": [
"Set #bins to be used for FFT sampling to 10000"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "9e94ee90",
"metadata": {
"collapsed": false,
"execution": {
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"shell.execute_reply": "2026-05-19T20:30:08.903638Z"
}
},
"outputs": [],
"source": [
"t.setBins(10000, \"cache\")"
]
},
{
"cell_type": "markdown",
"id": "94e46ad1",
"metadata": {},
"source": [
"Construct landau (x) gauss"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "29ec0c78",
"metadata": {
"collapsed": false,
"execution": {
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"shell.execute_reply": "2026-05-19T20:30:09.021719Z"
}
},
"outputs": [],
"source": [
"lxg = ROOT.RooFFTConvPdf(\"lxg\", \"landau (X) gauss\", t, landau, gauss)"
]
},
{
"cell_type": "markdown",
"id": "c38ddbc1",
"metadata": {},
"source": [
"Sample, fit and plot convoluted pdf\n",
"----------------------------------------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "8141027b",
"metadata": {},
"source": [
"Sample 1000 events in x from gxlx"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "dd7bc672",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:09.024526Z",
"iopub.status.busy": "2026-05-19T20:30:09.024402Z",
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"shell.execute_reply": "2026-05-19T20:30:09.162649Z"
}
},
"outputs": [],
"source": [
"data = lxg.generate({t}, 10000)"
]
},
{
"cell_type": "markdown",
"id": "f951d02b",
"metadata": {},
"source": [
"Fit gxlx to data"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "66e79f4d",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:09.165088Z",
"iopub.status.busy": "2026-05-19T20:30:09.164961Z",
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"shell.execute_reply": "2026-05-19T20:30:09.511740Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[#1] INFO:Eval -- RooRealVar::setRange(t) new range named 'refrange_fft_lxg' created with bounds [-10,30]\n",
"[#1] INFO:Caching -- RooAbsCachedPdf::getCache(lxg) creating new cache 0x5558a2748920 with pdf lx_CONV_gauss_CACHE_Obs[t]_NORM_t for nset (t) with code 0\n",
"[#1] INFO:Fitting -- RooAbsPdf::fitTo(lxg_over_lxg_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 34.3745 ms\n",
"[#1] INFO:Fitting -- RooAddition::defaultErrorLevel(nll_lxg_over_lxg_Int[t]_lxgData) Summation contains a RooNLLVar, using its error level\n",
"[#1] INFO:Minimization -- [fitFCN] No discrete parameters, performing continuous minimization only\n"
]
},
{
"data": {
"text/plain": [
""
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"lxg.fitTo(data, PrintLevel=-1)"
]
},
{
"cell_type": "markdown",
"id": "e54c1620",
"metadata": {},
"source": [
"Plot data, pdf, landau (X) gauss pdf"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "d0327244",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:09.514391Z",
"iopub.status.busy": "2026-05-19T20:30:09.514266Z",
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"shell.execute_reply": "2026-05-19T20:30:09.700036Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[#1] INFO:Caching -- RooAbsCachedPdf::getCache(lxg) creating new cache 0x5558a29b6fe0 with pdf lx_CONV_gauss_CACHE_Obs[t]_NORM_t for nset (t) with code 0\n"
]
},
{
"data": {
"text/plain": [
""
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"frame = t.frame(Title=\"landau (x) gauss convolution\")\n",
"data.plotOn(frame)\n",
"lxg.plotOn(frame)\n",
"landau.plotOn(frame, LineStyle=\"--\")"
]
},
{
"cell_type": "markdown",
"id": "91d52b08",
"metadata": {},
"source": [
"Draw frame on canvas"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "b08ee9bd",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:09.702338Z",
"iopub.status.busy": "2026-05-19T20:30:09.702214Z",
"iopub.status.idle": "2026-05-19T20:30:09.914893Z",
"shell.execute_reply": "2026-05-19T20:30:09.914113Z"
}
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Info in : png file rf208_convolution.png has been created\n"
]
}
],
"source": [
"c = ROOT.TCanvas(\"rf208_convolution\", \"rf208_convolution\", 600, 600)\n",
"ROOT.gPad.SetLeftMargin(0.15)\n",
"frame.GetYaxis().SetTitleOffset(1.4)\n",
"frame.Draw()\n",
"\n",
"c.SaveAs(\"rf208_convolution.png\")"
]
},
{
"cell_type": "markdown",
"id": "cf06f2ff",
"metadata": {},
"source": [
"Draw all canvases "
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "fff862f9",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:09.916683Z",
"iopub.status.busy": "2026-05-19T20:30:09.916537Z",
"iopub.status.idle": "2026-05-19T20:30:10.097299Z",
"shell.execute_reply": "2026-05-19T20:30:10.096588Z"
}
},
"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",
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"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
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