{
"cells": [
{
"cell_type": "markdown",
"id": "25fcba9f",
"metadata": {},
"source": [
"# rf307_fullpereventerrors\n",
"Multidimensional models: usage of full pdf with per-event errors\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": "5cc74ab7",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:53.591385Z",
"iopub.status.busy": "2026-05-19T20:30:53.591267Z",
"iopub.status.idle": "2026-05-19T20:30:54.577596Z",
"shell.execute_reply": "2026-05-19T20:30:54.577136Z"
}
},
"outputs": [],
"source": [
"import ROOT"
]
},
{
"cell_type": "markdown",
"id": "22284385",
"metadata": {},
"source": [
"B-physics pdf with per-event Gaussian resolution\n",
"----------------------------------------------------------------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "631aaeaa",
"metadata": {},
"source": [
"Observables"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "6ceb07f0",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:54.580260Z",
"iopub.status.busy": "2026-05-19T20:30:54.580126Z",
"iopub.status.idle": "2026-05-19T20:30:54.749936Z",
"shell.execute_reply": "2026-05-19T20:30:54.744349Z"
}
},
"outputs": [],
"source": [
"dt = ROOT.RooRealVar(\"dt\", \"dt\", -10, 10)\n",
"dterr = ROOT.RooRealVar(\"dterr\", \"per-event error on dt\", 0.01, 10)"
]
},
{
"cell_type": "markdown",
"id": "7aaec3ee",
"metadata": {},
"source": [
"Build a gaussian resolution model scaled by the per-error =\n",
"gauss(dt,bias,sigma*dterr)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "45baace7",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:54.751532Z",
"iopub.status.busy": "2026-05-19T20:30:54.751402Z",
"iopub.status.idle": "2026-05-19T20:30:54.880579Z",
"shell.execute_reply": "2026-05-19T20:30:54.879935Z"
}
},
"outputs": [],
"source": [
"bias = ROOT.RooRealVar(\"bias\", \"bias\", 0, -10, 10)\n",
"sigma = ROOT.RooRealVar(\"sigma\", \"per-event error scale factor\", 1, 0.1, 10)\n",
"gm = ROOT.RooGaussModel(\"gm1\", \"gauss model scaled bt per-event error\", dt, bias, sigma, dterr)"
]
},
{
"cell_type": "markdown",
"id": "9438c5ef",
"metadata": {},
"source": [
"Construct decay(dt) (x) gauss1(dt|dterr)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "32905029",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:54.882440Z",
"iopub.status.busy": "2026-05-19T20:30:54.882307Z",
"iopub.status.idle": "2026-05-19T20:30:55.016850Z",
"shell.execute_reply": "2026-05-19T20:30:55.015955Z"
}
},
"outputs": [],
"source": [
"tau = ROOT.RooRealVar(\"tau\", \"tau\", 1.548)\n",
"decay_gm = ROOT.RooDecay(\"decay_gm\", \"decay\", dt, tau, gm, type=\"DoubleSided\")"
]
},
{
"cell_type": "markdown",
"id": "18d651aa",
"metadata": {},
"source": [
"Construct empirical pdf for per-event error\n",
"-----------------------------------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "2df212a1",
"metadata": {},
"source": [
"Use landau pdf to get empirical distribution with long tail"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "bd634409",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:55.018503Z",
"iopub.status.busy": "2026-05-19T20:30:55.018369Z",
"iopub.status.idle": "2026-05-19T20:30:55.169453Z",
"shell.execute_reply": "2026-05-19T20:30:55.168801Z"
}
},
"outputs": [],
"source": [
"pdfDtErr = ROOT.RooLandau(\"pdfDtErr\", \"pdfDtErr\", dterr, 1.0, 0.25)\n",
"expDataDterr = pdfDtErr.generate({dterr}, 10000)"
]
},
{
"cell_type": "markdown",
"id": "8fc886f9",
"metadata": {},
"source": [
"Construct a histogram pdf to describe the shape of the dtErr distribution"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "9235aac0",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:55.171475Z",
"iopub.status.busy": "2026-05-19T20:30:55.171344Z",
"iopub.status.idle": "2026-05-19T20:30:55.294230Z",
"shell.execute_reply": "2026-05-19T20:30:55.293721Z"
}
},
"outputs": [],
"source": [
"expHistDterr = expDataDterr.binnedClone()\n",
"pdfErr = ROOT.RooHistPdf(\"pdfErr\", \"pdfErr\", {dterr}, expHistDterr)"
]
},
{
"cell_type": "markdown",
"id": "d0304629",
"metadata": {},
"source": [
"Construct conditional product decay_dm(dt|dterr)*pdf(dterr)\n",
"----------------------------------------------------------------------------------------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "12d80a62",
"metadata": {},
"source": [
"Construct production of conditional decay_dm(dt|dterr) with empirical\n",
"pdfErr(dterr)"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "0ea766b6",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:55.296138Z",
"iopub.status.busy": "2026-05-19T20:30:55.296011Z",
"iopub.status.idle": "2026-05-19T20:30:55.438216Z",
"shell.execute_reply": "2026-05-19T20:30:55.437698Z"
}
},
"outputs": [],
"source": [
"model = ROOT.RooProdPdf(\"model\", \"model\", {pdfErr}, Conditional=({decay_gm}, {dt}))"
]
},
{
"cell_type": "markdown",
"id": "7cb2d68b",
"metadata": {},
"source": [
"(Alternatively you could also use the landau shape pdfDtErr)\n",
"ROOT.RooProdPdf model(\"model\", \"model\",pdfDtErr,\n",
"ROOT.RooFit.Conditional(decay_gm,dt))"
]
},
{
"cell_type": "markdown",
"id": "98592ab8",
"metadata": {},
"source": [
"Sample, fit and plot product model\n",
"------------------------------------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "0d4faa44",
"metadata": {},
"source": [
"Specify external dataset with dterr values to use model_dm as\n",
"conditional pdf"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "263bbe7d",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:55.440087Z",
"iopub.status.busy": "2026-05-19T20:30:55.439967Z",
"iopub.status.idle": "2026-05-19T20:30:55.577418Z",
"shell.execute_reply": "2026-05-19T20:30:55.576857Z"
}
},
"outputs": [],
"source": [
"data = model.generate({dt, dterr}, 10000)"
]
},
{
"cell_type": "markdown",
"id": "d12c1059",
"metadata": {},
"source": [
"Fit conditional decay_dm(dt|dterr)\n",
"---------------------------------------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "ccd4950f",
"metadata": {},
"source": [
"Specify dterr as conditional observable"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "70ee24ab",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:55.579124Z",
"iopub.status.busy": "2026-05-19T20:30:55.578998Z",
"iopub.status.idle": "2026-05-19T20:30:55.841317Z",
"shell.execute_reply": "2026-05-19T20:30:55.840785Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[#1] INFO:Fitting -- RooAbsPdf::fitTo(model) 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 954.084 μs\n",
"[#1] INFO:Fitting -- RooAddition::defaultErrorLevel(nll_model_modelData) 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": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"model.fitTo(data, PrintLevel=-1)"
]
},
{
"cell_type": "markdown",
"id": "7152fd98",
"metadata": {},
"source": [
"Plot conditional decay_dm(dt|dterr)\n",
"---------------------------------------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "0f6aedf8",
"metadata": {},
"source": [
"Make two-dimensional plot of conditional pdf in (dt,dterr)"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "eaf099f5",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:55.843207Z",
"iopub.status.busy": "2026-05-19T20:30:55.843085Z",
"iopub.status.idle": "2026-05-19T20:30:55.997838Z",
"shell.execute_reply": "2026-05-19T20:30:55.997314Z"
}
},
"outputs": [],
"source": [
"hh_model = model.createHistogram(\"hh_model\", dt, Binning=50, YVar=dict(var=dterr, Binning=50))\n",
"hh_model.SetLineColor(\"kBlue\")"
]
},
{
"cell_type": "markdown",
"id": "bcf4fcfe",
"metadata": {},
"source": [
"Make projection of data an dt"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "28be1354",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:55.999747Z",
"iopub.status.busy": "2026-05-19T20:30:55.999619Z",
"iopub.status.idle": "2026-05-19T20:30:57.310448Z",
"shell.execute_reply": "2026-05-19T20:30:57.309940Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[#1] INFO:Plotting -- RooAbsReal::plotOn(model) plot on dt integrates over variables (dterr)\n",
"[#1] INFO:NumericIntegration -- RooRealIntegral::init(SPECINT[pdfErr_NORM[dterr]_X_decay_gm_NORM[dt]]_Int[dterr]) using numeric integrator RooIntegrator1D to calculate Int(dterr)\n"
]
},
{
"data": {
"text/plain": [
""
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"frame = dt.frame(Title=\"Projection of model(dt|dterr) on dt\")\n",
"data.plotOn(frame)\n",
"model.plotOn(frame)"
]
},
{
"cell_type": "markdown",
"id": "1e38c183",
"metadata": {},
"source": [
"Draw all frames on canvas"
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "26467369",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:57.312341Z",
"iopub.status.busy": "2026-05-19T20:30:57.312217Z",
"iopub.status.idle": "2026-05-19T20:30:57.545866Z",
"shell.execute_reply": "2026-05-19T20:30:57.545283Z"
}
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Info in : png file rf307_fullpereventerrors.png has been created\n"
]
}
],
"source": [
"c = ROOT.TCanvas(\"rf307_fullpereventerrors\", \"rf307_fullpereventerrors\", 800, 400)\n",
"c.Divide(2)\n",
"c.cd(1)\n",
"ROOT.gPad.SetLeftMargin(0.20)\n",
"hh_model.GetZaxis().SetTitleOffset(2.5)\n",
"hh_model.Draw(\"surf\")\n",
"c.cd(2)\n",
"ROOT.gPad.SetLeftMargin(0.15)\n",
"frame.GetYaxis().SetTitleOffset(1.6)\n",
"frame.Draw()\n",
"\n",
"c.SaveAs(\"rf307_fullpereventerrors.png\")"
]
},
{
"cell_type": "markdown",
"id": "c70b1b58",
"metadata": {},
"source": [
"Draw all canvases "
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "1597154d",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:57.547472Z",
"iopub.status.busy": "2026-05-19T20:30:57.547350Z",
"iopub.status.idle": "2026-05-19T20:30:57.731975Z",
"shell.execute_reply": "2026-05-19T20:30:57.731534Z"
}
},
"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": {
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"file_extension": ".py",
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"nbconvert_exporter": "python",
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