{
"cells": [
{
"cell_type": "markdown",
"id": "ef4f50e3",
"metadata": {},
"source": [
"# rf306_condpereventerrors\n",
"Multidimensional models: complete example with use of conditional 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": "f37b84e4",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:46.779547Z",
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"shell.execute_reply": "2026-05-19T20:30:47.762454Z"
}
},
"outputs": [],
"source": [
"import ROOT"
]
},
{
"cell_type": "markdown",
"id": "6743bafa",
"metadata": {},
"source": [
"B-physics pdf with per-event Gaussian resolution\n",
"----------------------------------------------------------------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "9df54a4a",
"metadata": {},
"source": [
"Observables"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "d9f07a67",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:47.765441Z",
"iopub.status.busy": "2026-05-19T20:30:47.765312Z",
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"shell.execute_reply": "2026-05-19T20:30:47.931751Z"
}
},
"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": "cf03c9d1",
"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": "92998625",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:47.934085Z",
"iopub.status.busy": "2026-05-19T20:30:47.933962Z",
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"shell.execute_reply": "2026-05-19T20:30:48.059648Z"
}
},
"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": "3820caed",
"metadata": {},
"source": [
"Construct decay(dt) (x) gauss1(dt|dterr)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "3ff0380a",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:48.061782Z",
"iopub.status.busy": "2026-05-19T20:30:48.061660Z",
"iopub.status.idle": "2026-05-19T20:30:48.187552Z",
"shell.execute_reply": "2026-05-19T20:30:48.187126Z"
}
},
"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": "06258748",
"metadata": {},
"source": [
"Construct fake 'external' data with per-event error\n",
"------------------------------------------------------------------------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "99f81739",
"metadata": {},
"source": [
"Use landau pdf to get somewhat realistic distribution with long tail"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "5abd618b",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:48.189135Z",
"iopub.status.busy": "2026-05-19T20:30:48.189020Z",
"iopub.status.idle": "2026-05-19T20:30:48.335986Z",
"shell.execute_reply": "2026-05-19T20:30:48.335534Z"
}
},
"outputs": [],
"source": [
"pdfDtErr = ROOT.RooLandau(\"pdfDtErr\", \"pdfDtErr\", dterr, 1.0, 0.25)\n",
"expDataDterr = pdfDtErr.generate({dterr}, 10000)"
]
},
{
"cell_type": "markdown",
"id": "e7669a15",
"metadata": {},
"source": [
"Sample data from conditional decay_gm(dt|dterr)\n",
"---------------------------------------------------------------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "25b14a05",
"metadata": {},
"source": [
"Specify external dataset with dterr values to use decay_dm as\n",
"conditional pdf"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "b17d34aa",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:48.337651Z",
"iopub.status.busy": "2026-05-19T20:30:48.337509Z",
"iopub.status.idle": "2026-05-19T20:30:48.484049Z",
"shell.execute_reply": "2026-05-19T20:30:48.483590Z"
}
},
"outputs": [],
"source": [
"data = decay_gm.generate({dt}, ProtoData=expDataDterr)"
]
},
{
"cell_type": "markdown",
"id": "fb1e8056",
"metadata": {},
"source": [
"Fit conditional decay_dm(dt|dterr)\n",
"---------------------------------------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "56d03abc",
"metadata": {},
"source": [
"Specify dterr as conditional observable"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "9020d9eb",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:48.485719Z",
"iopub.status.busy": "2026-05-19T20:30:48.485577Z",
"iopub.status.idle": "2026-05-19T20:30:48.748216Z",
"shell.execute_reply": "2026-05-19T20:30:48.747776Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[#1] INFO:Fitting -- RooAbsPdf::fitTo(gm1_conv_exp(-abs(@0)/@1)_dt_tau_[decay_gm]_over_gm1_conv_exp(-abs(@0)/@1)_dt_tau_[decay_gm]_Int[dt]) 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 838.084 μs\n",
"[#1] INFO:Fitting -- RooAddition::defaultErrorLevel(nll_gm1_conv_exp(-abs(@0)/@1)_dt_tau_[decay_gm]_over_gm1_conv_exp(-abs(@0)/@1)_dt_tau_[decay_gm]_Int[dt]_decay_gmData) 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": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"decay_gm.fitTo(data, ConditionalObservables={dterr}, PrintLevel=-1)"
]
},
{
"cell_type": "markdown",
"id": "0d84c8b1",
"metadata": {},
"source": [
"Plot conditional decay_dm(dt|dterr)\n",
"---------------------------------------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "487c9e21",
"metadata": {},
"source": [
"Make two-dimensional plot of conditional pdf in (dt,dterr)"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "a2fcf715",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:48.749906Z",
"iopub.status.busy": "2026-05-19T20:30:48.749785Z",
"iopub.status.idle": "2026-05-19T20:30:48.906026Z",
"shell.execute_reply": "2026-05-19T20:30:48.905560Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[#1] INFO:NumericIntegration -- RooRealIntegral::init(gm1_conv_exp(-abs(@0)/@1)_dt_tau_[decay_gm]_Int[dt,dterr]) using numeric integrator RooIntegrator1D to calculate Int(dterr)\n"
]
}
],
"source": [
"hh_decay = decay_gm.createHistogram(\"hh_decay\", dt, Binning=50, YVar=dict(var=dterr, Binning=50))\n",
"hh_decay.SetLineColor(\"kBlue\")"
]
},
{
"cell_type": "markdown",
"id": "945314f9",
"metadata": {},
"source": [
"Plot decay_gm(dt|dterr) at various values of dterr"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "2d1ced2e",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:48.907681Z",
"iopub.status.busy": "2026-05-19T20:30:48.907540Z",
"iopub.status.idle": "2026-05-19T20:30:49.068213Z",
"shell.execute_reply": "2026-05-19T20:30:49.067768Z"
}
},
"outputs": [],
"source": [
"frame = dt.frame(Title=\"Slices of decay(dt|dterr) at various dterr\")\n",
"for ibin in range(0, 100, 20):\n",
" dterr.setBin(ibin)\n",
" decay_gm.plotOn(frame, Normalization=5.0)"
]
},
{
"cell_type": "markdown",
"id": "a0128582",
"metadata": {},
"source": [
"Make projection of data an dt"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "26bc9dff",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:49.069842Z",
"iopub.status.busy": "2026-05-19T20:30:49.069723Z",
"iopub.status.idle": "2026-05-19T20:30:49.196157Z",
"shell.execute_reply": "2026-05-19T20:30:49.195722Z"
}
},
"outputs": [
{
"data": {
"text/plain": [
""
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"frame2 = dt.frame(Title=\"Projection of decay(dt|dterr) on dt\")\n",
"data.plotOn(frame2)"
]
},
{
"cell_type": "markdown",
"id": "e41c6c4b",
"metadata": {},
"source": [
"Make projection of decay(dt|dterr) on dt.\n",
"\n",
"Instead of integrating out dterr, a weighted average of curves\n",
"at values dterr_i as given in the external dataset.\n",
"(The kTRUE argument bins the data before projection to speed up the process)"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "f283c657",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:49.197867Z",
"iopub.status.busy": "2026-05-19T20:30:49.197747Z",
"iopub.status.idle": "2026-05-19T20:30:49.310810Z",
"shell.execute_reply": "2026-05-19T20:30:49.310397Z"
}
},
"outputs": [
{
"data": {
"text/plain": [
""
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"[#1] INFO:Plotting -- RooAbsReal::plotOn(decay_gm) plot on dt averages using data variables (dterr)\n"
]
}
],
"source": [
"decay_gm.plotOn(frame2, ProjWData=(expDataDterr, True))"
]
},
{
"cell_type": "markdown",
"id": "beb15255",
"metadata": {},
"source": [
"Draw all frames on canvas"
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "703c5758",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:49.312151Z",
"iopub.status.busy": "2026-05-19T20:30:49.312035Z",
"iopub.status.idle": "2026-05-19T20:30:49.556887Z",
"shell.execute_reply": "2026-05-19T20:30:49.556273Z"
}
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Info in : png file rf306_condpereventerrors.png has been created\n"
]
}
],
"source": [
"c = ROOT.TCanvas(\"rf306_condpereventerrors\", \"rf306_condperventerrors\", 1200, 400)\n",
"c.Divide(3)\n",
"c.cd(1)\n",
"ROOT.gPad.SetLeftMargin(0.20)\n",
"hh_decay.GetZaxis().SetTitleOffset(2.5)\n",
"hh_decay.Draw(\"surf\")\n",
"c.cd(2)\n",
"ROOT.gPad.SetLeftMargin(0.15)\n",
"frame.GetYaxis().SetTitleOffset(1.6)\n",
"frame.Draw()\n",
"c.cd(3)\n",
"ROOT.gPad.SetLeftMargin(0.15)\n",
"frame2.GetYaxis().SetTitleOffset(1.6)\n",
"frame2.Draw()\n",
"\n",
"c.SaveAs(\"rf306_condpereventerrors.png\")"
]
},
{
"cell_type": "markdown",
"id": "242e6795",
"metadata": {},
"source": [
"Draw all canvases "
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "b7eb8e7b",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:49.558474Z",
"iopub.status.busy": "2026-05-19T20:30:49.558352Z",
"iopub.status.idle": "2026-05-19T20:30:49.745114Z",
"shell.execute_reply": "2026-05-19T20:30:49.744514Z"
}
},
"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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