{
"cells": [
{
"cell_type": "markdown",
"id": "bbeb2a7a",
"metadata": {},
"source": [
"# rf608_fitresultaspdf\n",
"Likelihood and minimization: representing the parabolic approximation of the fit as a\n",
"multi-variate Gaussian on the parameters of the fitted pdf\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 08:33 PM."
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "f370688e",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:33:23.681911Z",
"iopub.status.busy": "2026-05-19T20:33:23.681793Z",
"iopub.status.idle": "2026-05-19T20:33:24.689811Z",
"shell.execute_reply": "2026-05-19T20:33:24.689230Z"
}
},
"outputs": [],
"source": [
"import ROOT"
]
},
{
"cell_type": "markdown",
"id": "e11d7f97",
"metadata": {},
"source": [
"Create model and dataset\n",
"-----------------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "c6a307a8",
"metadata": {},
"source": [
"Observable"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "6e175d1c",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:33:24.698016Z",
"iopub.status.busy": "2026-05-19T20:33:24.697864Z",
"iopub.status.idle": "2026-05-19T20:33:24.863499Z",
"shell.execute_reply": "2026-05-19T20:33:24.862884Z"
}
},
"outputs": [],
"source": [
"x = ROOT.RooRealVar(\"x\", \"x\", -20, 20)"
]
},
{
"cell_type": "markdown",
"id": "ffa85e41",
"metadata": {},
"source": [
"Model (intentional strong correlations)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "55b02556",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:33:24.865800Z",
"iopub.status.busy": "2026-05-19T20:33:24.865620Z",
"iopub.status.idle": "2026-05-19T20:33:25.077403Z",
"shell.execute_reply": "2026-05-19T20:33:25.076783Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[#0] WARNING:InputArguments -- The parameter 'sigma_g1' with range [-inf, inf] of the RooGaussian 'g1' exceeds the safe range of (0, inf). Advise to limit its range.\n"
]
}
],
"source": [
"mean = ROOT.RooRealVar(\"mean\", \"mean of g1 and g2\", 0, -1, 1)\n",
"sigma_g1 = ROOT.RooRealVar(\"sigma_g1\", \"width of g1\", 2)\n",
"g1 = ROOT.RooGaussian(\"g1\", \"g1\", x, mean, sigma_g1)\n",
"\n",
"sigma_g2 = ROOT.RooRealVar(\"sigma_g2\", \"width of g2\", 4, 3.0, 5.0)\n",
"g2 = ROOT.RooGaussian(\"g2\", \"g2\", x, mean, sigma_g2)\n",
"\n",
"frac = ROOT.RooRealVar(\"frac\", \"frac\", 0.5, 0.0, 1.0)\n",
"model = ROOT.RooAddPdf(\"model\", \"model\", [g1, g2], [frac])"
]
},
{
"cell_type": "markdown",
"id": "bb2cb407",
"metadata": {},
"source": [
"Generate 1000 events"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "e0d9ad41",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:33:25.079436Z",
"iopub.status.busy": "2026-05-19T20:33:25.079248Z",
"iopub.status.idle": "2026-05-19T20:33:25.218430Z",
"shell.execute_reply": "2026-05-19T20:33:25.217794Z"
}
},
"outputs": [],
"source": [
"data = model.generate({x}, 1000)"
]
},
{
"cell_type": "markdown",
"id": "d7dd8224",
"metadata": {},
"source": [
"Fit model to data\n",
"----------------------------------"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "b7ef3f8d",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:33:25.220424Z",
"iopub.status.busy": "2026-05-19T20:33:25.220270Z",
"iopub.status.idle": "2026-05-19T20:33:25.428391Z",
"shell.execute_reply": "2026-05-19T20:33:25.427757Z"
}
},
"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 7.755 ms\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"
]
}
],
"source": [
"r = model.fitTo(data, Save=True, PrintLevel=-1)"
]
},
{
"cell_type": "markdown",
"id": "a87f4ceb",
"metadata": {},
"source": [
"Create MV Gaussian pdf of fitted parameters\n",
"------------------------------------------------------------------------------------"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "05ab2c0f",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:33:25.430782Z",
"iopub.status.busy": "2026-05-19T20:33:25.430544Z",
"iopub.status.idle": "2026-05-19T20:33:25.549005Z",
"shell.execute_reply": "2026-05-19T20:33:25.548358Z"
}
},
"outputs": [],
"source": [
"parabPdf = r.createHessePdf({frac, mean, sigma_g2})"
]
},
{
"cell_type": "markdown",
"id": "a5eb2e1b",
"metadata": {},
"source": [
"Some exercises with the parameter pdf\n",
"-----------------------------------------------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "abae6ff3",
"metadata": {},
"source": [
"Generate 100K points in the parameter space, from the MVGaussian pdf"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "25be46be",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:33:25.550953Z",
"iopub.status.busy": "2026-05-19T20:33:25.550828Z",
"iopub.status.idle": "2026-05-19T20:33:25.676508Z",
"shell.execute_reply": "2026-05-19T20:33:25.675819Z"
}
},
"outputs": [],
"source": [
"d = parabPdf.generate({mean, sigma_g2, frac}, 100000)"
]
},
{
"cell_type": "markdown",
"id": "bb64e83a",
"metadata": {},
"source": [
"Sample a 3-D histogram of the pdf to be visualized as an error\n",
"ellipsoid using the GLISO draw option"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "8e33117a",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:33:25.678451Z",
"iopub.status.busy": "2026-05-19T20:33:25.678324Z",
"iopub.status.idle": "2026-05-19T20:33:25.849200Z",
"shell.execute_reply": "2026-05-19T20:33:25.848484Z"
}
},
"outputs": [],
"source": [
"hh_3d = parabPdf.createHistogram(\"mean,sigma_g2,frac\", 25, 25, 25)\n",
"hh_3d.SetFillColor(\"kBlue\")"
]
},
{
"cell_type": "markdown",
"id": "628ba15a",
"metadata": {},
"source": [
"Project 3D parameter pdf down to 3 permutations of two-dimensional pdfs\n",
"The integrations corresponding to these projections are performed analytically\n",
"by the MV Gaussian pdf"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "887c5800",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:33:25.851683Z",
"iopub.status.busy": "2026-05-19T20:33:25.851538Z",
"iopub.status.idle": "2026-05-19T20:33:25.961380Z",
"shell.execute_reply": "2026-05-19T20:33:25.960727Z"
}
},
"outputs": [],
"source": [
"pdf_sigmag2_frac = parabPdf.createProjection({mean})\n",
"pdf_mean_frac = parabPdf.createProjection({sigma_g2})\n",
"pdf_mean_sigmag2 = parabPdf.createProjection({frac})"
]
},
{
"cell_type": "markdown",
"id": "8fe99834",
"metadata": {},
"source": [
"Make 2D plots of the 3 two-dimensional pdf projections"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "e06ec50d",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:33:25.963628Z",
"iopub.status.busy": "2026-05-19T20:33:25.963488Z",
"iopub.status.idle": "2026-05-19T20:33:26.076150Z",
"shell.execute_reply": "2026-05-19T20:33:26.075458Z"
}
},
"outputs": [],
"source": [
"hh_sigmag2_frac = pdf_sigmag2_frac.createHistogram(\"sigma_g2,frac\", 50, 50)\n",
"hh_mean_frac = pdf_mean_frac.createHistogram(\"mean,frac\", 50, 50)\n",
"hh_mean_sigmag2 = pdf_mean_sigmag2.createHistogram(\"mean,sigma_g2\", 50, 50)\n",
"hh_mean_frac.SetLineColor(\"kBlue\")\n",
"hh_sigmag2_frac.SetLineColor(\"kBlue\")\n",
"hh_mean_sigmag2.SetLineColor(\"kBlue\")"
]
},
{
"cell_type": "markdown",
"id": "93e5f7e5",
"metadata": {},
"source": [
"Draw the 'sigar'"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "2f8aeb35",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:33:26.078383Z",
"iopub.status.busy": "2026-05-19T20:33:26.078259Z",
"iopub.status.idle": "2026-05-19T20:33:26.312130Z",
"shell.execute_reply": "2026-05-19T20:33:26.311293Z"
}
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Info in : png file rf608_fitresultaspdf_1.png has been created\n"
]
}
],
"source": [
"ROOT.gStyle.SetCanvasPreferGL(True)\n",
"ROOT.gStyle.SetPalette(1)\n",
"c1 = ROOT.TCanvas(\"rf608_fitresultaspdf_1\", \"rf608_fitresultaspdf_1\", 600, 600)\n",
"hh_3d.Draw(\"gliso\")\n",
"\n",
"c1.SaveAs(\"rf608_fitresultaspdf_1.png\")"
]
},
{
"cell_type": "markdown",
"id": "66b0bab6",
"metadata": {},
"source": [
"Draw the 2D projections of the 3D pdf"
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "0142b244",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:33:26.314012Z",
"iopub.status.busy": "2026-05-19T20:33:26.313892Z",
"iopub.status.idle": "2026-05-19T20:33:26.436760Z",
"shell.execute_reply": "2026-05-19T20:33:26.436114Z"
}
},
"outputs": [],
"source": [
"c2 = ROOT.TCanvas(\"rf608_fitresultaspdf_2\", \"rf608_fitresultaspdf_2\", 900, 600)\n",
"c2.Divide(3, 2)\n",
"c2.cd(1)\n",
"ROOT.gPad.SetLeftMargin(0.15)\n",
"hh_mean_sigmag2.GetZaxis().SetTitleOffset(1.4)\n",
"hh_mean_sigmag2.Draw(\"surf3\")\n",
"c2.cd(2)\n",
"ROOT.gPad.SetLeftMargin(0.15)\n",
"hh_sigmag2_frac.GetZaxis().SetTitleOffset(1.4)\n",
"hh_sigmag2_frac.Draw(\"surf3\")\n",
"c2.cd(3)\n",
"ROOT.gPad.SetLeftMargin(0.15)\n",
"hh_mean_frac.GetZaxis().SetTitleOffset(1.4)\n",
"hh_mean_frac.Draw(\"surf3\")"
]
},
{
"cell_type": "markdown",
"id": "055eb09e",
"metadata": {},
"source": [
"Draw the distributions of parameter points sampled from the pdf"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "dc9f8789",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:33:26.439020Z",
"iopub.status.busy": "2026-05-19T20:33:26.438898Z",
"iopub.status.idle": "2026-05-19T20:33:26.626156Z",
"shell.execute_reply": "2026-05-19T20:33:26.625329Z"
}
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Info in : png file rf608_fitresultaspdf_2.png has been created\n"
]
}
],
"source": [
"tmp1 = d.createHistogram(mean, sigma_g2, 50, 50)\n",
"tmp2 = d.createHistogram(sigma_g2, frac, 50, 50)\n",
"tmp3 = d.createHistogram(mean, frac, 50, 50)\n",
"\n",
"c2.cd(4)\n",
"ROOT.gPad.SetLeftMargin(0.15)\n",
"tmp1.GetZaxis().SetTitleOffset(1.4)\n",
"tmp1.Draw(\"lego3\")\n",
"c2.cd(5)\n",
"ROOT.gPad.SetLeftMargin(0.15)\n",
"tmp2.GetZaxis().SetTitleOffset(1.4)\n",
"tmp2.Draw(\"lego3\")\n",
"c2.cd(6)\n",
"ROOT.gPad.SetLeftMargin(0.15)\n",
"tmp3.GetZaxis().SetTitleOffset(1.4)\n",
"tmp3.Draw(\"lego3\")\n",
"\n",
"c2.SaveAs(\"rf608_fitresultaspdf_2.png\")"
]
},
{
"cell_type": "markdown",
"id": "3c580726",
"metadata": {},
"source": [
"Draw all canvases "
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "6995e300",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:33:26.627941Z",
"iopub.status.busy": "2026-05-19T20:33:26.627825Z",
"iopub.status.idle": "2026-05-19T20:33:26.920837Z",
"shell.execute_reply": "2026-05-19T20:33:26.920224Z"
}
},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"\n",
"
\n",
"\n",
"\n",
"\n"
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"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"
}
},
"nbformat": 4,
"nbformat_minor": 5
}