{ "cells": [ { "cell_type": "markdown", "id": "3c0e5171", "metadata": {}, "source": [ "# rf202_extendedmlfit\n", "Addition and convolution: setting up an extended maximum likelihood fit\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 08:29 PM." ] }, { "cell_type": "code", "execution_count": 1, "id": "a9bf7d26", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:29:37.974579Z", "iopub.status.busy": "2026-05-19T20:29:37.974464Z", "iopub.status.idle": "2026-05-19T20:29:38.945448Z", "shell.execute_reply": "2026-05-19T20:29:38.944775Z" } }, "outputs": [], "source": [ "import ROOT" ] }, { "cell_type": "markdown", "id": "868a2529", "metadata": {}, "source": [ "Set up component pdfs\n", "---------------------------------------" ] }, { "cell_type": "markdown", "id": "0f64266c", "metadata": {}, "source": [ "Declare observable x" ] }, { "cell_type": "code", "execution_count": 2, "id": "1c484c63", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:29:38.947237Z", "iopub.status.busy": "2026-05-19T20:29:38.947110Z", "iopub.status.idle": "2026-05-19T20:29:39.134710Z", "shell.execute_reply": "2026-05-19T20:29:39.134023Z" } }, "outputs": [], "source": [ "x = ROOT.RooRealVar(\"x\", \"x\", 0, 10)" ] }, { "cell_type": "markdown", "id": "22931bf3", "metadata": {}, "source": [ "Create two Gaussian PDFs g1(x,mean1,sigma) anf g2(x,mean2,sigma) and\n", "their parameters" ] }, { "cell_type": "code", "execution_count": 3, "id": "5ce780c4", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:29:39.144300Z", "iopub.status.busy": "2026-05-19T20:29:39.144173Z", "iopub.status.idle": "2026-05-19T20:29:39.272203Z", "shell.execute_reply": "2026-05-19T20:29:39.271608Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[#0] WARNING:InputArguments -- The parameter 'sigma1' with range [-inf, inf] of the RooGaussian 'sig1' exceeds the safe range of (0, inf). Advise to limit its range.\n", "[#0] WARNING:InputArguments -- The parameter 'sigma2' with range [-inf, inf] of the RooGaussian 'sig2' exceeds the safe range of (0, inf). Advise to limit its range.\n" ] } ], "source": [ "mean = ROOT.RooRealVar(\"mean\", \"mean of gaussians\", 5)\n", "sigma1 = ROOT.RooRealVar(\"sigma1\", \"width of gaussians\", 0.5)\n", "sigma2 = ROOT.RooRealVar(\"sigma2\", \"width of gaussians\", 1)\n", "\n", "sig1 = ROOT.RooGaussian(\"sig1\", \"Signal component 1\", x, mean, sigma1)\n", "sig2 = ROOT.RooGaussian(\"sig2\", \"Signal component 2\", x, mean, sigma2)" ] }, { "cell_type": "markdown", "id": "d109487b", "metadata": {}, "source": [ "Build Chebychev polynomial pdf" ] }, { "cell_type": "code", "execution_count": 4, "id": "3ecd5f53", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:29:39.274023Z", "iopub.status.busy": "2026-05-19T20:29:39.273902Z", "iopub.status.idle": "2026-05-19T20:29:39.453322Z", "shell.execute_reply": "2026-05-19T20:29:39.452647Z" } }, "outputs": [], "source": [ "a0 = ROOT.RooRealVar(\"a0\", \"a0\", 0.5, 0.0, 1.0)\n", "a1 = ROOT.RooRealVar(\"a1\", \"a1\", -0.2, 0.0, 1.0)\n", "bkg = ROOT.RooChebychev(\"bkg\", \"Background\", x, [a0, a1])" ] }, { "cell_type": "markdown", "id": "d7834f43", "metadata": {}, "source": [ "Sum the signal components into a composite signal pdf" ] }, { "cell_type": "code", "execution_count": 5, "id": "c3c151ab", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:29:39.454997Z", "iopub.status.busy": "2026-05-19T20:29:39.454793Z", "iopub.status.idle": "2026-05-19T20:29:39.567724Z", "shell.execute_reply": "2026-05-19T20:29:39.567107Z" } }, "outputs": [], "source": [ "sig1frac = ROOT.RooRealVar(\"sig1frac\", \"fraction of component 1 in signal\", 0.8, 0.0, 1.0)\n", "sig = ROOT.RooAddPdf(\"sig\", \"Signal\", [sig1, sig2], [sig1frac])" ] }, { "cell_type": "markdown", "id": "d0b203f0", "metadata": {}, "source": [ "Method 1 - Construct extended composite model\n", "-------------------------------------------------------------------" ] }, { "cell_type": "markdown", "id": "02223e8f", "metadata": {}, "source": [ "Sum the composite signal and background into an extended pdf\n", "nsig*sig+nbkg*bkg" ] }, { "cell_type": "code", "execution_count": 6, "id": "7c8079b1", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:29:39.569764Z", "iopub.status.busy": "2026-05-19T20:29:39.569619Z", "iopub.status.idle": "2026-05-19T20:29:39.673561Z", "shell.execute_reply": "2026-05-19T20:29:39.673004Z" } }, "outputs": [], "source": [ "nsig = ROOT.RooRealVar(\"nsig\", \"number of signal events\", 500, 0.0, 10000)\n", "nbkg = ROOT.RooRealVar(\"nbkg\", \"number of background events\", 500, 0, 10000)\n", "model = ROOT.RooAddPdf(\"model\", \"(g1+g2)+a\", [bkg, sig], [nbkg, nsig])" ] }, { "cell_type": "markdown", "id": "be58d700", "metadata": {}, "source": [ "Sample, fit and plot extended model\n", "---------------------------------------------------------------------" ] }, { "cell_type": "markdown", "id": "b9c70b36", "metadata": {}, "source": [ "Generate a data sample of expected number events in x from model\n", "= model.expectedEvents() = nsig+nbkg" ] }, { "cell_type": "code", "execution_count": 7, "id": "176de070", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:29:39.675669Z", "iopub.status.busy": "2026-05-19T20:29:39.675437Z", "iopub.status.idle": "2026-05-19T20:29:39.835652Z", "shell.execute_reply": "2026-05-19T20:29:39.835000Z" } }, "outputs": [], "source": [ "data = model.generate({x})" ] }, { "cell_type": "markdown", "id": "4344e5b3", "metadata": {}, "source": [ "Fit model to data, ML term automatically included" ] }, { "cell_type": "code", "execution_count": 8, "id": "d639c6e3", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:29:39.837618Z", "iopub.status.busy": "2026-05-19T20:29:39.837467Z", "iopub.status.idle": "2026-05-19T20:29:40.028036Z", "shell.execute_reply": "2026-05-19T20:29:40.027391Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[#1] INFO:Minimization -- p.d.f. provides expected number of events, including extended term in likelihood.\n", "[#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 853.884 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": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "model.fitTo(data, PrintLevel=-1)" ] }, { "cell_type": "markdown", "id": "deecf65d", "metadata": {}, "source": [ "Plot data and PDF overlaid" ] }, { "cell_type": "code", "execution_count": 9, "id": "b31410a0", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:29:40.029832Z", "iopub.status.busy": "2026-05-19T20:29:40.029699Z", "iopub.status.idle": "2026-05-19T20:29:40.207928Z", "shell.execute_reply": "2026-05-19T20:29:40.207249Z" } }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "xframe = x.frame(Title=\"extended ML fit example\")\n", "data.plotOn(xframe)\n", "model.plotOn(xframe)" ] }, { "cell_type": "markdown", "id": "bdd8fdd1", "metadata": {}, "source": [ "Overlay the background component of model with a dashed line" ] }, { "cell_type": "code", "execution_count": 10, "id": "2f737de4", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:29:40.210238Z", "iopub.status.busy": "2026-05-19T20:29:40.210115Z", "iopub.status.idle": "2026-05-19T20:29:40.328686Z", "shell.execute_reply": "2026-05-19T20:29:40.328053Z" } }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" }, { "name": "stdout", "output_type": "stream", "text": [ "[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) directly selected PDF components: (bkg)\n", "[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) indirectly selected PDF components: ()\n" ] } ], "source": [ "model.plotOn(xframe, Components={bkg}, LineStyle=\":\")" ] }, { "cell_type": "markdown", "id": "ccfe4ae1", "metadata": {}, "source": [ "Overlay the background+sig2 components of model with a dotted line" ] }, { "cell_type": "code", "execution_count": 11, "id": "e1aeee07", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:29:40.329988Z", "iopub.status.busy": "2026-05-19T20:29:40.329867Z", "iopub.status.idle": "2026-05-19T20:29:40.445796Z", "shell.execute_reply": "2026-05-19T20:29:40.445375Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) directly selected PDF components: (bkg,sig2)\n", "[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) indirectly selected PDF components: (sig)\n" ] }, { "data": { "text/plain": [ "" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ras_bkg_sig2 = {bkg, sig2}\n", "model.plotOn(xframe, Components=ras_bkg_sig2, LineStyle=\":\")" ] }, { "cell_type": "markdown", "id": "ecb29a88", "metadata": {}, "source": [ "Print structure of composite pdf" ] }, { "cell_type": "code", "execution_count": 12, "id": "44eb5be9", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:29:40.453780Z", "iopub.status.busy": "2026-05-19T20:29:40.453642Z", "iopub.status.idle": "2026-05-19T20:29:40.562957Z", "shell.execute_reply": "2026-05-19T20:29:40.562290Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0x5591c804da50 RooAddPdf::model = 0.885989/1 [Auto,Clean] \n", " 0x5591c7eb47e0/V- RooChebychev::bkg = 0.733482 [Auto,Dirty] \n", " 0x5591c784d220/V- RooRealVar::x = 5\n", " 0x5591c7a567f0/V- RooRealVar::a0 = 0.507382 +/- 0.0795949\n", " 0x5591c7b48330/V- RooRealVar::a1 = 0.266518 +/- 0.133887\n", " 0x5591c7efed10/V- RooRealVar::nbkg = 427.704 +/- 38.0644\n", " 0x5591c7ee7090/V- RooAddPdf::sig = 1/1 [Auto,Clean] \n", " 0x5591c7b34c90/V- RooGaussian::sig1 = 1 [Auto,Dirty] \n", " 0x5591c784d220/V- RooRealVar::x = 5\n", " 0x5591c7a05cb0/V- RooRealVar::mean = 5\n", " 0x5591c7a16c80/V- RooRealVar::sigma1 = 0.5\n", " 0x5591c7b60fb0/V- RooRealVar::sig1frac = 0.640056 +/- 0.0966619\n", " 0x5591c7b19c30/V- RooGaussian::sig2 = 1 [Auto,Dirty] \n", " 0x5591c784d220/V- RooRealVar::x = 5\n", " 0x5591c7a05cb0/V- RooRealVar::mean = 5\n", " 0x5591c7999830/V- RooRealVar::sigma2 = 1\n", " 0x5591c7f09f70/V- RooRealVar::nsig = 572.124 +/- 39.9094\n" ] } ], "source": [ "model.Print(\"t\")" ] }, { "cell_type": "markdown", "id": "2714a1d8", "metadata": {}, "source": [ "Method 2 - Construct extended components first\n", "---------------------------------------------------------------------" ] }, { "cell_type": "markdown", "id": "c6032707", "metadata": {}, "source": [ "Associated nsig/nbkg as expected number of events with sig/bkg" ] }, { "cell_type": "code", "execution_count": 13, "id": "09406f29", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:29:40.564767Z", "iopub.status.busy": "2026-05-19T20:29:40.564639Z", "iopub.status.idle": "2026-05-19T20:29:40.677822Z", "shell.execute_reply": "2026-05-19T20:29:40.677148Z" } }, "outputs": [], "source": [ "esig = ROOT.RooExtendPdf(\"esig\", \"extended signal pdf\", sig, nsig)\n", "ebkg = ROOT.RooExtendPdf(\"ebkg\", \"extended background pdf\", bkg, nbkg)" ] }, { "cell_type": "markdown", "id": "26b3b417", "metadata": {}, "source": [ "Sum extended components without coefs\n", "-------------------------------------------------------------------------" ] }, { "cell_type": "markdown", "id": "cf884780", "metadata": {}, "source": [ "Construct sum of two extended pdf (no coefficients required)" ] }, { "cell_type": "code", "execution_count": 14, "id": "a486c335", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:29:40.679998Z", "iopub.status.busy": "2026-05-19T20:29:40.679872Z", "iopub.status.idle": "2026-05-19T20:29:40.789397Z", "shell.execute_reply": "2026-05-19T20:29:40.788436Z" } }, "outputs": [], "source": [ "model2 = ROOT.RooAddPdf(\"model2\", \"(g1+g2)+a\", [ebkg, esig])" ] }, { "cell_type": "markdown", "id": "c417fb04", "metadata": {}, "source": [ "Draw the frame on the canvas" ] }, { "cell_type": "code", "execution_count": 15, "id": "de898fa2", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:29:40.791038Z", "iopub.status.busy": "2026-05-19T20:29:40.790908Z", "iopub.status.idle": "2026-05-19T20:29:41.008997Z", "shell.execute_reply": "2026-05-19T20:29:41.008191Z" } }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Info in : png file rf202_extendedmlfit.png has been created\n" ] } ], "source": [ "c = ROOT.TCanvas(\"rf202_extendedmlfit\", \"rf202_extendedmlfit\", 600, 600)\n", "ROOT.gPad.SetLeftMargin(0.15)\n", "xframe.GetYaxis().SetTitleOffset(1.4)\n", "xframe.Draw()\n", "\n", "c.SaveAs(\"rf202_extendedmlfit.png\")" ] }, { "cell_type": "markdown", "id": "37e0478a", "metadata": {}, "source": [ "Draw all canvases " ] }, { "cell_type": "code", "execution_count": 16, "id": "4b32692f", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:29:41.010747Z", "iopub.status.busy": "2026-05-19T20:29:41.010614Z", "iopub.status.idle": "2026-05-19T20:29:41.193382Z", "shell.execute_reply": "2026-05-19T20:29:41.192814Z" } }, "outputs": [ { "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 }