{ "cells": [ { "cell_type": "markdown", "id": "ec153369", "metadata": {}, "source": [ "# rf607_fitresult\n", "Likelihood and minimization: demonstration of options of the RooFitResult class\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": "2beb2a81", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:33:19.131010Z", "iopub.status.busy": "2026-05-19T20:33:19.130870Z", "iopub.status.idle": "2026-05-19T20:33:20.111429Z", "shell.execute_reply": "2026-05-19T20:33:20.110814Z" } }, "outputs": [], "source": [ "import ROOT" ] }, { "cell_type": "markdown", "id": "f801d03d", "metadata": {}, "source": [ "Create pdf, data\n", "--------------------------------" ] }, { "cell_type": "markdown", "id": "6e9acedb", "metadata": {}, "source": [ "Declare observable x" ] }, { "cell_type": "code", "execution_count": 2, "id": "f7a2cc62", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:33:20.113323Z", "iopub.status.busy": "2026-05-19T20:33:20.113186Z", "iopub.status.idle": "2026-05-19T20:33:20.280960Z", "shell.execute_reply": "2026-05-19T20:33:20.280323Z" } }, "outputs": [], "source": [ "x = ROOT.RooRealVar(\"x\", \"x\", 0, 10)" ] }, { "cell_type": "markdown", "id": "10e7fcd6", "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": "19e6aac2", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:33:20.282726Z", "iopub.status.busy": "2026-05-19T20:33:20.282567Z", "iopub.status.idle": "2026-05-19T20:33:20.422801Z", "shell.execute_reply": "2026-05-19T20:33:20.422141Z" } }, "outputs": [], "source": [ "mean = ROOT.RooRealVar(\"mean\", \"mean of gaussians\", 5, -10, 10)\n", "sigma1 = ROOT.RooRealVar(\"sigma1\", \"width of gaussians\", 0.5, 0.1, 10)\n", "sigma2 = ROOT.RooRealVar(\"sigma2\", \"width of gaussians\", 1, 0.1, 10)\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": "b1b78ac5", "metadata": {}, "source": [ "Build Chebychev polynomial pdf" ] }, { "cell_type": "code", "execution_count": 4, "id": "efb28ed8", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:33:20.424560Z", "iopub.status.busy": "2026-05-19T20:33:20.424433Z", "iopub.status.idle": "2026-05-19T20:33:20.620181Z", "shell.execute_reply": "2026-05-19T20:33:20.619494Z" } }, "outputs": [], "source": [ "a0 = ROOT.RooRealVar(\"a0\", \"a0\", 0.5, 0.0, 1.0)\n", "a1 = ROOT.RooRealVar(\"a1\", \"a1\", -0.2)\n", "bkg = ROOT.RooChebychev(\"bkg\", \"Background\", x, [a0, a1])" ] }, { "cell_type": "markdown", "id": "29cf81e2", "metadata": {}, "source": [ "Sum the signal components into a composite signal pdf" ] }, { "cell_type": "code", "execution_count": 5, "id": "bcfec7e7", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:33:20.622044Z", "iopub.status.busy": "2026-05-19T20:33:20.621898Z", "iopub.status.idle": "2026-05-19T20:33:20.736202Z", "shell.execute_reply": "2026-05-19T20:33:20.735411Z" } }, "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": "1ebbe5b7", "metadata": {}, "source": [ "Sum the composite signal and background" ] }, { "cell_type": "code", "execution_count": 6, "id": "c21b905d", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:33:20.738105Z", "iopub.status.busy": "2026-05-19T20:33:20.737947Z", "iopub.status.idle": "2026-05-19T20:33:20.842714Z", "shell.execute_reply": "2026-05-19T20:33:20.841568Z" } }, "outputs": [], "source": [ "bkgfrac = ROOT.RooRealVar(\"bkgfrac\", \"fraction of background\", 0.5, 0.0, 1.0)\n", "model = ROOT.RooAddPdf(\"model\", \"g1+g2+a\", [bkg, sig], [bkgfrac])" ] }, { "cell_type": "markdown", "id": "5e75d754", "metadata": {}, "source": [ "Generate 1000 events" ] }, { "cell_type": "code", "execution_count": 7, "id": "9b3a300a", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:33:20.844177Z", "iopub.status.busy": "2026-05-19T20:33:20.844054Z", "iopub.status.idle": "2026-05-19T20:33:20.990688Z", "shell.execute_reply": "2026-05-19T20:33:20.990038Z" } }, "outputs": [], "source": [ "data = model.generate({x}, 1000)" ] }, { "cell_type": "markdown", "id": "86381cfb", "metadata": {}, "source": [ "Fit pdf to data, save fit result\n", "-------------------------------------------------------------" ] }, { "cell_type": "markdown", "id": "af5f5c89", "metadata": {}, "source": [ "Perform fit and save result" ] }, { "cell_type": "code", "execution_count": 8, "id": "b8552112", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:33:20.992473Z", "iopub.status.busy": "2026-05-19T20:33:20.992350Z", "iopub.status.idle": "2026-05-19T20:33:21.185496Z", "shell.execute_reply": "2026-05-19T20:33:21.184810Z" } }, "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 839.504 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" ] } ], "source": [ "r = model.fitTo(data, Save=True, PrintLevel=-1)" ] }, { "cell_type": "markdown", "id": "668fc07e", "metadata": {}, "source": [ "Print fit results\n", "---------------------------------" ] }, { "cell_type": "markdown", "id": "2d21078b", "metadata": {}, "source": [ "Summary printing: Basic info plus final values of floating fit parameters" ] }, { "cell_type": "code", "execution_count": 9, "id": "1bf23e03", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:33:21.187330Z", "iopub.status.busy": "2026-05-19T20:33:21.187203Z", "iopub.status.idle": "2026-05-19T20:33:21.296540Z", "shell.execute_reply": "2026-05-19T20:33:21.295856Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", " RooFitResult: minimized FCN value: 1885.34, estimated distance to minimum: 0.000381082\n", " covariance matrix quality: Full, accurate covariance matrix\n", " Status : MINIMIZE=0 HESSE=0 \n", "\n", " Floating Parameter FinalValue +/- Error \n", " -------------------- --------------------------\n", " a0 7.2873e-01 +/- 1.13e-01\n", " bkgfrac 4.3445e-01 +/- 8.57e-02\n", " mean 5.0345e+00 +/- 3.36e-02\n", " sig1frac 7.7758e-01 +/- 9.71e-02\n", " sigma1 5.2318e-01 +/- 4.55e-02\n", " sigma2 1.7671e+00 +/- 1.18e+00\n", "\n" ] } ], "source": [ "r.Print()" ] }, { "cell_type": "markdown", "id": "dab63eb3", "metadata": {}, "source": [ "Verbose printing: Basic info, of constant parameters, and\n", "final values of floating parameters, correlations" ] }, { "cell_type": "code", "execution_count": 10, "id": "8931e361", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:33:21.298085Z", "iopub.status.busy": "2026-05-19T20:33:21.297952Z", "iopub.status.idle": "2026-05-19T20:33:21.403021Z", "shell.execute_reply": "2026-05-19T20:33:21.402096Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", " RooFitResult: minimized FCN value: 1885.34, estimated distance to minimum: 0.000381082\n", " covariance matrix quality: Full, accurate covariance matrix\n", " Status : MINIMIZE=0 HESSE=0 \n", "\n", " Constant Parameter Value \n", " -------------------- ------------\n", " a1 -2.0000e-01\n", "\n", " Floating Parameter InitialValue FinalValue +/- Error GblCorr.\n", " -------------------- ------------ -------------------------- --------\n", " a0 5.0000e-01 7.2873e-01 +/- 1.13e-01 \n", " bkgfrac 5.0000e-01 4.3445e-01 +/- 8.57e-02 \n", " mean 5.0000e+00 5.0345e+00 +/- 3.36e-02 \n", " sig1frac 8.0000e-01 7.7758e-01 +/- 9.71e-02 \n", " sigma1 5.0000e-01 5.2318e-01 +/- 4.55e-02 \n", " sigma2 1.0000e+00 1.7671e+00 +/- 1.18e+00 \n", "\n" ] } ], "source": [ "r.Print(\"v\")" ] }, { "cell_type": "markdown", "id": "bc9e4452", "metadata": {}, "source": [ "Visualize correlation matrix\n", "-------------------------------------------------------" ] }, { "cell_type": "markdown", "id": "d5ec7d60", "metadata": {}, "source": [ "Construct 2D color plot of correlation matrix" ] }, { "cell_type": "code", "execution_count": 11, "id": "23f85c03", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:33:21.404424Z", "iopub.status.busy": "2026-05-19T20:33:21.404299Z", "iopub.status.idle": "2026-05-19T20:33:21.533881Z", "shell.execute_reply": "2026-05-19T20:33:21.532792Z" } }, "outputs": [], "source": [ "ROOT.gStyle.SetOptStat(0)\n", "ROOT.gStyle.SetPalette(1)\n", "hcorr = r.correlationHist()" ] }, { "cell_type": "markdown", "id": "4dd43c4c", "metadata": {}, "source": [ "Visualize ellipse corresponding to single correlation matrix element" ] }, { "cell_type": "code", "execution_count": 12, "id": "32ec699a", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:33:21.535353Z", "iopub.status.busy": "2026-05-19T20:33:21.535228Z", "iopub.status.idle": "2026-05-19T20:33:21.654257Z", "shell.execute_reply": "2026-05-19T20:33:21.653623Z" } }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "frame = ROOT.RooPlot(sigma1, sig1frac, 0.45, 0.60, 0.65, 0.90)\n", "frame.SetTitle(\"Covariance between sigma1 and sig1frac\")\n", "r.plotOn(frame, sigma1, sig1frac, \"ME12ABHV\")" ] }, { "cell_type": "markdown", "id": "7da7fba3", "metadata": {}, "source": [ "Access fit result information\n", "---------------------------------------------------------" ] }, { "cell_type": "markdown", "id": "87a3fa59", "metadata": {}, "source": [ "Access basic information" ] }, { "cell_type": "code", "execution_count": 13, "id": "bc0ed769", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:33:21.656047Z", "iopub.status.busy": "2026-05-19T20:33:21.655922Z", "iopub.status.idle": "2026-05-19T20:33:21.768086Z", "shell.execute_reply": "2026-05-19T20:33:21.767060Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "EDM = 0.0003810824542340818\n", "-log(L) minimum = 1885.3440933934653\n" ] } ], "source": [ "print(\"EDM = \", r.edm())\n", "print(\"-log(L) minimum = \", r.minNll())" ] }, { "cell_type": "markdown", "id": "089bd0c0", "metadata": {}, "source": [ "Access list of final fit parameter values" ] }, { "cell_type": "code", "execution_count": 14, "id": "f3b9d651", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:33:21.769750Z", "iopub.status.busy": "2026-05-19T20:33:21.769561Z", "iopub.status.idle": "2026-05-19T20:33:21.882042Z", "shell.execute_reply": "2026-05-19T20:33:21.881372Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "final value of floating parameters\n", " 1) RooRealVar:: a0 = 0.72873 +/- 0.112573\n", " 2) RooRealVar:: bkgfrac = 0.43445 +/- 0.085744\n", " 3) RooRealVar:: mean = 5.03451 +/- 0.0336279\n", " 4) RooRealVar:: sig1frac = 0.777578 +/- 0.0971233\n", " 5) RooRealVar:: sigma1 = 0.523178 +/- 0.0455077\n", " 6) RooRealVar:: sigma2 = 1.76714 +/- 1.18159\n" ] } ], "source": [ "print(\"final value of floating parameters\")\n", "r.floatParsFinal().Print(\"s\")" ] }, { "cell_type": "markdown", "id": "cf8c67af", "metadata": {}, "source": [ "Access correlation matrix elements" ] }, { "cell_type": "code", "execution_count": 15, "id": "71d5ba5a", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:33:21.884197Z", "iopub.status.busy": "2026-05-19T20:33:21.884063Z", "iopub.status.idle": "2026-05-19T20:33:21.995565Z", "shell.execute_reply": "2026-05-19T20:33:21.994592Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "correlation between sig1frac and a0 is -0.38371276390446235\n", "correlation between bkgfrac and mean is -0.051612510229553044\n" ] } ], "source": [ "print(\"correlation between sig1frac and a0 is \", r.correlation(sig1frac, a0))\n", "print(\"correlation between bkgfrac and mean is \", r.correlation(\"bkgfrac\", \"mean\"))" ] }, { "cell_type": "markdown", "id": "a13fbedb", "metadata": {}, "source": [ "Extract covariance and correlation matrix as ROOT.TMatrixDSym" ] }, { "cell_type": "code", "execution_count": 16, "id": "f74d4089", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:33:21.997001Z", "iopub.status.busy": "2026-05-19T20:33:21.996875Z", "iopub.status.idle": "2026-05-19T20:33:22.137939Z", "shell.execute_reply": "2026-05-19T20:33:22.137212Z" } }, "outputs": [], "source": [ "cor = r.correlationMatrix()\n", "cov = r.covarianceMatrix()" ] }, { "cell_type": "markdown", "id": "f44b49ae", "metadata": {}, "source": [ "Print correlation, matrix" ] }, { "cell_type": "code", "execution_count": 17, "id": "7e1a6e41", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:33:22.139758Z", "iopub.status.busy": "2026-05-19T20:33:22.139618Z", "iopub.status.idle": "2026-05-19T20:33:22.249388Z", "shell.execute_reply": "2026-05-19T20:33:22.248753Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "correlation matrix\n", "covariance matrix\n", "\n", "6x6 matrix is as follows\n", "\n", " | 0 | 1 | 2 | 3 | 4 |\n", "----------------------------------------------------------------------\n", " 0 | 1 -0.8038 -0.02304 -0.3837 0.4249 \n", " 1 | -0.8038 1 -0.05161 0.6011 -0.4042 \n", " 2 | -0.02304 -0.05161 1 -0.08752 -0.04055 \n", " 3 | -0.3837 0.6011 -0.08752 1 0.2836 \n", " 4 | 0.4249 -0.4042 -0.04055 0.2836 1 \n", " 5 | 0.8347 -0.8794 0.0146 -0.2731 0.5878 \n", "\n", "\n", " | 5 |\n", "----------------------------------------------------------------------\n", " 0 | 0.8347 \n", " 1 | -0.8794 \n", " 2 | 0.0146 \n", " 3 | -0.2731 \n", " 4 | 0.5878 \n", " 5 | 1 \n", "\n", "\n", "6x6 matrix is as follows\n", "\n", " | 0 | 1 | 2 | 3 | 4 |\n", "----------------------------------------------------------------------\n", " 0 | 0.01295 -0.007884 -8.818e-05 -0.004281 0.002201 \n", " 1 | -0.007884 0.007427 -0.0001496 0.005078 -0.001585 \n", " 2 | -8.818e-05 -0.0001496 0.001131 -0.0002885 -6.206e-05 \n", " 3 | -0.004281 0.005078 -0.0002885 0.00961 0.001265 \n", " 4 | 0.002201 -0.001585 -6.206e-05 0.001265 0.002071 \n", " 5 | 0.1142 -0.09113 0.0005905 -0.0322 0.03217 \n", "\n", "\n", " | 5 |\n", "----------------------------------------------------------------------\n", " 0 | 0.1142 \n", " 1 | -0.09113 \n", " 2 | 0.0005905 \n", " 3 | -0.0322 \n", " 4 | 0.03217 \n", " 5 | 1.446 \n", "\n" ] } ], "source": [ "print(\"correlation matrix\")\n", "cor.Print()\n", "print(\"covariance matrix\")\n", "cov.Print()" ] }, { "cell_type": "markdown", "id": "0421716c", "metadata": {}, "source": [ "Persist fit result in root file\n", "-------------------------------------------------------------" ] }, { "cell_type": "markdown", "id": "9a1c3041", "metadata": {}, "source": [ "Open ROOT file save save result" ] }, { "cell_type": "code", "execution_count": 18, "id": "c406d8cd", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:33:22.250944Z", "iopub.status.busy": "2026-05-19T20:33:22.250822Z", "iopub.status.idle": "2026-05-19T20:33:22.489264Z", "shell.execute_reply": "2026-05-19T20:33:22.488103Z" } }, "outputs": [], "source": [ "f = ROOT.TFile(\"rf607_fitresult.root\", \"RECREATE\")\n", "r.Write(\"rf607\")\n", "f.Close()" ] }, { "cell_type": "markdown", "id": "7f2db58c", "metadata": {}, "source": [ "In a clean ROOT session retrieve the persisted fit result as follows:\n", "r = gDirectory.Get(\"rf607\")" ] }, { "cell_type": "code", "execution_count": 19, "id": "8e580f8a", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:33:22.490920Z", "iopub.status.busy": "2026-05-19T20:33:22.490789Z", "iopub.status.idle": "2026-05-19T20:33:22.717542Z", "shell.execute_reply": "2026-05-19T20:33:22.716883Z" } }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Info in : png file rf607_fitresult.png has been created\n" ] } ], "source": [ "c = ROOT.TCanvas(\"rf607_fitresult\", \"rf607_fitresult\", 800, 400)\n", "c.Divide(2)\n", "c.cd(1)\n", "ROOT.gPad.SetLeftMargin(0.15)\n", "hcorr.GetYaxis().SetTitleOffset(1.4)\n", "hcorr.Draw(\"colz\")\n", "c.cd(2)\n", "ROOT.gPad.SetLeftMargin(0.15)\n", "frame.GetYaxis().SetTitleOffset(1.6)\n", "frame.Draw()\n", "\n", "c.SaveAs(\"rf607_fitresult.png\")" ] }, { "cell_type": "markdown", "id": "7e5c7284", "metadata": {}, "source": [ "Draw all canvases " ] }, { "cell_type": "code", "execution_count": 20, "id": "58b11dc8", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:33:22.719388Z", "iopub.status.busy": "2026-05-19T20:33:22.719264Z", "iopub.status.idle": "2026-05-19T20:33:22.904802Z", "shell.execute_reply": "2026-05-19T20:33:22.904146Z" } }, "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 }