{ "cells": [ { "cell_type": "markdown", "id": "48af628b", "metadata": {}, "source": [ "# rf312_multirangefit\n", "Multidimensional models: performing fits in multiple (disjoint) ranges in one or more dimensions\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 08:31 PM." ] }, { "cell_type": "code", "execution_count": 1, "id": "1ddaa538", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:31:10.629356Z", "iopub.status.busy": "2026-05-19T20:31:10.629241Z", "iopub.status.idle": "2026-05-19T20:31:11.592187Z", "shell.execute_reply": "2026-05-19T20:31:11.590991Z" } }, "outputs": [], "source": [ "import ROOT" ] }, { "cell_type": "markdown", "id": "b7d1220c", "metadata": {}, "source": [ "Create 2D pdf and data\n", "-------------------------------------------" ] }, { "cell_type": "markdown", "id": "d450e99f", "metadata": {}, "source": [ "Define observables x,y" ] }, { "cell_type": "code", "execution_count": 2, "id": "bbe0cf8d", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:31:11.593802Z", "iopub.status.busy": "2026-05-19T20:31:11.593646Z", "iopub.status.idle": "2026-05-19T20:31:11.754193Z", "shell.execute_reply": "2026-05-19T20:31:11.753063Z" } }, "outputs": [], "source": [ "x = ROOT.RooRealVar(\"x\", \"x\", -10, 10)\n", "y = ROOT.RooRealVar(\"y\", \"y\", -10, 10)" ] }, { "cell_type": "markdown", "id": "a3ad780a", "metadata": {}, "source": [ "Construct the signal pdf gauss(x)*gauss(y)" ] }, { "cell_type": "code", "execution_count": 3, "id": "00b64458", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:31:11.755710Z", "iopub.status.busy": "2026-05-19T20:31:11.755555Z", "iopub.status.idle": "2026-05-19T20:31:11.895750Z", "shell.execute_reply": "2026-05-19T20:31:11.895057Z" } }, "outputs": [], "source": [ "mx = ROOT.RooRealVar(\"mx\", \"mx\", 1, -10, 10)\n", "my = ROOT.RooRealVar(\"my\", \"my\", 1, -10, 10)\n", "\n", "gx = ROOT.RooGaussian(\"gx\", \"gx\", x, mx, 1.0)\n", "gy = ROOT.RooGaussian(\"gy\", \"gy\", y, my, 1.0)\n", "\n", "sig = ROOT.RooProdPdf(\"sig\", \"sig\", gx, gy)" ] }, { "cell_type": "markdown", "id": "c64809eb", "metadata": {}, "source": [ "Construct the background pdf (flat in x,y)" ] }, { "cell_type": "code", "execution_count": 4, "id": "c48184be", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:31:11.897537Z", "iopub.status.busy": "2026-05-19T20:31:11.897416Z", "iopub.status.idle": "2026-05-19T20:31:12.008499Z", "shell.execute_reply": "2026-05-19T20:31:12.007861Z" } }, "outputs": [], "source": [ "px = ROOT.RooPolynomial(\"px\", \"px\", x)\n", "py = ROOT.RooPolynomial(\"py\", \"py\", y)\n", "bkg = ROOT.RooProdPdf(\"bkg\", \"bkg\", px, py)" ] }, { "cell_type": "markdown", "id": "52f4cbea", "metadata": {}, "source": [ "Construct the composite model sig+bkg" ] }, { "cell_type": "code", "execution_count": 5, "id": "98a808d5", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:31:12.010250Z", "iopub.status.busy": "2026-05-19T20:31:12.010125Z", "iopub.status.idle": "2026-05-19T20:31:12.188470Z", "shell.execute_reply": "2026-05-19T20:31:12.187786Z" } }, "outputs": [], "source": [ "f = ROOT.RooRealVar(\"f\", \"f\", 0.0, 1.0)\n", "model = ROOT.RooAddPdf(\"model\", \"model\", [sig, bkg], [f])" ] }, { "cell_type": "markdown", "id": "a3549582", "metadata": {}, "source": [ "Sample 10000 events in (x,y) from the model" ] }, { "cell_type": "code", "execution_count": 6, "id": "39fbcd4e", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:31:12.190258Z", "iopub.status.busy": "2026-05-19T20:31:12.190131Z", "iopub.status.idle": "2026-05-19T20:31:12.344307Z", "shell.execute_reply": "2026-05-19T20:31:12.343651Z" } }, "outputs": [], "source": [ "modelData = model.generate({x, y}, 10000)" ] }, { "cell_type": "markdown", "id": "4de56eb8", "metadata": {}, "source": [ "Define signal and sideband regions\n", "-------------------------------------------------------------------" ] }, { "cell_type": "markdown", "id": "76324a57", "metadata": {}, "source": [ "Construct the SideBand1,SideBand2, regions\n", "\n", " |\n", " +-------------+-----------+\n", " | | |\n", " | Side | Sig |\n", " | Band1 | nal |\n", " | | |\n", " --+-------------+-----------+--\n", " | |\n", " | Side |\n", " | Band2 |\n", " | |\n", " +-------------+-----------+\n", " |" ] }, { "cell_type": "code", "execution_count": 7, "id": "058fa767", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:31:12.346128Z", "iopub.status.busy": "2026-05-19T20:31:12.346003Z", "iopub.status.idle": "2026-05-19T20:31:12.461884Z", "shell.execute_reply": "2026-05-19T20:31:12.461195Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[#1] INFO:Eval -- RooRealVar::setRange(x) new range named 'SB1' created with bounds [-10,10]\n", "[#1] INFO:Eval -- RooRealVar::setRange(y) new range named 'SB1' created with bounds [-10,0]\n", "[#1] INFO:Eval -- RooRealVar::setRange(x) new range named 'SB2' created with bounds [-10,0]\n", "[#1] INFO:Eval -- RooRealVar::setRange(y) new range named 'SB2' created with bounds [0,10]\n", "[#1] INFO:Eval -- RooRealVar::setRange(x) new range named 'SIG' created with bounds [0,10]\n", "[#1] INFO:Eval -- RooRealVar::setRange(y) new range named 'SIG' created with bounds [0,10]\n", "[#1] INFO:Eval -- RooRealVar::setRange(x) new range named 'FULL' created with bounds [-10,10]\n", "[#1] INFO:Eval -- RooRealVar::setRange(y) new range named 'FULL' created with bounds [-10,10]\n" ] } ], "source": [ "x.setRange(\"SB1\", -10, +10)\n", "y.setRange(\"SB1\", -10, 0)\n", "\n", "x.setRange(\"SB2\", -10, 0)\n", "y.setRange(\"SB2\", 0, +10)\n", "\n", "x.setRange(\"SIG\", 0, +10)\n", "y.setRange(\"SIG\", 0, +10)\n", "\n", "x.setRange(\"FULL\", -10, +10)\n", "y.setRange(\"FULL\", -10, +10)" ] }, { "cell_type": "markdown", "id": "e186c5a0", "metadata": {}, "source": [ "Perform fits in individual sideband regions\n", "-------------------------------------------------------------------------------------" ] }, { "cell_type": "markdown", "id": "2e36f71c", "metadata": {}, "source": [ "Perform fit in SideBand1 region (ROOT.RooAddPdf coefficients will be\n", "interpreted in full range)" ] }, { "cell_type": "code", "execution_count": 8, "id": "9f927e4e", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:31:12.463395Z", "iopub.status.busy": "2026-05-19T20:31:12.463259Z", "iopub.status.idle": "2026-05-19T20:31:12.667727Z", "shell.execute_reply": "2026-05-19T20:31:12.667056Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[#1] INFO:Eval -- RooRealVar::setRange(x) new range named 'fit_nll_model_modelData' created with bounds [-10,10]\n", "[#1] INFO:Eval -- RooRealVar::setRange(y) new range named 'fit_nll_model_modelData' created with bounds [-10,0]\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 1.39779 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_sb1 = model.fitTo(modelData, Range=\"SB1\", Save=True, PrintLevel=-1)" ] }, { "cell_type": "markdown", "id": "52dffbfb", "metadata": {}, "source": [ "Perform fit in SideBand2 region (ROOT.RooAddPdf coefficients will be\n", "interpreted in full range)" ] }, { "cell_type": "code", "execution_count": 9, "id": "21f54cb3", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:31:12.669462Z", "iopub.status.busy": "2026-05-19T20:31:12.669338Z", "iopub.status.idle": "2026-05-19T20:31:12.777648Z", "shell.execute_reply": "2026-05-19T20:31:12.776976Z" } }, "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 -- Creation of NLL object took 647.203 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_sb2 = model.fitTo(modelData, Range=\"SB2\", Save=True, PrintLevel=-1)" ] }, { "cell_type": "markdown", "id": "5a49350f", "metadata": {}, "source": [ "Perform fits in joint sideband regions\n", "-----------------------------------------------------------------------------" ] }, { "cell_type": "markdown", "id": "1ca28ea6", "metadata": {}, "source": [ "Now perform fit to joint 'L-shaped' sideband region 'SB1|SB2'\n", "(ROOT.RooAddPdf coefficients will be interpreted in full range)" ] }, { "cell_type": "code", "execution_count": 10, "id": "c777086e", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:31:12.779281Z", "iopub.status.busy": "2026-05-19T20:31:12.779161Z", "iopub.status.idle": "2026-05-19T20:31:12.892458Z", "shell.execute_reply": "2026-05-19T20:31:12.891860Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[#1] INFO:Eval -- RooRealVar::setRange(x) new range named 'fit_nll_model_modelData_SB1' created with bounds [-10,10]\n", "[#1] INFO:Eval -- RooRealVar::setRange(y) new range named 'fit_nll_model_modelData_SB1' created with bounds [-10,0]\n", "[#1] INFO:Eval -- RooRealVar::setRange(x) new range named 'fit_nll_model_modelData_SB2' created with bounds [-10,0]\n", "[#1] INFO:Eval -- RooRealVar::setRange(y) new range named 'fit_nll_model_modelData_SB2' created with bounds [0,10]\n", "[#1] INFO:Fitting -- RooAbsPdf::fitTo(model) fixing normalization set for coefficient determination to observables in data\n", "[#1] INFO:Fitting -- Creation of NLL object took 941.023 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_sb12 = model.fitTo(modelData, Range=\"SB1,SB2\", Save=True, PrintLevel=-1)" ] }, { "cell_type": "markdown", "id": "b4cd7126", "metadata": {}, "source": [ "Print results for comparison" ] }, { "cell_type": "code", "execution_count": 11, "id": "e9e9bb12", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:31:12.894007Z", "iopub.status.busy": "2026-05-19T20:31:12.893884Z", "iopub.status.idle": "2026-05-19T20:31:13.003588Z", "shell.execute_reply": "2026-05-19T20:31:13.002937Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", " RooFitResult: minimized FCN value: 16261.4, estimated distance to minimum: 5.06415e-07\n", " covariance matrix quality: Full, accurate covariance matrix\n", " Status : MINIMIZE=0 HESSE=0 \n", "\n", " Floating Parameter FinalValue +/- Error \n", " -------------------- --------------------------\n", " f 5.1135e-01 +/- 3.58e-02\n", " mx 9.8740e-01 +/- 4.03e-02\n", " my 9.9305e-01 +/- 9.39e-02\n", "\n", "\n", " RooFitResult: minimized FCN value: 7578.28, estimated distance to minimum: 3.07865e-06\n", " covariance matrix quality: Full, accurate covariance matrix\n", " Status : MINIMIZE=0 HESSE=0 \n", "\n", " Floating Parameter FinalValue +/- Error \n", " -------------------- --------------------------\n", " f 5.4586e-01 +/- 4.46e-02\n", " mx 1.1276e+00 +/- 1.10e-01\n", " my 9.6462e-01 +/- 5.60e-02\n", "\n", "\n", " RooFitResult: minimized FCN value: 27252.6, estimated distance to minimum: 2.25202e-06\n", " covariance matrix quality: Full, accurate covariance matrix\n", " Status : MINIMIZE=0 HESSE=0 \n", "\n", " Floating Parameter FinalValue +/- Error \n", " -------------------- --------------------------\n", " f 5.0082e-01 +/- 1.29e-02\n", " mx 1.0100e+00 +/- 3.26e-02\n", " my 9.6348e-01 +/- 3.31e-02\n", "\n" ] } ], "source": [ "r_sb1.Print()\n", "r_sb2.Print()\n", "r_sb12.Print()" ] } ], "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 }