{ "cells": [ { "cell_type": "markdown", "id": "b3bcad3a", "metadata": {}, "source": [ "# rf501_simultaneouspdf\n", "Organization and simultaneous fits: using simultaneous pdfs to describe simultaneous\n", "fits to multiple datasets\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 08:32 PM." ] }, { "cell_type": "code", "execution_count": 1, "id": "4ac7a92c", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:32:05.455972Z", "iopub.status.busy": "2026-05-19T20:32:05.455848Z", "iopub.status.idle": "2026-05-19T20:32:06.409622Z", "shell.execute_reply": "2026-05-19T20:32:06.409172Z" } }, "outputs": [], "source": [ "import ROOT" ] }, { "cell_type": "markdown", "id": "83997a10", "metadata": {}, "source": [ "Create model for physics sample\n", "-------------------------------------------------------------" ] }, { "cell_type": "markdown", "id": "ceed8068", "metadata": {}, "source": [ "Create observables" ] }, { "cell_type": "code", "execution_count": 2, "id": "8503e75a", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:32:06.433273Z", "iopub.status.busy": "2026-05-19T20:32:06.433117Z", "iopub.status.idle": "2026-05-19T20:32:06.600937Z", "shell.execute_reply": "2026-05-19T20:32:06.600251Z" } }, "outputs": [], "source": [ "x = ROOT.RooRealVar(\"x\", \"x\", -8, 8)" ] }, { "cell_type": "markdown", "id": "d370a2a9", "metadata": {}, "source": [ "Construct signal pdf" ] }, { "cell_type": "code", "execution_count": 3, "id": "07f85fc5", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:32:06.603247Z", "iopub.status.busy": "2026-05-19T20:32:06.603116Z", "iopub.status.idle": "2026-05-19T20:32:06.730034Z", "shell.execute_reply": "2026-05-19T20:32:06.729273Z" } }, "outputs": [], "source": [ "mean = ROOT.RooRealVar(\"mean\", \"mean\", 0, -8, 8)\n", "sigma = ROOT.RooRealVar(\"sigma\", \"sigma\", 0.3, 0.1, 10)\n", "gx = ROOT.RooGaussian(\"gx\", \"gx\", x, mean, sigma)" ] }, { "cell_type": "markdown", "id": "ee0ca0bd", "metadata": {}, "source": [ "Construct background pdf" ] }, { "cell_type": "code", "execution_count": 4, "id": "70360f4f", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:32:06.738067Z", "iopub.status.busy": "2026-05-19T20:32:06.737920Z", "iopub.status.idle": "2026-05-19T20:32:06.921721Z", "shell.execute_reply": "2026-05-19T20:32:06.920947Z" } }, "outputs": [], "source": [ "a0 = ROOT.RooRealVar(\"a0\", \"a0\", -0.1, -1, 1)\n", "a1 = ROOT.RooRealVar(\"a1\", \"a1\", 0.004, -1, 1)\n", "px = ROOT.RooChebychev(\"px\", \"px\", x, [a0, a1])" ] }, { "cell_type": "markdown", "id": "aa9251af", "metadata": {}, "source": [ "Construct composite pdf" ] }, { "cell_type": "code", "execution_count": 5, "id": "6ac7c11f", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:32:06.923511Z", "iopub.status.busy": "2026-05-19T20:32:06.923352Z", "iopub.status.idle": "2026-05-19T20:32:07.040907Z", "shell.execute_reply": "2026-05-19T20:32:07.040243Z" } }, "outputs": [], "source": [ "f = ROOT.RooRealVar(\"f\", \"f\", 0.2, 0.0, 1.0)\n", "model = ROOT.RooAddPdf(\"model\", \"model\", [gx, px], [f])" ] }, { "cell_type": "markdown", "id": "ce844c44", "metadata": {}, "source": [ "Create model for control sample\n", "--------------------------------------------------------------" ] }, { "cell_type": "markdown", "id": "2e0fcf1c", "metadata": {}, "source": [ "Construct signal pdf.\n", "NOTE that sigma is shared with the signal sample model" ] }, { "cell_type": "code", "execution_count": 6, "id": "5b21e2e3", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:32:07.043072Z", "iopub.status.busy": "2026-05-19T20:32:07.042912Z", "iopub.status.idle": "2026-05-19T20:32:07.147186Z", "shell.execute_reply": "2026-05-19T20:32:07.146485Z" } }, "outputs": [], "source": [ "mean_ctl = ROOT.RooRealVar(\"mean_ctl\", \"mean_ctl\", -3, -8, 8)\n", "gx_ctl = ROOT.RooGaussian(\"gx_ctl\", \"gx_ctl\", x, mean_ctl, sigma)" ] }, { "cell_type": "markdown", "id": "1672883b", "metadata": {}, "source": [ "Construct the background pdf" ] }, { "cell_type": "code", "execution_count": 7, "id": "50d3cbe4", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:32:07.149482Z", "iopub.status.busy": "2026-05-19T20:32:07.149310Z", "iopub.status.idle": "2026-05-19T20:32:07.253342Z", "shell.execute_reply": "2026-05-19T20:32:07.252749Z" } }, "outputs": [], "source": [ "a0_ctl = ROOT.RooRealVar(\"a0_ctl\", \"a0_ctl\", -0.1, -1, 1)\n", "a1_ctl = ROOT.RooRealVar(\"a1_ctl\", \"a1_ctl\", 0.5, -0.1, 1)\n", "px_ctl = ROOT.RooChebychev(\"px_ctl\", \"px_ctl\", x, [a0_ctl, a1_ctl])" ] }, { "cell_type": "markdown", "id": "21d17cf3", "metadata": {}, "source": [ "Construct the composite model" ] }, { "cell_type": "code", "execution_count": 8, "id": "98402487", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:32:07.255332Z", "iopub.status.busy": "2026-05-19T20:32:07.255207Z", "iopub.status.idle": "2026-05-19T20:32:07.358769Z", "shell.execute_reply": "2026-05-19T20:32:07.358237Z" } }, "outputs": [], "source": [ "f_ctl = ROOT.RooRealVar(\"f_ctl\", \"f_ctl\", 0.5, 0.0, 1.0)\n", "model_ctl = ROOT.RooAddPdf(\"model_ctl\", \"model_ctl\", [gx_ctl, px_ctl], [f_ctl])" ] }, { "cell_type": "markdown", "id": "7091310f", "metadata": {}, "source": [ "Generate events for both samples\n", "---------------------------------------------------------------" ] }, { "cell_type": "markdown", "id": "f0313815", "metadata": {}, "source": [ "Generate 1000 events in x and y from model" ] }, { "cell_type": "code", "execution_count": 9, "id": "ce83e33f", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:32:07.361078Z", "iopub.status.busy": "2026-05-19T20:32:07.360957Z", "iopub.status.idle": "2026-05-19T20:32:07.508729Z", "shell.execute_reply": "2026-05-19T20:32:07.508256Z" } }, "outputs": [], "source": [ "data = model.generate({x}, 1000)\n", "data_ctl = model_ctl.generate({x}, 2000)" ] }, { "cell_type": "markdown", "id": "2cb043f5", "metadata": {}, "source": [ "Create index category and join samples\n", "---------------------------------------------------------------------------" ] }, { "cell_type": "markdown", "id": "3f00b9c1", "metadata": {}, "source": [ "Define category to distinguish physics and control samples events" ] }, { "cell_type": "code", "execution_count": 10, "id": "901c2f4e", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:32:07.510681Z", "iopub.status.busy": "2026-05-19T20:32:07.510544Z", "iopub.status.idle": "2026-05-19T20:32:07.629359Z", "shell.execute_reply": "2026-05-19T20:32:07.628646Z" } }, "outputs": [ { "data": { "text/plain": [ "False" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sample = ROOT.RooCategory(\"sample\", \"sample\")\n", "sample.defineType(\"physics\")\n", "sample.defineType(\"control\")" ] }, { "cell_type": "markdown", "id": "133f97d8", "metadata": {}, "source": [ "Construct combined dataset in (x,sample)" ] }, { "cell_type": "code", "execution_count": 11, "id": "a08b3ac1", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:32:07.631028Z", "iopub.status.busy": "2026-05-19T20:32:07.630905Z", "iopub.status.idle": "2026-05-19T20:32:07.927797Z", "shell.execute_reply": "2026-05-19T20:32:07.927168Z" } }, "outputs": [], "source": [ "combData = ROOT.RooDataSet(\n", " \"combData\",\n", " \"combined data\",\n", " {x},\n", " Index=sample,\n", " Import={\"physics\": data, \"control\": data_ctl},\n", ")" ] }, { "cell_type": "markdown", "id": "e0b748e0", "metadata": {}, "source": [ "Construct a simultaneous pdf in (x, sample)\n", "-----------------------------------------------------------------------------------" ] }, { "cell_type": "markdown", "id": "242e488f", "metadata": {}, "source": [ "Construct a simultaneous pdf using category sample as index: associate model\n", "with the physics state and model_ctl with the control state" ] }, { "cell_type": "code", "execution_count": 12, "id": "e12700c2", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:32:07.929618Z", "iopub.status.busy": "2026-05-19T20:32:07.929485Z", "iopub.status.idle": "2026-05-19T20:32:08.105257Z", "shell.execute_reply": "2026-05-19T20:32:08.104766Z" } }, "outputs": [], "source": [ "simPdf = ROOT.RooSimultaneous(\"simPdf\", \"simultaneous pdf\", {\"physics\": model, \"control\": model_ctl}, sample)" ] }, { "cell_type": "markdown", "id": "1808d3fc", "metadata": {}, "source": [ "Perform a simultaneous fit\n", "---------------------------------------------------" ] }, { "cell_type": "markdown", "id": "e50269f9", "metadata": {}, "source": [ "Perform simultaneous fit of model to data and model_ctl to data_ctl" ] }, { "cell_type": "code", "execution_count": 13, "id": "a34be389", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:32:08.107104Z", "iopub.status.busy": "2026-05-19T20:32:08.106971Z", "iopub.status.idle": "2026-05-19T20:32:08.301107Z", "shell.execute_reply": "2026-05-19T20:32:08.300538Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[#1] INFO:Fitting -- RooAbsPdf::fitTo(simPdf) 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 1.25343 ms\n", "[#1] INFO:Fitting -- RooAddition::defaultErrorLevel(nll_simPdf_combData) Summation contains a RooNLLVar, using its error level\n", "[#1] INFO:Minimization -- [fitFCN] No discrete parameters, performing continuous minimization only\n", "\n", " RooFitResult: minimized FCN value: 8630.62, estimated distance to minimum: 0.000174671\n", " covariance matrix quality: Full, accurate covariance matrix\n", " Status : MINIMIZE=0 HESSE=0 \n", "\n", " Floating Parameter FinalValue +/- Error \n", " -------------------- --------------------------\n", " a0 6.7634e-02 +/- 6.04e-02\n", " a0_ctl -1.5627e-01 +/- 5.53e-02\n", " a1 -3.8353e-03 +/- 6.32e-02\n", " a1_ctl 3.8442e-01 +/- 4.35e-02\n", " f 1.7952e-01 +/- 1.55e-02\n", " f_ctl 5.2710e-01 +/- 1.25e-02\n", " mean 1.4991e-02 +/- 3.34e-02\n", " mean_ctl -3.0079e+00 +/- 1.04e-02\n", " sigma 3.0450e-01 +/- 8.33e-03\n", "\n" ] } ], "source": [ "fitResult = simPdf.fitTo(combData, PrintLevel=-1, Save=True)\n", "fitResult.Print()" ] }, { "cell_type": "markdown", "id": "4e0a1e27", "metadata": {}, "source": [ "Plot model slices on data slices\n", "----------------------------------------------------------------" ] }, { "cell_type": "markdown", "id": "8198aaf0", "metadata": {}, "source": [ "Make a frame for the physics sample" ] }, { "cell_type": "code", "execution_count": 14, "id": "a5d6b771", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:32:08.302667Z", "iopub.status.busy": "2026-05-19T20:32:08.302518Z", "iopub.status.idle": "2026-05-19T20:32:08.433708Z", "shell.execute_reply": "2026-05-19T20:32:08.433151Z" } }, "outputs": [], "source": [ "frame1 = x.frame(Title=\"Physics sample\")" ] }, { "cell_type": "markdown", "id": "cc7360c4", "metadata": {}, "source": [ "Plot all data tagged as physics sample" ] }, { "cell_type": "code", "execution_count": 15, "id": "b5c82da2", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:32:08.435378Z", "iopub.status.busy": "2026-05-19T20:32:08.435260Z", "iopub.status.idle": "2026-05-19T20:32:08.586297Z", "shell.execute_reply": "2026-05-19T20:32:08.585714Z" } }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "slicedData1 = combData.reduce(Cut=\"sample==sample::physics\")\n", "slicedData1.plotOn(frame1)" ] }, { "cell_type": "markdown", "id": "f3186bc7", "metadata": {}, "source": [ "Plot \"physics\" slice of simultaneous pdf." ] }, { "cell_type": "code", "execution_count": 16, "id": "8fa883a8", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:32:08.588074Z", "iopub.status.busy": "2026-05-19T20:32:08.587956Z", "iopub.status.idle": "2026-05-19T20:32:08.737625Z", "shell.execute_reply": "2026-05-19T20:32:08.737059Z" } }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" }, { "name": "stdout", "output_type": "stream", "text": [ "[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) directly selected PDF components: (px)\n", "[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) indirectly selected PDF components: ()\n" ] } ], "source": [ "simPdf.getPdf(\"physics\").plotOn(frame1)\n", "simPdf.getPdf(\"physics\").plotOn(frame1, Components=\"px\", LineStyle=\"--\")" ] }, { "cell_type": "markdown", "id": "de3b65ea", "metadata": {}, "source": [ "The same plot for the control sample slice. We do this with a different\n", "approach, using the data slice for the projection. This approach is more\n", "general, because you can plot sums of slices by using logical or in the\n", "Cut() command.\n", "NBL You _must_ project the sample index category with data using ProjWData\n", "as a RooSimultaneous makes no prediction on the shape in the index category\n", "and can thus not be integrated.\n", "In other words: Since the PDF doesn't know the number of events in the different\n", "category states, it doesn't know how much of each component it has to project out.\n", "This information is read from the data." ] }, { "cell_type": "code", "execution_count": 17, "id": "72871de3", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:32:08.739259Z", "iopub.status.busy": "2026-05-19T20:32:08.739094Z", "iopub.status.idle": "2026-05-19T20:32:08.892149Z", "shell.execute_reply": "2026-05-19T20:32:08.891549Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[#1] INFO:Plotting -- RooSimultaneous::plotOn(simPdf) plot on x averages with data index category (sample)\n" ] }, { "data": { "text/plain": [ "" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" }, { "name": "stdout", "output_type": "stream", "text": [ "[#1] INFO:Plotting -- RooSimultaneous::plotOn(simPdf) plot on x averages with data index category (sample)\n", "[#1] INFO:Plotting -- RooAbsPdf::plotOn(simPdf) directly selected PDF components: (px_ctl)\n", "[#1] INFO:Plotting -- RooAbsPdf::plotOn(simPdf) indirectly selected PDF components: (model_ctl)\n" ] } ], "source": [ "frame2 = x.frame(Title=\"Control sample\")\n", "slicedData2 = combData.reduce(Cut=\"sample==sample::control\")\n", "slicedData2.plotOn(frame2)\n", "simPdf.plotOn(frame2, ProjWData=(sample, slicedData2))\n", "simPdf.plotOn(frame2, Components=\"px_ctl\", ProjWData=(sample, slicedData2), LineStyle=\"--\")" ] }, { "cell_type": "markdown", "id": "e0e0b07a", "metadata": {}, "source": [ "The same plot for all the phase space. Here, we can just use the original\n", "combined dataset." ] }, { "cell_type": "code", "execution_count": 18, "id": "9a801cab", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:32:08.893558Z", "iopub.status.busy": "2026-05-19T20:32:08.893430Z", "iopub.status.idle": "2026-05-19T20:32:09.155057Z", "shell.execute_reply": "2026-05-19T20:32:09.154522Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[#1] INFO:Plotting -- RooSimultaneous::plotOn(simPdf) plot on x averages with data index category (sample)\n", "[#1] INFO:Plotting -- RooSimultaneous::plotOn(simPdf) plot on x averages with data index category (sample)\n", "[#1] INFO:Plotting -- RooAbsPdf::plotOn(simPdf) directly selected PDF components: (px,px_ctl)\n", "[#1] INFO:Plotting -- RooAbsPdf::plotOn(simPdf) indirectly selected PDF components: (model_ctl,model)\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "Info in : png file rf501_simultaneouspdf.png has been created\n" ] } ], "source": [ "frame3 = x.frame(Title=\"Both samples\")\n", "combData.plotOn(frame3)\n", "simPdf.plotOn(frame3, ProjWData=(sample, combData))\n", "simPdf.plotOn(frame3, Components=\"px,px_ctl\", ProjWData=(sample, combData), LineStyle=\"--\")\n", "\n", "c = ROOT.TCanvas(\"rf501_simultaneouspdf\", \"rf501_simultaneouspdf\", 1200, 400)\n", "c.Divide(3)\n", "\n", "\n", "def draw(i, frame):\n", " c.cd(i)\n", " ROOT.gPad.SetLeftMargin(0.15)\n", " frame.GetYaxis().SetTitleOffset(1.4)\n", " frame.Draw()\n", "\n", "\n", "draw(1, frame1)\n", "draw(2, frame2)\n", "draw(3, frame3)\n", "\n", "c.SaveAs(\"rf501_simultaneouspdf.png\")" ] }, { "cell_type": "markdown", "id": "cf520b55", "metadata": {}, "source": [ "Draw all canvases " ] }, { "cell_type": "code", "execution_count": 19, "id": "e9202b9b", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:32:09.156969Z", "iopub.status.busy": "2026-05-19T20:32:09.156850Z", "iopub.status.idle": "2026-05-19T20:32:09.337745Z", "shell.execute_reply": "2026-05-19T20:32:09.337135Z" } }, "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 }