{ "cells": [ { "cell_type": "markdown", "id": "c7d1d455", "metadata": {}, "source": [ "# rf103_interprfuncs\n", "Basic functionality: interpreted functions and pdfs\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 08:28 PM." ] }, { "cell_type": "code", "execution_count": 1, "id": "d1e10ae9", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:28:34.560571Z", "iopub.status.busy": "2026-05-19T20:28:34.560454Z", "iopub.status.idle": "2026-05-19T20:28:35.496305Z", "shell.execute_reply": "2026-05-19T20:28:35.495646Z" } }, "outputs": [], "source": [ "import ROOT" ] }, { "cell_type": "markdown", "id": "98d9bb17", "metadata": {}, "source": [ "Generic interpreted pdf\n", "------------------------------" ] }, { "cell_type": "markdown", "id": "d8583891", "metadata": {}, "source": [ "Declare observable x" ] }, { "cell_type": "code", "execution_count": 2, "id": "2d9af52c", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:28:35.498342Z", "iopub.status.busy": "2026-05-19T20:28:35.498208Z", "iopub.status.idle": "2026-05-19T20:28:35.660852Z", "shell.execute_reply": "2026-05-19T20:28:35.660131Z" } }, "outputs": [], "source": [ "x = ROOT.RooRealVar(\"x\", \"x\", -20, 20)" ] }, { "cell_type": "markdown", "id": "920c2c9e", "metadata": {}, "source": [ "Construct generic pdf from interpreted expression\n", "------------------------------------------------------" ] }, { "cell_type": "markdown", "id": "0fe5dbeb", "metadata": {}, "source": [ "ROOT.To construct a proper pdf, the formula expression is explicitly normalized internally by dividing\n", "it by a numeric integral of the expression over x in the range [-20,20]" ] }, { "cell_type": "code", "execution_count": 3, "id": "630c73c9", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:28:35.662895Z", "iopub.status.busy": "2026-05-19T20:28:35.662768Z", "iopub.status.idle": "2026-05-19T20:28:35.853877Z", "shell.execute_reply": "2026-05-19T20:28:35.853332Z" } }, "outputs": [], "source": [ "alpha = ROOT.RooRealVar(\"alpha\", \"alpha\", 5, 0.1, 10)\n", "genpdf = ROOT.RooGenericPdf(\"genpdf\", \"genpdf\", \"(1+0.1*abs(x)+sin(sqrt(abs(x*alpha+0.1))))\", [x, alpha])" ] }, { "cell_type": "markdown", "id": "565be49e", "metadata": {}, "source": [ "Sample, fit and plot generic pdf\n", "---------------------------------------------------------------" ] }, { "cell_type": "markdown", "id": "556bc2ae", "metadata": {}, "source": [ "Generate a toy dataset from the interpreted pdf" ] }, { "cell_type": "code", "execution_count": 4, "id": "2e2bf05a", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:28:35.856021Z", "iopub.status.busy": "2026-05-19T20:28:35.855900Z", "iopub.status.idle": "2026-05-19T20:28:36.010648Z", "shell.execute_reply": "2026-05-19T20:28:36.010014Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[#1] INFO:NumericIntegration -- RooRealIntegral::init(genpdf_Int[x]) using numeric integrator RooIntegrator1D to calculate Int(x)\n", "[#1] INFO:NumericIntegration -- RooRealIntegral::init(genpdf_Int[x]) using numeric integrator RooIntegrator1D to calculate Int(x)\n" ] } ], "source": [ "data = genpdf.generate({x}, 10000)" ] }, { "cell_type": "markdown", "id": "7df8ada2", "metadata": {}, "source": [ "Fit the interpreted pdf to the generated data" ] }, { "cell_type": "code", "execution_count": 5, "id": "7d449c1d", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:28:36.012699Z", "iopub.status.busy": "2026-05-19T20:28:36.012556Z", "iopub.status.idle": "2026-05-19T20:28:36.213697Z", "shell.execute_reply": "2026-05-19T20:28:36.213078Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[#1] INFO:Fitting -- RooAbsPdf::fitTo(genpdf_over_genpdf_Int[x]) 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 877.084 μs\n", "[#1] INFO:Fitting -- RooAddition::defaultErrorLevel(nll_genpdf_over_genpdf_Int[x]_genpdfData) Summation contains a RooNLLVar, using its error level\n", "[#1] INFO:Minimization -- [fitFCN] No discrete parameters, performing continuous minimization only\n", "[#1] INFO:NumericIntegration -- RooRealIntegral::init(genpdf_Int[x]) using numeric integrator RooIntegrator1D to calculate Int(x)\n" ] }, { "data": { "text/plain": [ "" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "genpdf.fitTo(data, PrintLevel=-1)" ] }, { "cell_type": "markdown", "id": "449e9e75", "metadata": {}, "source": [ "Make a plot of the data and the pdf overlaid" ] }, { "cell_type": "code", "execution_count": 6, "id": "aeaecad3", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:28:36.215673Z", "iopub.status.busy": "2026-05-19T20:28:36.215535Z", "iopub.status.idle": "2026-05-19T20:28:36.391287Z", "shell.execute_reply": "2026-05-19T20:28:36.390613Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[#1] INFO:NumericIntegration -- RooRealIntegral::init(genpdf_Int[x]) using numeric integrator RooIntegrator1D to calculate Int(x)\n" ] }, { "data": { "text/plain": [ "" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "xframe = x.frame(Title=\"Interpreted expression pdf\")\n", "data.plotOn(xframe)\n", "genpdf.plotOn(xframe)" ] }, { "cell_type": "markdown", "id": "92fe289f", "metadata": {}, "source": [ "Standard pdf adjust with interpreted helper function\n", "------------------------------------------------------------------------------------------------------------\n", "Make a gauss(x,sqrt(mean2),sigma) from a standard ROOT.RooGaussian #\n", "\n", "Construct standard pdf with formula replacing parameter\n", "------------------------------------------------------------------------------------------------------------" ] }, { "cell_type": "markdown", "id": "37f9e274", "metadata": {}, "source": [ "Construct parameter mean2 and sigma" ] }, { "cell_type": "code", "execution_count": 7, "id": "8f0c317a", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:28:36.393483Z", "iopub.status.busy": "2026-05-19T20:28:36.393364Z", "iopub.status.idle": "2026-05-19T20:28:36.496893Z", "shell.execute_reply": "2026-05-19T20:28:36.496138Z" } }, "outputs": [], "source": [ "mean2 = ROOT.RooRealVar(\"mean2\", \"mean^2\", 10, 0, 200)\n", "sigma = ROOT.RooRealVar(\"sigma\", \"sigma\", 3, 0.1, 10)" ] }, { "cell_type": "markdown", "id": "a9ab0bcf", "metadata": {}, "source": [ "Construct interpreted function mean = sqrt(mean^2)" ] }, { "cell_type": "code", "execution_count": 8, "id": "20abc5c0", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:28:36.498784Z", "iopub.status.busy": "2026-05-19T20:28:36.498662Z", "iopub.status.idle": "2026-05-19T20:28:36.616215Z", "shell.execute_reply": "2026-05-19T20:28:36.615582Z" } }, "outputs": [], "source": [ "mean = ROOT.RooFormulaVar(\"mean\", \"mean\", \"sqrt(mean2)\", [mean2])" ] }, { "cell_type": "markdown", "id": "8e231978", "metadata": {}, "source": [ "Construct a gaussian g2(x,sqrt(mean2),sigma)" ] }, { "cell_type": "code", "execution_count": 9, "id": "2dff2954", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:28:36.618337Z", "iopub.status.busy": "2026-05-19T20:28:36.618217Z", "iopub.status.idle": "2026-05-19T20:28:36.729773Z", "shell.execute_reply": "2026-05-19T20:28:36.729103Z" } }, "outputs": [], "source": [ "g2 = ROOT.RooGaussian(\"g2\", \"h2\", x, mean, sigma)" ] }, { "cell_type": "markdown", "id": "7db531d7", "metadata": {}, "source": [ "Generate toy data\n", "---------------------------------" ] }, { "cell_type": "markdown", "id": "6a2b4e28", "metadata": {}, "source": [ "Construct a separate gaussian g1(x,10,3) to generate a toy Gaussian\n", "dataset with mean 10 and width 3" ] }, { "cell_type": "code", "execution_count": 10, "id": "b2e97907", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:28:36.731940Z", "iopub.status.busy": "2026-05-19T20:28:36.731817Z", "iopub.status.idle": "2026-05-19T20:28:36.846301Z", "shell.execute_reply": "2026-05-19T20:28:36.845811Z" } }, "outputs": [], "source": [ "g1 = ROOT.RooGaussian(\"g1\", \"g1\", x, 10, 3)\n", "data2 = g1.generate({x}, 1000)" ] }, { "cell_type": "markdown", "id": "fa60cade", "metadata": {}, "source": [ "Fit and plot tailored standard pdf\n", "-------------------------------------------------------------------" ] }, { "cell_type": "markdown", "id": "b8007c29", "metadata": {}, "source": [ "Fit g2 to data from g1" ] }, { "cell_type": "code", "execution_count": 11, "id": "67e731b0", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:28:36.848036Z", "iopub.status.busy": "2026-05-19T20:28:36.847919Z", "iopub.status.idle": "2026-05-19T20:28:36.961560Z", "shell.execute_reply": "2026-05-19T20:28:36.961132Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[#1] INFO:Fitting -- RooAbsPdf::fitTo(g2_over_g2_Int[x]) fixing normalization set for coefficient determination to observables in data\n", "[#1] INFO:Fitting -- Creation of NLL object took 197.932 μs\n", "[#1] INFO:Fitting -- RooAddition::defaultErrorLevel(nll_g2_over_g2_Int[x]_g1Data) Summation contains a RooNLLVar, using its error level\n", "[#1] INFO:Minimization -- [fitFCN] No discrete parameters, performing continuous minimization only\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\n", " RooFitResult: minimized FCN value: 2551.39, estimated distance to minimum: 4.39288e-06\n", " covariance matrix quality: Full, accurate covariance matrix\n", " Status : MINIMIZE=0 HESSE=0 \n", "\n", " Floating Parameter FinalValue +/- Error \n", " -------------------- --------------------------\n", " mean2 1.0010e+02 +/- 1.98e+00\n", " sigma 3.1172e+00 +/- 7.12e-02\n", "\n" ] } ], "source": [ "r = g2.fitTo(data2, Save=True, PrintLevel=-1) # ROOT.RooFitResult\n", "r.Print()" ] }, { "cell_type": "markdown", "id": "094f634e", "metadata": {}, "source": [ "Plot data on frame and overlay projection of g2" ] }, { "cell_type": "code", "execution_count": 12, "id": "8f56bcf8", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:28:36.962954Z", "iopub.status.busy": "2026-05-19T20:28:36.962839Z", "iopub.status.idle": "2026-05-19T20:28:37.067319Z", "shell.execute_reply": "2026-05-19T20:28:37.066813Z" } }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "xframe2 = x.frame(Title=\"Tailored Gaussian pdf\")\n", "data2.plotOn(xframe2)\n", "g2.plotOn(xframe2)" ] }, { "cell_type": "markdown", "id": "d0886a7e", "metadata": {}, "source": [ "Draw all frames on a canvas" ] }, { "cell_type": "code", "execution_count": 13, "id": "a3bd5b49", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:28:37.069009Z", "iopub.status.busy": "2026-05-19T20:28:37.068895Z", "iopub.status.idle": "2026-05-19T20:28:37.305798Z", "shell.execute_reply": "2026-05-19T20:28:37.299355Z" } }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Info in : png file rf103_interprfuncs.png has been created\n" ] } ], "source": [ "c = ROOT.TCanvas(\"rf103_interprfuncs\", \"rf103_interprfuncs\", 800, 400)\n", "c.Divide(2)\n", "c.cd(1)\n", "ROOT.gPad.SetLeftMargin(0.15)\n", "xframe.GetYaxis().SetTitleOffset(1.4)\n", "xframe.Draw()\n", "c.cd(2)\n", "ROOT.gPad.SetLeftMargin(0.15)\n", "xframe2.GetYaxis().SetTitleOffset(1.4)\n", "xframe2.Draw()\n", "\n", "c.SaveAs(\"rf103_interprfuncs.png\")" ] }, { "cell_type": "markdown", "id": "049231a6", "metadata": {}, "source": [ "Draw all canvases " ] }, { "cell_type": "code", "execution_count": 14, "id": "b63300ed", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:28:37.307503Z", "iopub.status.busy": "2026-05-19T20:28:37.307331Z", "iopub.status.idle": "2026-05-19T20:28:37.489371Z", "shell.execute_reply": "2026-05-19T20:28:37.488817Z" } }, "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 }