{ "cells": [ { "cell_type": "markdown", "id": "893cf7f4", "metadata": {}, "source": [ "# rf616_morphing\n", "Use Morphing in RooFit.\n", "\n", "This tutorial shows how to use template morphing inside RooFit. As input we have several\n", "Gaussian distributions. The output is one gaussian, with a specific mean value.\n", "Since likelihoods are often used within the framework of morphing, we provide a\n", "way to estimate the negative log likelihood (nll).\n", "\n", "Based on example of Kyle Cranmer https://gist.github.com/cranmer/46fff8d22015e5a26619.\n", "\n", "\n", "\n", "\n", "**Author:** Robin Syring \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": "3cece6f8", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:33:57.904544Z", "iopub.status.busy": "2026-05-19T20:33:57.904424Z", "iopub.status.idle": "2026-05-19T20:33:58.874058Z", "shell.execute_reply": "2026-05-19T20:33:58.865435Z" } }, "outputs": [], "source": [ "import ROOT" ] }, { "cell_type": "markdown", "id": "cdede8ed", "metadata": {}, "source": [ "Number of samples to fill the histograms" ] }, { "cell_type": "code", "execution_count": 2, "id": "e4409e39", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:33:58.875765Z", "iopub.status.busy": "2026-05-19T20:33:58.875621Z", "iopub.status.idle": "2026-05-19T20:33:59.031424Z", "shell.execute_reply": "2026-05-19T20:33:59.019646Z" } }, "outputs": [], "source": [ "n_samples = 1000" ] }, { "cell_type": "markdown", "id": "082aa65f", "metadata": {}, "source": [ "Kills warning messages" ] }, { "cell_type": "code", "execution_count": 3, "id": "9073a6a1", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:33:59.040348Z", "iopub.status.busy": "2026-05-19T20:33:59.040209Z", "iopub.status.idle": "2026-05-19T20:33:59.215248Z", "shell.execute_reply": "2026-05-19T20:33:59.214208Z" } }, "outputs": [], "source": [ "ROOT.RooMsgService.instance().setGlobalKillBelow(ROOT.RooFit.WARNING)" ] }, { "cell_type": "markdown", "id": "5237c1da", "metadata": {}, "source": [ "morphing as a baseline" ] }, { "cell_type": "code", "execution_count": 4, "id": "93d70008", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:33:59.216798Z", "iopub.status.busy": "2026-05-19T20:33:59.216659Z", "iopub.status.idle": "2026-05-19T20:33:59.322377Z", "shell.execute_reply": "2026-05-19T20:33:59.321262Z" } }, "outputs": [], "source": [ "def morphing(setting):\n", " # set up a frame for plotting\n", " frame1 = x_var.frame()\n", "\n", " # define binning for morphing\n", " bin_mu_x = ROOT.RooBinning(4, 0.0, 4.0)\n", " grid = ROOT.RooMomentMorphFuncND.Grid(bin_mu_x)\n", " x_var.setBins(50)\n", "\n", " # number of 'sampled' Gaussians, if you change it, adjust the binning properly\n", " for i in range(5):\n", " # Create the sampled Gaussian\n", " workspace.factory(f\"Gaussian::g{i}(x, mu{i}[{i}], {sigma})\".format(i=i))\n", "\n", " # Fill the histograms\n", " hist = workspace[f\"g{i}\"].generateBinned([x_var], n_samples * 100)\n", " # Make sure that every bin is filled and we don't get zero probability\n", " for i_bin in range(hist.numEntries()):\n", " hist.add(hist.get(i_bin), 1.0)\n", "\n", " # Add the pdf to the workspace, the inOrder of 1 is necessary for calculation of the nll\n", " # Adjust it to 0 to see binning\n", " workspace.Import(ROOT.RooHistPdf(f\"histpdf{i}\", f\"histpdf{i}\", [x_var], hist, intOrder=1))\n", "\n", " # Add the pdf to the grid and to the plot\n", " grid.addPdf(workspace[f\"histpdf{i}\"], int(i))\n", " workspace[f\"histpdf{i}\"].plotOn(frame1)\n", "\n", " # Create the morphing and add it to the workspace\n", " morph_func = ROOT.RooMomentMorphFuncND(\"morph_func\", \"morph_func\", [mu_var], [x_var], grid, setting)\n", "\n", " # Normalizes the morphed object to be a pdf, set it false to prevent warning messages and gain computational speed up\n", " morph_func.setPdfMode()\n", "\n", " # Creating the morphed pdf\n", " morph = ROOT.RooWrapperPdf(\"morph\", \"morph\", morph_func, True)\n", " workspace.Import(morph)\n", " workspace[\"morph\"].plotOn(frame1, LineColor=\"r\")\n", "\n", " return frame1" ] }, { "cell_type": "markdown", "id": "02597efc", "metadata": {}, "source": [ "Define the \"observed\" data in a workspade" ] }, { "cell_type": "code", "execution_count": 5, "id": "202c2a7e", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:33:59.323870Z", "iopub.status.busy": "2026-05-19T20:33:59.323737Z", "iopub.status.idle": "2026-05-19T20:33:59.427880Z", "shell.execute_reply": "2026-05-19T20:33:59.426761Z" } }, "outputs": [], "source": [ "def build_ws(mu_observed, sigma):\n", " ws = ROOT.RooWorkspace()\n", " ws.factory(f\"Gaussian::gauss(x[-5,15], mu[{mu_observed},0,4], {sigma})\".format(mu_observed=mu_observed))\n", "\n", " return ws" ] }, { "cell_type": "markdown", "id": "90d8db90", "metadata": {}, "source": [ "The \"observed\" data" ] }, { "cell_type": "code", "execution_count": 6, "id": "872ef9cc", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:33:59.429360Z", "iopub.status.busy": "2026-05-19T20:33:59.429227Z", "iopub.status.idle": "2026-05-19T20:33:59.658862Z", "shell.execute_reply": "2026-05-19T20:33:59.658221Z" } }, "outputs": [], "source": [ "mu_observed = 2.5\n", "sigma = 1.5\n", "workspace = build_ws(mu_observed, sigma)\n", "x_var = workspace[\"x\"]\n", "mu_var = workspace[\"mu\"]\n", "gauss = workspace.pdf(\"gauss\")\n", "obs_data = gauss.generate(x_var, n_samples)" ] }, { "cell_type": "markdown", "id": "669ed5d4", "metadata": {}, "source": [ "Create the exact negative log likelihood functions for Gaussian model" ] }, { "cell_type": "code", "execution_count": 7, "id": "1133ad47", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:33:59.660525Z", "iopub.status.busy": "2026-05-19T20:33:59.660402Z", "iopub.status.idle": "2026-05-19T20:33:59.808027Z", "shell.execute_reply": "2026-05-19T20:33:59.807410Z" } }, "outputs": [], "source": [ "nll_gauss = gauss.createNLL(obs_data)" ] }, { "cell_type": "markdown", "id": "6162b054", "metadata": {}, "source": [ "Compute the morphed nll" ] }, { "cell_type": "code", "execution_count": 8, "id": "61184238", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:33:59.809730Z", "iopub.status.busy": "2026-05-19T20:33:59.809585Z", "iopub.status.idle": "2026-05-19T20:34:00.227775Z", "shell.execute_reply": "2026-05-19T20:34:00.227142Z" } }, "outputs": [], "source": [ "frame1 = morphing(ROOT.RooMomentMorphFuncND.Linear)\n", "\n", "nll_morph = workspace[\"morph\"].createNLL(obs_data)" ] }, { "cell_type": "markdown", "id": "00a69ecd", "metadata": {}, "source": [ "Plot the negative logarithmic summed likelihood" ] }, { "cell_type": "code", "execution_count": 9, "id": "2ed56e7f", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:34:00.229433Z", "iopub.status.busy": "2026-05-19T20:34:00.229310Z", "iopub.status.idle": "2026-05-19T20:34:00.482100Z", "shell.execute_reply": "2026-05-19T20:34:00.481470Z" } }, "outputs": [], "source": [ "frame2 = mu_var.frame(Title=\"Negative log Likelihood\")\n", "nll_gauss.plotOn(frame2, LineColor=\"b\", ShiftToZero=True, Name=\"gauss\")\n", "nll_morph.plotOn(frame2, LineColor=\"r\", ShiftToZero=True, Name=\"morphed\")\n", "\n", "c = ROOT.TCanvas(\"rf616_morphing\", \"rf616_morphing\", 800, 400)\n", "c.Divide(2)\n", "c.cd(1)\n", "ROOT.gPad.SetLeftMargin(0.15)\n", "frame1.GetYaxis().SetTitleOffset(1.8)\n", "frame1.Draw()\n", "c.cd(2)\n", "ROOT.gPad.SetLeftMargin(0.15)\n", "frame2.GetYaxis().SetTitleOffset(1.8)\n", "frame2.Draw()" ] }, { "cell_type": "markdown", "id": "841b769f", "metadata": {}, "source": [ "Compute the minimum via minuit and display the results" ] }, { "cell_type": "code", "execution_count": 10, "id": "a025b264", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:34:00.483821Z", "iopub.status.busy": "2026-05-19T20:34:00.483696Z", "iopub.status.idle": "2026-05-19T20:34:00.647906Z", "shell.execute_reply": "2026-05-19T20:34:00.647278Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", " RooFitResult: minimized FCN value: 1862.97, estimated distance to minimum: 2.32702e-05\n", " covariance matrix quality: Full, accurate covariance matrix\n", " Status : MINIMIZE=0 \n", "\n", " Floating Parameter FinalValue +/- Error \n", " -------------------- --------------------------\n", " mu 2.5399e+00 +/- 4.74e-02\n", "\n", "\n", " RooFitResult: minimized FCN value: 1862.82, estimated distance to minimum: 9.31473e-06\n", " covariance matrix quality: Full, accurate covariance matrix\n", " Status : MINIMIZE=0 \n", "\n", " Floating Parameter FinalValue +/- Error \n", " -------------------- --------------------------\n", " mu 2.5372e+00 +/- 4.08e-02\n", "\n" ] } ], "source": [ "for nll in [nll_gauss, nll_morph]:\n", " minimizer = ROOT.RooMinimizer(nll)\n", " minimizer.setPrintLevel(-1)\n", " minimizer.minimize(\"Minuit2\")\n", " result = minimizer.save()\n", " result.Print()" ] }, { "cell_type": "markdown", "id": "e471ecde", "metadata": {}, "source": [ "Draw all canvases " ] }, { "cell_type": "code", "execution_count": 11, "id": "aa8c7270", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:34:00.649275Z", "iopub.status.busy": "2026-05-19T20:34:00.649150Z", "iopub.status.idle": "2026-05-19T20:34:00.844119Z", "shell.execute_reply": "2026-05-19T20:34:00.843548Z" } }, "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 }