{ "cells": [ { "cell_type": "markdown", "id": "8862214f", "metadata": {}, "source": [ "# rf618_mixture_models\n", "Use of mixture models in RooFit.\n", "\n", "This tutorial shows, how to use mixture models for Likelihood Calculation in ROOT. Instead of directly\n", "calculating the likelihood we use simulation based inference (SBI) as shown in tutorial 'rf615_simulation_based_inference.py'.\n", "We train the classifier to discriminate between samples from an background hypothesis here the zz samples and a target\n", "hypothesis, here the higgs samples. The data preparation is based on the tutorial 'df106_HiggsToFourLeptons.py'.\n", "\n", "An introduction to mixture models can be found here https://arxiv.org/pdf/1506.02169.\n", "\n", "A short summary:\n", "We assume the whole probability distribution can be written as a mixture of several components, i.e.\n", "$$p(x|\\theta)= \\sum_{c}w_{c}(\\theta)p_{c}(x|\\theta)$$\n", "We can write the likelihood ratio in terms of pairwise classification problems\n", " \\frac{p(x|\\mu)}{p(x|0)}&= \\frac{\\sum_{c}w_{c}(\\mu)p_{c}(x|\\mu)}{\\sum_{c'}w_{c'}(0)p_{c'}(x|0)}\\\\\n", " &=\\sum_{c}\\Bigg[\\sum_{c'}\\frac{w_{c'}(0)}{w_{c}(\\mu)}\\frac{p_{c'}(x|0)}{p_{c}(x|\\mu)}\\Bigg]^{-1},\n", "where mu is the signal strength, and a value of 0 corresponds to the background hypothesis. Using this decomposition, one is able to use the pairwise likelihood ratios.\n", "\n", "Since the only free parameter in our case is mu, the distributions are independent of this parameter and the dependence on the signal strength can be encoded into the weights.\n", "Thus, the subratios simplify dramatically since they are independent of theta and these ratios can be pre-computed and the classifier does\n", "not need to be parametrized.\n", "\n", "If you wish to see an analysis done with template histograms see 'hf001_example.py'.\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 08:34 PM." ] }, { "cell_type": "code", "execution_count": 1, "id": "1ffb7a1a", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:34:03.133332Z", "iopub.status.busy": "2026-05-19T20:34:03.133212Z", "iopub.status.idle": "2026-05-19T20:34:04.953044Z", "shell.execute_reply": "2026-05-19T20:34:04.952095Z" } }, "outputs": [], "source": [ "import ROOT\n", "import os\n", "import numpy as np\n", "import xgboost as xgb" ] }, { "cell_type": "markdown", "id": "892e479a", "metadata": {}, "source": [ "Get Dataframe from tutorial df106_HiggsToFourLeptons.py\n", "Adjust the path if running locally" ] }, { "cell_type": "code", "execution_count": 2, "id": "5014b1ee", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:34:04.955388Z", "iopub.status.busy": "2026-05-19T20:34:04.955153Z", "iopub.status.idle": "2026-05-19T20:34:05.490758Z", "shell.execute_reply": "2026-05-19T20:34:05.490288Z" } }, "outputs": [], "source": [ "df = ROOT.RDataFrame(\"tree\", ROOT.gROOT.GetTutorialDir().Data() + \"/analysis/dataframe/df106_HiggsToFourLeptons.root\")" ] }, { "cell_type": "markdown", "id": "c1698f37", "metadata": {}, "source": [ "Initialize a dictionary to store counts and weight sums for each category" ] }, { "cell_type": "code", "execution_count": 3, "id": "64846862", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:34:05.499625Z", "iopub.status.busy": "2026-05-19T20:34:05.499477Z", "iopub.status.idle": "2026-05-19T20:34:05.603013Z", "shell.execute_reply": "2026-05-19T20:34:05.602313Z" } }, "outputs": [], "source": [ "results = {}" ] }, { "cell_type": "markdown", "id": "23da4439", "metadata": {}, "source": [ "Extract the relevant columns once and avoid repeated calls" ] }, { "cell_type": "code", "execution_count": 4, "id": "785aa879", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:34:05.605277Z", "iopub.status.busy": "2026-05-19T20:34:05.605148Z", "iopub.status.idle": "2026-05-19T20:34:07.899484Z", "shell.execute_reply": "2026-05-19T20:34:07.898753Z" } }, "outputs": [], "source": [ "data_dict = df.AsNumpy(columns=[\"m4l\", \"sample_category\", \"weight\"])\n", "\n", "\n", "weights_dict = {\n", " name: data_dict[\"weight\"][data_dict[\"sample_category\"] == [name]].sum() for name in (\"data\", \"zz\", \"other\", \"higgs\")\n", "}" ] }, { "cell_type": "markdown", "id": "e0a15209", "metadata": {}, "source": [ "Loop over each sample category" ] }, { "cell_type": "code", "execution_count": 5, "id": "2a8e2dc7", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:34:07.901383Z", "iopub.status.busy": "2026-05-19T20:34:07.901248Z", "iopub.status.idle": "2026-05-19T20:34:08.037147Z", "shell.execute_reply": "2026-05-19T20:34:08.036487Z" } }, "outputs": [], "source": [ "for sample_category in [\"data\", \"higgs\", \"zz\", \"other\"]:\n", "\n", " weight_sum = weights_dict[sample_category]\n", "\n", " mask = data_dict[\"sample_category\"] == sample_category\n", " # Normalize each weight\n", " weights = data_dict[\"weight\"][mask]\n", " # Extract the weight_modified\n", " weight_modified = weights / weight_sum\n", "\n", " count = np.sum(mask)\n", "\n", " # Store the count and weight sum in the dictionary\n", " results[sample_category] = {\n", " \"weight_sum\": weight_sum,\n", " \"weight_modified\": weight_modified,\n", " \"count\": count,\n", " \"weight\": weights,\n", " }" ] }, { "cell_type": "markdown", "id": "54afbae5", "metadata": {}, "source": [ "Extract the mass for higgs and zz" ] }, { "cell_type": "code", "execution_count": 6, "id": "acef7a45", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:34:08.039247Z", "iopub.status.busy": "2026-05-19T20:34:08.039116Z", "iopub.status.idle": "2026-05-19T20:34:08.157289Z", "shell.execute_reply": "2026-05-19T20:34:08.156588Z" } }, "outputs": [], "source": [ "higgs_data = data_dict[\"m4l\"][data_dict[\"sample_category\"] == [\"higgs\"]]\n", "zz_data = data_dict[\"m4l\"][data_dict[\"sample_category\"] == [\"zz\"]]" ] }, { "cell_type": "markdown", "id": "a37bc19b", "metadata": {}, "source": [ "Prepare sample weights" ] }, { "cell_type": "code", "execution_count": 7, "id": "2fbe290b", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:34:08.159454Z", "iopub.status.busy": "2026-05-19T20:34:08.159326Z", "iopub.status.idle": "2026-05-19T20:34:08.265956Z", "shell.execute_reply": "2026-05-19T20:34:08.265291Z" } }, "outputs": [], "source": [ "sample_weight_higgs = np.array([results[\"higgs\"][\"weight_modified\"]]).flatten()\n", "sample_weight_zz = np.array([results[\"zz\"][\"weight_modified\"]]).flatten()" ] }, { "cell_type": "markdown", "id": "d8ff7945", "metadata": {}, "source": [ "Putting sample weights together in the same manner as the training data" ] }, { "cell_type": "code", "execution_count": 8, "id": "7ab346e3", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:34:08.268118Z", "iopub.status.busy": "2026-05-19T20:34:08.267988Z", "iopub.status.idle": "2026-05-19T20:34:08.372692Z", "shell.execute_reply": "2026-05-19T20:34:08.372019Z" } }, "outputs": [], "source": [ "sample_weight = np.concatenate([sample_weight_higgs, sample_weight_zz])" ] }, { "cell_type": "markdown", "id": "af966f85", "metadata": {}, "source": [ "For Training purposes we have to get rid of the negative weights, since xgb can't handle them" ] }, { "cell_type": "code", "execution_count": 9, "id": "7cecbc5b", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:34:08.374783Z", "iopub.status.busy": "2026-05-19T20:34:08.374650Z", "iopub.status.idle": "2026-05-19T20:34:08.479196Z", "shell.execute_reply": "2026-05-19T20:34:08.478611Z" } }, "outputs": [], "source": [ "sample_weight[sample_weight < 0] = 1e-6" ] }, { "cell_type": "markdown", "id": "9319657e", "metadata": {}, "source": [ "Prepare the features and labels" ] }, { "cell_type": "code", "execution_count": 10, "id": "c5e13121", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:34:08.481403Z", "iopub.status.busy": "2026-05-19T20:34:08.481271Z", "iopub.status.idle": "2026-05-19T20:34:08.587087Z", "shell.execute_reply": "2026-05-19T20:34:08.586354Z" } }, "outputs": [], "source": [ "X = np.concatenate((higgs_data, zz_data), axis=0).reshape(-1, 1)\n", "y = np.concatenate([np.ones(len(higgs_data)), np.zeros(len(zz_data))])" ] }, { "cell_type": "markdown", "id": "4b81053e", "metadata": {}, "source": [ "Train the Classifier to discriminate between higgs and zz" ] }, { "cell_type": "code", "execution_count": 11, "id": "320726f5", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:34:08.588972Z", "iopub.status.busy": "2026-05-19T20:34:08.588840Z", "iopub.status.idle": "2026-05-19T20:34:20.067030Z", "shell.execute_reply": "2026-05-19T20:34:20.066185Z" } }, "outputs": [ { "data": { "text/html": [ "
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" ], "text/plain": [ "XGBClassifier(base_score=None, booster=None, callbacks=None,\n", " colsample_bylevel=None, colsample_bynode=None,\n", " colsample_bytree=None, device=None, early_stopping_rounds=None,\n", " enable_categorical=False, eta=0.2, eval_metric=None,\n", " feature_types=None, feature_weights=None, gamma=None,\n", " grow_policy=None, importance_type=None,\n", " interaction_constraints=None, learning_rate=None, max_bin=None,\n", " max_cat_threshold=None, max_cat_to_onehot=None,\n", " max_delta_step=None, max_depth=5, max_leaves=None,\n", " min_child_weight=1e-06, missing=nan, monotone_constraints=None,\n", " multi_strategy=None, n_estimators=1000, n_jobs=None, ...)" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "model_xgb = xgb.XGBClassifier(n_estimators=1000, max_depth=5, eta=0.2, min_child_weight=1e-6, nthread=1)\n", "model_xgb.fit(X, y, sample_weight=sample_weight)" ] }, { "cell_type": "markdown", "id": "b5174a03", "metadata": {}, "source": [ "Building a RooRealVar based on the observed data" ] }, { "cell_type": "code", "execution_count": 12, "id": "c4cc5783", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:34:20.068894Z", "iopub.status.busy": "2026-05-19T20:34:20.068759Z", "iopub.status.idle": "2026-05-19T20:34:20.232756Z", "shell.execute_reply": "2026-05-19T20:34:20.232045Z" } }, "outputs": [], "source": [ "m4l = ROOT.RooRealVar(\"m4l\", \"Four Lepton Invariant Mass\", 0.0)" ] }, { "cell_type": "markdown", "id": "c91196fc", "metadata": {}, "source": [ "Define functions to compute the learned likelihood." ] }, { "cell_type": "code", "execution_count": 13, "id": "20443647", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:34:20.234982Z", "iopub.status.busy": "2026-05-19T20:34:20.234855Z", "iopub.status.idle": "2026-05-19T20:34:20.731967Z", "shell.execute_reply": "2026-05-19T20:34:20.731498Z" } }, "outputs": [], "source": [ "def calculate_likelihood_xgb(m4l_arr: np.ndarray) -> np.ndarray:\n", " prob = model_xgb.predict_proba(m4l_arr.T)[:, 0]\n", " return (1 - prob) / prob\n", "\n", "\n", "llh = ROOT.RooFit.bindFunction(f\"llh\", calculate_likelihood_xgb, m4l)" ] }, { "cell_type": "markdown", "id": "430345cb", "metadata": {}, "source": [ "Number of signals and background" ] }, { "cell_type": "code", "execution_count": 14, "id": "ae2ab961", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:34:20.741465Z", "iopub.status.busy": "2026-05-19T20:34:20.741316Z", "iopub.status.idle": "2026-05-19T20:34:20.845305Z", "shell.execute_reply": "2026-05-19T20:34:20.844710Z" } }, "outputs": [], "source": [ "n_signal = results[\"higgs\"][\"weight\"].sum()\n", "n_back = results[\"zz\"][\"weight\"].sum()" ] }, { "cell_type": "markdown", "id": "b50a3771", "metadata": {}, "source": [ "Define weight functions" ] }, { "cell_type": "code", "execution_count": 15, "id": "bfccdf9d", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:34:20.847385Z", "iopub.status.busy": "2026-05-19T20:34:20.847251Z", "iopub.status.idle": "2026-05-19T20:34:20.950799Z", "shell.execute_reply": "2026-05-19T20:34:20.950174Z" } }, "outputs": [], "source": [ "def weight_back(mu):\n", " return n_back / (n_back + mu * n_signal)\n", "\n", "\n", "def weight_signal(mu):\n", " return 1 - weight_back(mu)" ] }, { "cell_type": "markdown", "id": "c0814111", "metadata": {}, "source": [ "Define the likelihood ratio accordingly to mixture models" ] }, { "cell_type": "code", "execution_count": 16, "id": "19e3ee59", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:34:20.952741Z", "iopub.status.busy": "2026-05-19T20:34:20.952589Z", "iopub.status.idle": "2026-05-19T20:34:21.172438Z", "shell.execute_reply": "2026-05-19T20:34:21.171833Z" } }, "outputs": [], "source": [ "def likelihood_ratio(llr: np.ndarray, mu: np.ndarray) -> np.ndarray:\n", "\n", " m = 2\n", "\n", " w_0 = np.array([weight_back(0), weight_signal(0)])\n", " w_1 = np.array([weight_back(mu[0]), weight_signal(mu[0])])\n", "\n", " w = np.outer(w_1, 1.0 / w_0)\n", "\n", " p = np.ones((m, m, len(llr)))\n", " p[1, 0] = llr\n", " for i in range(m):\n", " for j in range(i):\n", " p[j, i] = 1.0 / p[i, j]\n", "\n", " return 1.0 / np.sum(1.0 / np.sum(np.expand_dims(w, axis=2) * p, axis=0), axis=0)\n", "\n", "\n", "mu_var = ROOT.RooRealVar(\"mu\", \"mu\", 0.1, 5)\n", "\n", "nll_ratio = ROOT.RooFit.bindFunction(f\"nll\", likelihood_ratio, llh, mu_var)\n", "pdf_learned = ROOT.RooWrapperPdf(\"learned_pdf\", \"learned_pdf\", nll_ratio, selfNormalized=True)" ] }, { "cell_type": "markdown", "id": "b1c1c334", "metadata": {}, "source": [ "Plot the likelihood" ] }, { "cell_type": "code", "execution_count": 17, "id": "58c538b6", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:34:21.174708Z", "iopub.status.busy": "2026-05-19T20:34:21.174561Z", "iopub.status.idle": "2026-05-19T20:34:21.305845Z", "shell.execute_reply": "2026-05-19T20:34:21.305196Z" } }, "outputs": [], "source": [ "frame1 = m4l.frame(Title=\"Likelihood ratio r(m_{4l}|#mu=1);m_{4l};p(#mu=1)/p(#mu=0)\", Range=(80, 170))" ] }, { "cell_type": "markdown", "id": "aa7efdc6", "metadata": {}, "source": [ "llh.plotOn(frame1, ShiftToZero=False, LineColor=\"kP6Blue\")" ] }, { "cell_type": "code", "execution_count": 18, "id": "10f661f9", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:34:21.307571Z", "iopub.status.busy": "2026-05-19T20:34:21.307446Z", "iopub.status.idle": "2026-05-19T20:34:21.663549Z", "shell.execute_reply": "2026-05-19T20:34:21.662953Z" } }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/tmp/ipykernel_583254/3977165901.py:8: RuntimeWarning: divide by zero encountered in divide\n", " w = np.outer(w_1, 1.0 / w_0)\n" ] } ], "source": [ "nll_ratio.plotOn(frame1, ShiftToZero=False, LineColor=\"kP6Blue\")\n", "\n", "n_pred = ROOT.RooFormulaVar(\"n_pred\", f\"{n_back} + mu * {n_signal}\", [mu_var])\n", "pdf_learned_extended = ROOT.RooExtendPdf(\"final_pdf\", \"final_pdf\", pdf_learned, n_pred)" ] }, { "cell_type": "markdown", "id": "b2a36cee", "metadata": {}, "source": [ "Prepare the observed data set and NLL" ] }, { "cell_type": "code", "execution_count": 19, "id": "fa0b3e75", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:34:21.665373Z", "iopub.status.busy": "2026-05-19T20:34:21.665238Z", "iopub.status.idle": "2026-05-19T20:34:21.956195Z", "shell.execute_reply": "2026-05-19T20:34:21.955625Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[#1] INFO:Fitting -- RooAbsPdf::fitTo(final_pdf) 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 1.2029 ms\n" ] } ], "source": [ "data = ROOT.RooDataSet.from_numpy({\"m4l\": data_dict[\"m4l\"][data_dict[\"sample_category\"] == [\"data\"]]}, [m4l])\n", "nll = pdf_learned_extended.createNLL(data, Extended=True)" ] }, { "cell_type": "markdown", "id": "f73025bc", "metadata": {}, "source": [ "Plot the nll computet by the mixture model" ] }, { "cell_type": "code", "execution_count": 20, "id": "9d7010d9", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:34:21.958263Z", "iopub.status.busy": "2026-05-19T20:34:21.958115Z", "iopub.status.idle": "2026-05-19T20:34:22.122073Z", "shell.execute_reply": "2026-05-19T20:34:22.121365Z" } }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/tmp/ipykernel_583254/3977165901.py:8: RuntimeWarning: divide by zero encountered in divide\n", " w = np.outer(w_1, 1.0 / w_0)\n" ] }, { "data": { "text/plain": [ "" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "frame2 = mu_var.frame(Title=\"NLL sum;#mu (signal strength);#Delta NLL\", Range=(0.5, 4))\n", "nll.plotOn(frame2, ShiftToZero=True, LineColor=\"kP6Blue\")" ] }, { "cell_type": "markdown", "id": "cdacfc4d", "metadata": {}, "source": [ "Write the plots into one canvas to show, or into separate canvases for saving." ] }, { "cell_type": "code", "execution_count": 21, "id": "37473efd", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:34:22.124576Z", "iopub.status.busy": "2026-05-19T20:34:22.124428Z", "iopub.status.idle": "2026-05-19T20:34:22.282238Z", "shell.execute_reply": "2026-05-19T20:34:22.281798Z" } }, "outputs": [], "source": [ "single_canvas = True\n", "\n", "c = ROOT.TCanvas(\"\", \"\", 1200 if single_canvas else 600, 600)\n", "if single_canvas:\n", " c.Divide(2)\n", " c.cd(1)\n", " ROOT.gPad.SetLeftMargin(0.15)\n", " frame1.GetYaxis().SetTitleOffset(1.8)\n", "frame1.Draw()\n", "\n", "if single_canvas:\n", " c.cd(2)\n", " ROOT.gPad.SetLeftMargin(0.15)\n", " frame2.GetYaxis().SetTitleOffset(1.8)\n", "else:\n", " c.SaveAs(\"rf618_plot_1.png\")\n", " c = ROOT.TCanvas(\"\", \"\", 600, 600)\n", "\n", "frame2.Draw()\n", "\n", "if not single_canvas:\n", " c.SaveAs(\"rf618_plot_2.png\")" ] }, { "cell_type": "markdown", "id": "1fb82ec6", "metadata": {}, "source": [ "Compute the minimum via minuit and display the results" ] }, { "cell_type": "code", "execution_count": 22, "id": "1ce44724", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:34:22.284462Z", "iopub.status.busy": "2026-05-19T20:34:22.284326Z", "iopub.status.idle": "2026-05-19T20:34:22.547422Z", "shell.execute_reply": "2026-05-19T20:34:22.546810Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[#1] INFO:Fitting -- RooAddition::defaultErrorLevel(nll_final_pdf_) Summation contains a RooNLLVar, using its error level\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "[#1] INFO:Minimization -- [fitFCN] No discrete parameters, performing continuous minimization only\n", "\n", " RooFitResult: minimized FCN value: -1538.33, estimated distance to minimum: 1.0744e-09\n", " covariance matrix quality: Full, accurate covariance matrix\n", " Status : MINIMIZE=0 \n", "\n", " Floating Parameter FinalValue +/- Error \n", " -------------------- --------------------------\n", " mu 1.7049e+00 +/- 5.93e-01\n", "\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/tmp/ipykernel_583254/3977165901.py:8: RuntimeWarning: divide by zero encountered in divide\n", " w = np.outer(w_1, 1.0 / w_0)\n" ] } ], "source": [ "minimizer = ROOT.RooMinimizer(nll)\n", "minimizer.setErrorLevel(0.5) # Adjust the error level in the minimization to work with likelihoods\n", "minimizer.setPrintLevel(-1)\n", "minimizer.minimize(\"Minuit2\")\n", "result = minimizer.save()\n", "ROOT.SetOwnership(result, True)\n", "result.Print()\n", "\n", "del minimizer\n", "del nll\n", "del pdf_learned_extended\n", "del n_pred\n", "del llh\n", "del nll_ratio" ] }, { "cell_type": "markdown", "id": "ea625f9a", "metadata": {}, "source": [ "Draw all canvases " ] }, { "cell_type": "code", "execution_count": 23, "id": "aca3dfdb", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:34:22.549199Z", "iopub.status.busy": "2026-05-19T20:34:22.549074Z", "iopub.status.idle": "2026-05-19T20:34:22.740403Z", "shell.execute_reply": "2026-05-19T20:34:22.739786Z" } }, "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 }