{ "cells": [ { "cell_type": "markdown", "id": "38d75eda", "metadata": {}, "source": [ "# rf601_intminuit\n", "'LIKELIHOOD AND MINIMIZATION' RooFit tutorial macro #601\n", "\n", "Interactive minimization with MINUIT\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": "7ab060f9", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:32:56.836720Z", "iopub.status.busy": "2026-05-19T20:32:56.836562Z", "iopub.status.idle": "2026-05-19T20:32:57.804911Z", "shell.execute_reply": "2026-05-19T20:32:57.804226Z" } }, "outputs": [], "source": [ "import ROOT" ] }, { "cell_type": "markdown", "id": "3d47e29c", "metadata": {}, "source": [ "Setup pdf and likelihood\n", "-----------------------------------------------" ] }, { "cell_type": "markdown", "id": "7094ff11", "metadata": {}, "source": [ "Observable" ] }, { "cell_type": "code", "execution_count": 2, "id": "2e2b60b0", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:32:57.807075Z", "iopub.status.busy": "2026-05-19T20:32:57.806942Z", "iopub.status.idle": "2026-05-19T20:32:57.965221Z", "shell.execute_reply": "2026-05-19T20:32:57.964445Z" } }, "outputs": [], "source": [ "x = ROOT.RooRealVar(\"x\", \"x\", -20, 20)" ] }, { "cell_type": "markdown", "id": "d88822cd", "metadata": {}, "source": [ "Model (intentional strong correlations)" ] }, { "cell_type": "code", "execution_count": 3, "id": "46f833e2", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:32:57.967066Z", "iopub.status.busy": "2026-05-19T20:32:57.966939Z", "iopub.status.idle": "2026-05-19T20:32:58.170411Z", "shell.execute_reply": "2026-05-19T20:32:58.169747Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[#0] WARNING:InputArguments -- The parameter 'sigma_g1' with range [-inf, inf] of the RooGaussian 'g1' exceeds the safe range of (0, inf). Advise to limit its range.\n" ] } ], "source": [ "mean = ROOT.RooRealVar(\"mean\", \"mean of g1 and g2\", 0)\n", "sigma_g1 = ROOT.RooRealVar(\"sigma_g1\", \"width of g1\", 3)\n", "g1 = ROOT.RooGaussian(\"g1\", \"g1\", x, mean, sigma_g1)\n", "\n", "sigma_g2 = ROOT.RooRealVar(\"sigma_g2\", \"width of g2\", 4, 3.0, 6.0)\n", "g2 = ROOT.RooGaussian(\"g2\", \"g2\", x, mean, sigma_g2)\n", "\n", "frac = ROOT.RooRealVar(\"frac\", \"frac\", 0.5, 0.0, 1.0)\n", "model = ROOT.RooAddPdf(\"model\", \"model\", [g1, g2], [frac])" ] }, { "cell_type": "markdown", "id": "3aa45b3f", "metadata": {}, "source": [ "Generate 1000 events" ] }, { "cell_type": "code", "execution_count": 4, "id": "729b01b6", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:32:58.172468Z", "iopub.status.busy": "2026-05-19T20:32:58.172251Z", "iopub.status.idle": "2026-05-19T20:32:58.309702Z", "shell.execute_reply": "2026-05-19T20:32:58.309248Z" } }, "outputs": [], "source": [ "data = model.generate({x}, 1000)" ] }, { "cell_type": "markdown", "id": "760b0f27", "metadata": {}, "source": [ "Construct unbinned likelihood of model w.r.t. data" ] }, { "cell_type": "code", "execution_count": 5, "id": "199a86a5", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:32:58.330402Z", "iopub.status.busy": "2026-05-19T20:32:58.330243Z", "iopub.status.idle": "2026-05-19T20:32:58.478829Z", "shell.execute_reply": "2026-05-19T20:32:58.478121Z" } }, "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 -- using generic CPU library compiled with no vectorizations\n", "[#1] INFO:Fitting -- Creation of NLL object took 6.69691 ms\n" ] } ], "source": [ "nll = model.createNLL(data)" ] }, { "cell_type": "markdown", "id": "2b25edf3", "metadata": {}, "source": [ "Interactive minimization, error analysis\n", "-------------------------------------------------------------------------------" ] }, { "cell_type": "markdown", "id": "eafcfd43", "metadata": {}, "source": [ "Create MINUIT interface object" ] }, { "cell_type": "code", "execution_count": 6, "id": "f7cc8c2c", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:32:58.481037Z", "iopub.status.busy": "2026-05-19T20:32:58.480900Z", "iopub.status.idle": "2026-05-19T20:32:58.601211Z", "shell.execute_reply": "2026-05-19T20:32:58.600498Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[#1] INFO:Fitting -- RooAddition::defaultErrorLevel(nll_model_modelData) Summation contains a RooNLLVar, using its error level\n" ] } ], "source": [ "m = ROOT.RooMinimizer(nll)" ] }, { "cell_type": "markdown", "id": "811b1c3e", "metadata": {}, "source": [ "Activate verbose logging of MINUIT parameter space stepping" ] }, { "cell_type": "code", "execution_count": 7, "id": "8bde0fb5", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:32:58.603327Z", "iopub.status.busy": "2026-05-19T20:32:58.603199Z", "iopub.status.idle": "2026-05-19T20:32:58.711473Z", "shell.execute_reply": "2026-05-19T20:32:58.710815Z" } }, "outputs": [], "source": [ "m.setVerbose(True)" ] }, { "cell_type": "markdown", "id": "efc82510", "metadata": {}, "source": [ "Call MIGRAD to minimize the likelihood" ] }, { "cell_type": "code", "execution_count": 8, "id": "a35d2dfd", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:32:58.713733Z", "iopub.status.busy": "2026-05-19T20:32:58.713538Z", "iopub.status.idle": "2026-05-19T20:32:58.860502Z", "shell.execute_reply": "2026-05-19T20:32:58.859783Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[#0] WARNING:Minimization -- RooAbsMinimizerFcn::synchronize: WARNING: no initial error estimate available for frac: using 0.1\n", "[#0] WARNING:Minimization -- RooAbsMinimizerFcn::synchronize: WARNING: no initial error estimate available for sigma_g2: using 0.3\n", "[#1] INFO:Minimization -- [fitFCN] No discrete parameters, performing continuous minimization only\n", "Minuit2Minimizer: Minimize with max-calls 1000 convergence for edm < 1 strategy 1\n", "\n", "prevFCN = 2660.220684 frac=0.5036, \n", "prevFCN = 2660.181264 frac=0.4964, \n", "prevFCN = 2660.261875 frac=0.5, sigma_g2=4.011, \n", "prevFCN = 2660.278974 sigma_g2=3.989, \n", "prevFCN = 2660.167705 sigma_g2=4.005, \n", "prevFCN = 2660.248509 sigma_g2=3.995, \n", "prevFCN = 2660.194127 frac=0.5812, sigma_g2=3.889, \n", "prevFCN = 2660.146969 frac=0.5429, sigma_g2=3.941, \n", "prevFCN = 2659.83839 frac=0.5459, \n", "prevFCN = 2659.836693 frac=0.5398, \n", "prevFCN = 2659.841351 frac=0.5429, sigma_g2=3.946, \n", "prevFCN = 2659.835035 sigma_g2=3.936, \n", "prevFCN = 2659.842919 frac=0.5497, sigma_g2=3.955, \n", "prevFCN = 2659.823248 frac=0.5767, sigma_g2=4.011, \n", "prevFCN = 2659.774616 frac=0.6314, sigma_g2=4.128, \n", "prevFCN = 2659.73914 frac=0.6266, sigma_g2=4.117, \n", "prevFCN = 2659.738319 frac=0.6296, \n", "prevFCN = 2659.740343 frac=0.6237, \n", "prevFCN = 2659.737969 frac=0.6266, sigma_g2=4.123, \n", "prevFCN = 2659.737996 sigma_g2=4.112, \n", "prevFCN = 2659.739643 frac=0.6227, sigma_g2=4.114, \n", "prevFCN = 2659.737959 frac=0.6236, sigma_g2=4.115, \n", "prevFCN = 2659.737923 frac=0.6262, \n", "prevFCN = 2659.738617 frac=0.621, \n", "prevFCN = 2659.738491 frac=0.6236, sigma_g2=4.121, \n", "prevFCN = 2659.738401 sigma_g2=4.108, \n", "prevFCN = 2659.738723 sigma_g2=4.115, \n", "prevFCN = 2659.737923 frac=0.6262, \n", "prevFCN = 2659.738617 frac=0.621, \n", "prevFCN = 2659.738491 frac=0.6236, sigma_g2=4.121, \n", "prevFCN = 2659.738401 sigma_g2=4.108, \n", "prevFCN = 2659.738723 frac=0.6241, sigma_g2=4.115, \n", "prevFCN = 2659.737961 frac=0.6231, \n", "prevFCN = 2659.737935 frac=0.6236, sigma_g2=4.116, \n", "prevFCN = 2659.737916 sigma_g2=4.113, \n", "prevFCN = 2659.737981 frac=0.6262, sigma_g2=4.121, \n", "prevFCN = 2659.737949 Minuit2Minimizer : Valid minimum - status = 0\n", "FVAL = 2659.73792283928833\n", "Edm = 2.40279108894231903e-05\n", "Nfcn = 37\n", "frac\t = 0.6236\t +/- 0.164\t(limited)\n", "sigma_g2\t = 4.115\t +/- 0.405\t(limited)\n", "frac=0.6236, sigma_g2=4.115, " ] }, { "data": { "text/plain": [ "0" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" }, { "name": "stderr", "output_type": "stream", "text": [ "Info in : MnSeedGenerator Computing seed using NumericalGradient calculator\n", "Info in : MnSeedGenerator Evaluated function and gradient in 327.811 μs\n", "Info in : MnSeedGenerator Initial state: FCN = 2660.220684 Edm = 0.7499658139 NCalls = 7\n", "Info in : MnSeedGenerator Initial state \n", " Minimum value : 2660.220684\n", " Edm : 0.7499658139\n", " Internal parameters:\t[ 0 -0.3398369095]\t\n", " Internal gradient :\t[ -5.61967122 7.285345928]\t\n", " Internal covariance matrix:\n", "[[ 0.058086658 0]\n", " [ 0 0.021957944]]]\n", "Info in : VariableMetricBuilder Start iterating until Edm is < 0.001 with call limit = 1000\n", "Info in : VariableMetricBuilder 0 - FCN = 2660.220684 Edm = 0.7499658139 NCalls = 7\n", "Info in : VariableMetricBuilder 1 - FCN = 2659.83839 Edm = 0.008262338758 NCalls = 13\n", "Info in : VariableMetricBuilder 2 - FCN = 2659.738319 Edm = 0.0004391718866 NCalls = 21\n", "Info in : VariableMetricBuilder 3 - FCN = 2659.737923 Edm = 2.063673983e-05 NCalls = 27\n", "Info in : MnHesse Done after 279.311 μs\n", "Info in : VariableMetricBuilder After Hessian\n", "Info in : VariableMetricBuilder 4 - FCN = 2659.737923 Edm = 2.402791089e-05 NCalls = 37\n", "Info in : VariableMetricBuilder Stop iterating after 826.334 μs\n" ] } ], "source": [ "m.migrad()" ] }, { "cell_type": "markdown", "id": "c898a807", "metadata": {}, "source": [ "Print values of all parameters, reflect values (and error estimates)\n", "that are back propagated from MINUIT" ] }, { "cell_type": "code", "execution_count": 9, "id": "2b657fdc", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:32:58.862449Z", "iopub.status.busy": "2026-05-19T20:32:58.862317Z", "iopub.status.idle": "2026-05-19T20:32:58.974425Z", "shell.execute_reply": "2026-05-19T20:32:58.973801Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " 1) RooRealVar:: frac = 0.6236 +/- 0.164\n", " 2) RooRealVar:: mean = 0\n", " 3) RooRealVar:: sigma_g1 = 3\n", " 4) RooRealVar:: sigma_g2 = 4.115 +/- 0.405\n" ] } ], "source": [ "model.getParameters({x}).Print(\"s\")" ] }, { "cell_type": "markdown", "id": "f2f54223", "metadata": {}, "source": [ "Disable verbose logging" ] }, { "cell_type": "code", "execution_count": 10, "id": "131bdc2e", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:32:58.976169Z", "iopub.status.busy": "2026-05-19T20:32:58.976039Z", "iopub.status.idle": "2026-05-19T20:32:59.079611Z", "shell.execute_reply": "2026-05-19T20:32:59.078876Z" } }, "outputs": [], "source": [ "m.setVerbose(False)" ] }, { "cell_type": "markdown", "id": "5b728402", "metadata": {}, "source": [ "Run HESSE to calculate errors from d2L/dp2" ] }, { "cell_type": "code", "execution_count": 11, "id": "23bc0642", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:32:59.081759Z", "iopub.status.busy": "2026-05-19T20:32:59.081622Z", "iopub.status.idle": "2026-05-19T20:32:59.191082Z", "shell.execute_reply": "2026-05-19T20:32:59.190441Z" } }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Info in : Minuit2Minimizer::Hesse Using max-calls 1000\n", "Info in : MnHesse Done after 171.09 μs\n", "Info in : Minuit2Minimizer::Hesse Hesse is valid - matrix is accurate\n" ] }, { "data": { "text/plain": [ "0" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "m.hesse()" ] }, { "cell_type": "markdown", "id": "12a861e4", "metadata": {}, "source": [ "Print value (and error) of sigma_g2 parameter, reflects\n", "value and error back propagated from MINUIT" ] }, { "cell_type": "code", "execution_count": 12, "id": "f621def6", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:32:59.193247Z", "iopub.status.busy": "2026-05-19T20:32:59.193112Z", "iopub.status.idle": "2026-05-19T20:32:59.301643Z", "shell.execute_reply": "2026-05-19T20:32:59.300997Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "RooRealVar::sigma_g2 = 4.115 +/- 0.4057 L(3 - 6) \n" ] } ], "source": [ "sigma_g2.Print()" ] }, { "cell_type": "markdown", "id": "fb2edddc", "metadata": {}, "source": [ "Run MINOS on sigma_g2 parameter only" ] }, { "cell_type": "code", "execution_count": 13, "id": "12f35561", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:32:59.303413Z", "iopub.status.busy": "2026-05-19T20:32:59.303283Z", "iopub.status.idle": "2026-05-19T20:32:59.419254Z", "shell.execute_reply": "2026-05-19T20:32:59.418589Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "******************************************************************************************************\n", "Minuit2Minimizer::GetMinosError - Run MINOS LOWER error for parameter #1 : sigma_g2 using max-calls 1000, tolerance 1\n", "******************************************************************************************************\n", "Minuit2Minimizer::GetMinosError - Run MINOS UPPER error for parameter #1 : sigma_g2 using max-calls 1000, tolerance 1\n", "Minos: Lower error for parameter sigma_g2 : -0.3794\n", "Minos: Upper error for parameter sigma_g2 : 0.4574\n" ] }, { "data": { "text/plain": [ "0" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" }, { "name": "stderr", "output_type": "stream", "text": [ "Info in : MnMinos Determination of lower Minos error for parameter 1\n", "Info in : MnFunctionCross Run Migrad with fixed parameters:\n", " Pos 1: sigma_g2 = 3.70891\n", "Info in : MnSeedGenerator Computing seed using NumericalGradient calculator\n", "Info in : MnSeedGenerator Evaluated function and gradient in 61.551 μs\n", "Info in : MnSeedGenerator Initial state: FCN = 2660.551181 Edm = 0.1133084751 NCalls = 3\n", "Info in : MnSeedGenerator Initial state \n", " Minimum value : 2660.551181\n", " Edm : 0.1133084751\n", " Internal parameters:\t[ -0.062266279]\t\n", " Internal gradient :\t[ 3.194420928]\t\n", " Internal covariance matrix:\n", "[[ 0.044415863]]]\n", "Info in : VariableMetricBuilder Start iterating until Edm is < 0.0005 with call limit = 1000\n", "Info in : VariableMetricBuilder 0 - FCN = 2660.551181 Edm = 0.1133084751 NCalls = 3\n", "Info in : VariableMetricBuilder 1 - FCN = 2660.315058 Edm = 0.0002150023274 NCalls = 7\n", "Info in : VariableMetricBuilder Stop iterating after 54.751 μs\n", "Info in : MnFunctionCross Result after Migrad FCN = 2660.315058 Edm = 0.0002150023274 NCalls = 7 \n", " Pos | Name | type | Value | Error +/-\n", " 0 | frac | limited | 0.3972435352 | 0.1056591236\n", " 1 | sigma_g2 | fixed | 3.708914333 | 0.4056662206\n", "Info in : MnFunctionCross Run Migrad again (2nd) with fixed parameters:\n", " Pos 1: sigma_g2 = 3.737\n", "Info in : MnSeedGenerator Computing seed using NumericalGradient calculator\n", "Info in : MnSeedGenerator Evaluated function and gradient in 34.061 μs\n", "Info in : MnSeedGenerator Initial state: FCN = 2660.250576 Edm = 0.01729037624 NCalls = 3\n", "Info in : MnSeedGenerator Initial state \n", " Minimum value : 2660.250576\n", " Edm : 0.01729037624\n", " Internal parameters:\t[ -0.2069877956]\t\n", " Internal gradient :\t[ -0.8544281469]\t\n", " Internal covariance matrix:\n", "[[ 0.094735629]]]\n", "Info in : VariableMetricBuilder Start iterating until Edm is < 0.0005 with call limit = 1000\n", "Info in : VariableMetricBuilder 0 - FCN = 2660.250576 Edm = 0.01729037624 NCalls = 3\n", "Info in : VariableMetricBuilder 1 - FCN = 2660.232876 Edm = 4.007061453e-06 NCalls = 6\n", "Info in : VariableMetricBuilder Stop iterating after 49.851 μs\n", "Info in : MnFunctionCross Result after 2nd Migrad FCN = 2660.232876 Edm = 4.007061453e-06 NCalls = 6 \n", " Pos | Name | type | Value | Error +/-\n", " 0 | frac | limited | 0.4171265191 | 0.1072770092\n", " 1 | sigma_g2 | fixed | 3.736995132 | 0.4056662206\n", "Info in : MnFunctionCross Run Migrad again (3rd) with fixed parameters:\n", " Pos 1: sigma_g2 = 3.73527\n", "Info in : MnSeedGenerator Computing seed using NumericalGradient calculator\n", "Info in : MnSeedGenerator Evaluated function and gradient in 40.12 μs\n", "Info in : MnSeedGenerator Initial state: FCN = 2660.237741 Edm = 5.406696249e-05 NCalls = 3\n", "Info in : MnSeedGenerator Initial state \n", " Minimum value : 2660.237741\n", " Edm : 5.406696249e-05\n", " Internal parameters:\t[ -0.1665154017]\t\n", " Internal gradient :\t[ 0.04741417272]\t\n", " Internal covariance matrix:\n", "[[ 0.096200119]]]\n", "Info in : VariableMetricBuilder Start iterating until Edm is < 0.0005 with call limit = 1000\n", "Info in : VariableMetricBuilder 0 - FCN = 2660.237741 Edm = 5.406696249e-05 NCalls = 3\n", "Info in : VariableMetricBuilder 1 - FCN = 2660.237689 Edm = 2.190000736e-08 NCalls = 6\n", "Info in : VariableMetricBuilder Stop iterating after 34.24 μs\n", "Info in : MnFunctionCross Result after Migrad (3rd): FCN = 2660.237689 Edm = 2.190000736e-08 NCalls = 6 \n", " Pos | Name | type | Value | Error +/-\n", " 0 | frac | limited | 0.4160021957 | 0.1061893687\n", " 1 | sigma_g2 | fixed | 3.735270747 | 0.4056662206\n", "Info in : MnMinos end of Minos scan for low interval for parameter sigma_g2\n", "Info in : MnMinos Determination of upper Minos error for parameter 1\n", "Info in : MnFunctionCross Run Migrad with fixed parameters:\n", " Pos 1: sigma_g2 = 4.52025\n", "Info in : MnSeedGenerator Computing seed using NumericalGradient calculator\n", "Info in : MnSeedGenerator Evaluated function and gradient in 50.35 μs\n", "Info in : MnSeedGenerator Initial state: FCN = 2660.321661 Edm = 0.2677306814 NCalls = 5\n", "Info in : MnSeedGenerator Initial state \n", " Minimum value : 2660.321661\n", " Edm : 0.2677306814\n", " Internal parameters:\t[ 0.5618487643]\t\n", " Internal gradient :\t[ 4.9103225]\t\n", " Internal covariance matrix:\n", "[[ 0.044415863]]]\n", "Info in : VariableMetricBuilder Start iterating until Edm is < 0.0005 with call limit = 1000\n", "Info in : VariableMetricBuilder 0 - FCN = 2660.321661 Edm = 0.2677306814 NCalls = 5\n", "Info in : VariableMetricBuilder 1 - FCN = 2660.139576 Edm = 5.875660685e-08 NCalls = 9\n", "Info in : VariableMetricBuilder Stop iterating after 42.24 μs\n", "Info in : MnFunctionCross Result after Migrad FCN = 2660.139576 Edm = 5.875660685e-08 NCalls = 9 \n", " Pos | Name | type | Value | Error +/-\n", " 0 | frac | limited | 0.7343787978 | 0.05405769968\n", " 1 | sigma_g2 | fixed | 4.520246774 | 0.4056662206\n", "Info in : MnFunctionCross Run Migrad again (2nd) with fixed parameters:\n", " Pos 1: sigma_g2 = 4.56719\n", "Info in : MnSeedGenerator Computing seed using NumericalGradient calculator\n", "Info in : MnSeedGenerator Evaluated function and gradient in 33.03 μs\n", "Info in : MnSeedGenerator Initial state: FCN = 2660.244047 Edm = 0.01621248945 NCalls = 3\n", "Info in : MnSeedGenerator Initial state \n", " Minimum value : 2660.244047\n", " Edm : 0.01621248945\n", " Internal parameters:\t[ 0.4878837463]\t\n", " Internal gradient :\t[ -1.467517802]\t\n", " Internal covariance matrix:\n", "[[ 0.030112232]]]\n", "Info in : VariableMetricBuilder Start iterating until Edm is < 0.0005 with call limit = 1000\n", "Info in : VariableMetricBuilder 0 - FCN = 2660.244047 Edm = 0.01621248945 NCalls = 3\n", "Info in : VariableMetricBuilder 1 - FCN = 2660.228567 Edm = 3.216979859e-05 NCalls = 6\n", "Info in : VariableMetricBuilder Stop iterating after 33.611 μs\n", "Info in : MnFunctionCross Result after 2nd Migrad FCN = 2660.228567 Edm = 3.216979859e-05 NCalls = 6 \n", " Pos | Name | type | Value | Error +/-\n", " 0 | frac | limited | 0.7440794003 | 0.05226504469\n", " 1 | sigma_g2 | fixed | 4.567194797 | 0.4056662206\n", "Info in : MnFunctionCross Run Migrad again (3rd) with fixed parameters:\n", " Pos 1: sigma_g2 = 4.57213\n", "Info in : MnSeedGenerator Computing seed using NumericalGradient calculator\n", "Info in : MnSeedGenerator Evaluated function and gradient in 32.78 μs\n", "Info in : MnSeedGenerator Initial state: FCN = 2660.238339 Edm = 5.179528976e-05 NCalls = 3\n", "Info in : MnSeedGenerator Initial state \n", " Minimum value : 2660.238339\n", " Edm : 5.179528976e-05\n", " Internal parameters:\t[ 0.5099788642]\t\n", " Internal gradient :\t[ -0.08477489166]\t\n", " Internal covariance matrix:\n", "[[ 0.028828084]]]\n", "Info in : VariableMetricBuilder Start iterating until Edm is < 0.0005 with call limit = 1000\n", "Info in : VariableMetricBuilder 0 - FCN = 2660.238339 Edm = 5.179528976e-05 NCalls = 3\n", "Info in : VariableMetricBuilder 1 - FCN = 2660.238288 Edm = 1.944200952e-10 NCalls = 6\n", "Info in : VariableMetricBuilder Stop iterating after 34.39 μs\n", "Info in : MnFunctionCross Result after Migrad (3rd): FCN = 2660.238288 Edm = 1.944200952e-10 NCalls = 6 \n", " Pos | Name | type | Value | Error +/-\n", " 0 | frac | limited | 0.7446124488 | 0.05217900468\n", " 1 | sigma_g2 | fixed | 4.572130423 | 0.4056662206\n", "Info in : MnMinos end of Minos scan for up interval for parameter sigma_g2\n" ] } ], "source": [ "m.minos({sigma_g2})" ] }, { "cell_type": "markdown", "id": "d8294282", "metadata": {}, "source": [ "Print value (and error) of sigma_g2 parameter, reflects\n", "value and error back propagated from MINUIT" ] }, { "cell_type": "code", "execution_count": 14, "id": "2f615efd", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:32:59.421393Z", "iopub.status.busy": "2026-05-19T20:32:59.421267Z", "iopub.status.idle": "2026-05-19T20:32:59.525211Z", "shell.execute_reply": "2026-05-19T20:32:59.524558Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "RooRealVar::sigma_g2 = 4.115 +/- (-0.3794,0.4574) L(3 - 6) \n" ] } ], "source": [ "sigma_g2.Print()" ] }, { "cell_type": "markdown", "id": "d073cbf1", "metadata": {}, "source": [ "Saving results, contour plots\n", "---------------------------------------------------------" ] }, { "cell_type": "markdown", "id": "04688ad3", "metadata": {}, "source": [ "Save a snapshot of the fit result. ROOT.This object contains the initial\n", "fit parameters, final fit parameters, complete correlation\n", "matrix, EDM, minimized FCN , last MINUIT status code and\n", "the number of times the ROOT.RooFit function object has indicated evaluation\n", "problems (e.g. zero probabilities during likelihood evaluation)" ] }, { "cell_type": "code", "execution_count": 15, "id": "85c0f9ec", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:32:59.527022Z", "iopub.status.busy": "2026-05-19T20:32:59.526899Z", "iopub.status.idle": "2026-05-19T20:32:59.638107Z", "shell.execute_reply": "2026-05-19T20:32:59.637352Z" } }, "outputs": [], "source": [ "r = m.save()" ] }, { "cell_type": "markdown", "id": "fa9372ae", "metadata": {}, "source": [ "Make contour plot of mx vs sx at 1,2, sigma" ] }, { "cell_type": "code", "execution_count": 16, "id": "85a6a338", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:32:59.639858Z", "iopub.status.busy": "2026-05-19T20:32:59.639730Z", "iopub.status.idle": "2026-05-19T20:32:59.782722Z", "shell.execute_reply": "2026-05-19T20:32:59.782295Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[#0] WARNING:InputArguments -- Value -1.15669e-17 is slightly outside the default range [0, 1] of the variable \"frac\"!\n", "The value will be clipped. To restore the dangerous old behavior of silently clipping the value to the range, call `RooRealVar::enableSilentClipping()`.\n", "[#0] WARNING:InputArguments -- Value -1.15669e-17 is slightly outside the default range [0, 1] of the variable \"frac\"!\n", "The value will be clipped. To restore the dangerous old behavior of silently clipping the value to the range, call `RooRealVar::enableSilentClipping()`.\n", "[#0] WARNING:InputArguments -- Value -1.15669e-17 is slightly outside the default range [0, 1] of the variable \"frac\"!\n", "The value will be clipped. To restore the dangerous old behavior of silently clipping the value to the range, call `RooRealVar::enableSilentClipping()`.\n", "[#0] WARNING:InputArguments -- Value -1.15669e-17 is slightly outside the default range [0, 1] of the variable \"frac\"!\n", "The value will be clipped. To restore the dangerous old behavior of silently clipping the value to the range, call `RooRealVar::enableSilentClipping()`.\n", "[#0] WARNING:InputArguments -- Value -1.15669e-17 is slightly outside the default range [0, 1] of the variable \"frac\"!\n", "The value will be clipped. To restore the dangerous old behavior of silently clipping the value to the range, call `RooRealVar::enableSilentClipping()`.\n", "[#0] WARNING:InputArguments -- Value -1.15669e-17 is slightly outside the default range [0, 1] of the variable \"frac\"!\n", "The value will be clipped. To restore the dangerous old behavior of silently clipping the value to the range, call `RooRealVar::enableSilentClipping()`.\n", "[#0] WARNING:InputArguments -- Value -1.15669e-17 is slightly outside the default range [0, 1] of the variable \"frac\"!\n", "The value will be clipped. To restore the dangerous old behavior of silently clipping the value to the range, call `RooRealVar::enableSilentClipping()`.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "Info in : Minuit2Minimizer::Contour Computing contours at level - 0.5\n", "Info in : Minuit2Minimizer::Contour Computed 50 points at level 0.5\n", "( 0.397204, 3.75645) ( 0.416069, 3.73525) ( 0.443681, 3.74275) ( 0.468572, 3.75686) ( 0.491424, 3.77374) \n", "( 0.512763, 3.7925) ( 0.532576, 3.81249) ( 0.551172, 3.83362) ( 0.568618, 3.8557) ( 0.584976, 3.8786) \n", "( 0.600107, 3.90189) ( 0.614278, 3.92578) ( 0.627536, 3.95019) ( 0.639931, 3.97505) ( 0.651505, 4.00029) \n", "( 0.662308, 4.02586) ( 0.681774, 4.07786) ( 0.69833, 4.12967) ( 0.712664, 4.18214) ( 0.724985, 4.23512) \n", "( 0.735451, 4.28849) ( 0.744147, 4.34217) ( 0.751057, 4.39612) ( 0.755974, 4.4503) ( 0.75818, 4.50465) \n", "( 0.756965, 4.53937) ( 0.744894, 4.57195) ( 0.725496, 4.55142) ( 0.712825, 4.52618) ( 0.700766, 4.50094) \n", "( 0.69117, 4.47466) ( 0.670342, 4.42313) ( 0.651447, 4.37086) ( 0.632444, 4.31878) ( 0.611816, 4.26732) \n", "( 0.592713, 4.21525) ( 0.581033, 4.19009) ( 0.570487, 4.16444) ( 0.550417, 4.11274) ( 0.537968, 4.08796) \n", "( 0.526798, 4.06257) ( 0.505119, 4.01155) ( 0.492422, 3.9869) ( 0.480697, 3.96178) ( 0.469366, 3.93644) \n", "( 0.456767, 3.91171) ( 0.445324, 3.88643) ( 0.433481, 3.86134) ( 0.421376, 3.83626) ( 0.411377, 3.81026) \n", "\n", "\n", "Info in : Minuit2Minimizer::Contour Computing contours at level - 2\n", "Info in : Minuit2Minimizer::Contour Computed 50 points at level 2\n", "( 0, 3.52619) ( 0, 3.40406) ( 0.000304375, 3.40406) ( 0.0630768, 3.40963) ( 0.121838, 3.4324) \n", "( 0.181402, 3.45105) ( 0.239929, 3.47275) ( 0.297221, 3.49773) ( 0.352834, 3.52626) ( 0.406331, 3.55861) \n", "( 0.457173, 3.59499) ( 0.505114, 3.63575) ( 0.549309, 3.68054) ( 0.589399, 3.72903) ( 0.625236, 3.78075) \n", "( 0.656828, 3.83501) ( 0.684506, 3.89137) ( 0.729578, 4.00849) ( 0.762032, 4.12287) ( 0.786939, 4.23912) \n", "( 0.806098, 4.35642) ( 0.820806, 4.47436) ( 0.831925, 4.59256) ( 0.840006, 4.71101) ( 0.845246, 4.82962) \n", "( 0.847335, 4.94833) ( 0.845371, 5.04869) ( 0.825769, 5.14714) ( 0.78052, 5.04063) ( 0.750009, 4.92901) \n", "( 0.722873, 4.81674) ( 0.689415, 4.70619) ( 0.652659, 4.58209) ( 0.612693, 4.45899) ( 0.594621, 4.3967) \n", "( 0.568676, 4.33726) ( 0.544881, 4.27707) ( 0.519745, 4.21742) ( 0.493087, 4.15829) ( 0.46484, 4.0999) \n", "( 0.43488, 4.04237) ( 0.403087, 3.98583) ( 0.369336, 3.93041) ( 0.333541, 3.87628) ( 0.295626, 3.82362) \n", "( 0.255547, 3.77258) ( 0.197107, 3.70555) ( 0.134747, 3.64215) ( 0.0688327, 3.58247) ( 0.0358561, 3.55257) \n", "\n", "\n", "Info in : Minuit2Minimizer::Contour Computing contours at level - 4.5\n", "Info in : Minuit2Minimizer::Contour Computed 50 points at level 4.5\n", "( 0, 3.65632) ( 0, 3.28839) ( 0.000118912, 3.28838) ( 0.0433327, 3.29515) ( 0.0846458, 3.30952) \n", "( 0.127838, 3.31705) ( 0.168254, 3.33405) ( 0.25054, 3.36278) ( 0.330847, 3.39665) ( 0.408664, 3.43698) \n", "( 0.482236, 3.48461) ( 0.550023, 3.54027) ( 0.610426, 3.60387) ( 0.662196, 3.67405) ( 0.705642, 3.74966) \n", "( 0.741454, 3.8291) ( 0.770781, 3.91115) ( 0.814432, 4.07901) ( 0.844344, 4.24985) ( 0.864018, 4.40872) \n", "( 0.878473, 4.56816) ( 0.889201, 4.72787) ( 0.89715, 4.88774) ( 0.902923, 5.04767) ( 0.906887, 5.20765) \n", "( 0.909214, 5.36766) ( 0.909872, 5.52768) ( 0.907255, 5.73496) ( 0.885755, 5.94113) ( 0.846212, 5.79043) \n", "( 0.820098, 5.63683) ( 0.796561, 5.48294) ( 0.767105, 5.33008) ( 0.748441, 5.21448) ( 0.722136, 5.10037) \n", "( 0.69715, 4.98603) ( 0.670097, 4.87217) ( 0.640625, 4.75886) ( 0.608354, 4.64632) ( 0.572833, 4.53475) \n", "( 0.533544, 4.42445) ( 0.489386, 4.31463) ( 0.440075, 4.20702) ( 0.384852, 4.10229) ( 0.322986, 4.00134) \n", "( 0.253654, 3.90498) ( 0.176625, 3.81466) ( 0.135204, 3.77212) ( 0.0919029, 3.73149) ( 0.0467995, 3.69287) \n", "\n", "\n" ] } ], "source": [ "frame = m.contour(frac, sigma_g2, 1, 2, 3)\n", "frame.SetTitle(\"Contour plot\")" ] }, { "cell_type": "markdown", "id": "8daf2f2c", "metadata": {}, "source": [ "Print the fit result snapshot" ] }, { "cell_type": "code", "execution_count": 17, "id": "7f204ed8", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:32:59.785213Z", "iopub.status.busy": "2026-05-19T20:32:59.785057Z", "iopub.status.idle": "2026-05-19T20:32:59.894472Z", "shell.execute_reply": "2026-05-19T20:32:59.893830Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", " RooFitResult: minimized FCN value: 2660, estimated distance to minimum: 2.409e-05\n", " covariance matrix quality: Full, accurate covariance matrix\n", " Status : MIGRAD=0 HESSE=0 MINOS=0 \n", "\n", " Constant Parameter Value \n", " -------------------- ------------\n", " mean 0.0000e+00\n", " sigma_g1 3.0000e+00\n", "\n", " Floating Parameter InitialValue FinalValue (+HiError,-LoError) GblCorr.\n", " -------------------- ------------ ---------------------------------- --------\n", " frac 5.0000e-01 6.2360e-01 +/- 1.64e-01 \n", " sigma_g2 4.0000e+00 4.1146e+00 (+4.57e-01,-3.79e-01) \n", "\n" ] } ], "source": [ "r.Print(\"v\")" ] }, { "cell_type": "markdown", "id": "632f435c", "metadata": {}, "source": [ "Change parameter values, plotting\n", "-----------------------------------------------------------------" ] }, { "cell_type": "markdown", "id": "29b1e0ae", "metadata": {}, "source": [ "At any moment you can manually change the value of a (constant)\n", "parameter" ] }, { "cell_type": "code", "execution_count": 18, "id": "ddab9345", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:32:59.896311Z", "iopub.status.busy": "2026-05-19T20:32:59.896184Z", "iopub.status.idle": "2026-05-19T20:33:00.003694Z", "shell.execute_reply": "2026-05-19T20:33:00.003256Z" } }, "outputs": [], "source": [ "mean.setVal(0.3)" ] }, { "cell_type": "markdown", "id": "53660b2a", "metadata": {}, "source": [ "Rerun MIGRAD,HESSE" ] }, { "cell_type": "code", "execution_count": 19, "id": "8b19714f", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:33:00.019365Z", "iopub.status.busy": "2026-05-19T20:33:00.019221Z", "iopub.status.idle": "2026-05-19T20:33:00.125866Z", "shell.execute_reply": "2026-05-19T20:33:00.125209Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[#1] INFO:Minimization -- [fitFCN] No discrete parameters, performing continuous minimization only\n", "Minuit2Minimizer: Minimize with max-calls 1000 convergence for edm < 1 strategy 1\n", "Minuit2Minimizer : Valid minimum - status = 0\n", "FVAL = 2663.35774508719987\n", "Edm = 9.5636987971879807e-05\n", "Nfcn = 38\n", "frac\t = 0.5655\t +/- 0.1961\t(limited)\n", "sigma_g2\t = 4.005\t +/- 0.3917\t(limited)\n", "RooRealVar::frac = 0.5655 +/- 0.1961 L(0 - 1) \n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "Info in : MnSeedGenerator Computing seed using NumericalGradient calculator\n", "Info in : MnSeedGenerator Evaluated function and gradient in 149.151 μs\n", "Info in : MnSeedGenerator Initial state: FCN = 2663.411598 Edm = 0.0145493914 NCalls = 9\n", "Info in : MnSeedGenerator Initial state \n", " Minimum value : 2663.411598\n", " Edm : 0.0145493914\n", " Internal parameters:\t[ 0.2497912426 -0.2598610789]\t\n", " Internal gradient :\t[ 1.120322622 -0.2622810123]\t\n", " Internal covariance matrix:\n", "[[ 0.044738711 0]\n", " [ 0 0.029727437]]]\n", "Info in : VariableMetricBuilder Start iterating until Edm is < 0.001 with call limit = 1000\n", "Info in : VariableMetricBuilder 0 - FCN = 2663.411598 Edm = 0.0145493914 NCalls = 9\n", "Info in : VariableMetricBuilder 1 - FCN = 2663.400666 Edm = 0.005796742294 NCalls = 15\n", "Info in : VariableMetricBuilder 2 - FCN = 2663.35958 Edm = 0.001729013892 NCalls = 22\n", "Info in : VariableMetricBuilder 3 - FCN = 2663.357745 Edm = 8.583255995e-05 NCalls = 28\n", "Info in : MnHesse Done after 159.18 μs\n", "Info in : VariableMetricBuilder After Hessian\n", "Info in : VariableMetricBuilder 4 - FCN = 2663.357745 Edm = 9.563698797e-05 NCalls = 38\n", "Info in : VariableMetricBuilder Stop iterating after 445.132 μs\n", "Info in : Minuit2Minimizer::Hesse Using max-calls 1000\n", "Info in : MnHesse Done after 131.859 μs\n", "Info in : Minuit2Minimizer::Hesse Hesse is valid - matrix is accurate\n" ] } ], "source": [ "m.migrad()\n", "m.hesse()\n", "frac.Print()" ] }, { "cell_type": "markdown", "id": "8d36af25", "metadata": {}, "source": [ "Now fix sigma_g2" ] }, { "cell_type": "code", "execution_count": 20, "id": "e86c70e3", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:33:00.127586Z", "iopub.status.busy": "2026-05-19T20:33:00.127460Z", "iopub.status.idle": "2026-05-19T20:33:00.237347Z", "shell.execute_reply": "2026-05-19T20:33:00.236701Z" } }, "outputs": [], "source": [ "sigma_g2.setConstant(True)" ] }, { "cell_type": "markdown", "id": "caab2566", "metadata": {}, "source": [ "Rerun MIGRAD,HESSE" ] }, { "cell_type": "code", "execution_count": 21, "id": "805b8d6b", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:33:00.239471Z", "iopub.status.busy": "2026-05-19T20:33:00.239255Z", "iopub.status.idle": "2026-05-19T20:33:00.443142Z", "shell.execute_reply": "2026-05-19T20:33:00.442512Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[#1] INFO:Minimization -- [fitFCN] No discrete parameters, performing continuous minimization only\n", "Minuit2Minimizer: Minimize with max-calls 1000 convergence for edm < 1 strategy 1\n", "Minuit2Minimizer : Valid minimum - status = 0\n", "FVAL = 2663.35774092453494\n", "Edm = 1.35711170955699541e-10\n", "Nfcn = 15\n", "frac\t = 0.5652\t +/- 0.08029\t(limited)\n", "sigma_g2\t = 4.005\t (fixed)\n", "RooRealVar::frac = 0.5652 +/- 0.08029 L(0 - 1) \n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "Info in : MnSeedGenerator Computing seed using NumericalGradient calculator\n", "Info in : MnSeedGenerator Evaluated function and gradient in 80.451 μs\n", "Info in : MnSeedGenerator Initial state: FCN = 2663.357745 Edm = 4.211167067e-06 NCalls = 5\n", "Info in : MnSeedGenerator Initial state \n", " Minimum value : 2663.357745\n", " Edm : 4.211167067e-06\n", " Internal parameters:\t[ 0.1313437863]\t\n", " Internal gradient :\t[ 0.01784069119]\t\n", " Internal covariance matrix:\n", "[[ 0.052922349]]]\n", "Info in : VariableMetricBuilder Start iterating until Edm is < 0.001 with call limit = 1000\n", "Info in : VariableMetricBuilder 0 - FCN = 2663.357745 Edm = 4.211167067e-06 NCalls = 5\n", "Info in : VariableMetricBuilder 1 - FCN = 2663.357741 Edm = 6.315904677e-14 NCalls = 8\n", "Info in : MnHesse Done after 61.21 μs\n", "Info in : VariableMetricBuilder After Hessian\n", "Info in : VariableMetricBuilder 2 - FCN = 2663.357741 Edm = 1.35711171e-10 NCalls = 15\n", "Info in : VariableMetricBuilder Stop iterating after 120.47 μs\n", "Info in : Minuit2Minimizer::Hesse Using max-calls 1000\n", "Info in : MnHesse Done after 43.5 μs\n", "Info in : Minuit2Minimizer::Hesse Hesse is valid - matrix is accurate\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "Info in : png file rf601_intminuit.png has been created\n" ] } ], "source": [ "m.migrad()\n", "m.hesse()\n", "frac.Print()\n", "\n", "c = ROOT.TCanvas(\"rf601_intminuit\", \"rf601_intminuit\", 600, 600)\n", "ROOT.gPad.SetLeftMargin(0.15)\n", "frame.GetYaxis().SetTitleOffset(1.4)\n", "frame.Draw()\n", "\n", "c.SaveAs(\"rf601_intminuit.png\")" ] }, { "cell_type": "markdown", "id": "9fb411de", "metadata": {}, "source": [ "Draw all canvases " ] }, { "cell_type": "code", "execution_count": 22, "id": "068f972f", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:33:00.444729Z", "iopub.status.busy": "2026-05-19T20:33:00.444584Z", "iopub.status.idle": "2026-05-19T20:33:00.624422Z", "shell.execute_reply": "2026-05-19T20:33:00.623768Z" } }, "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 }