{ "cells": [ { "cell_type": "markdown", "id": "67aba2b5", "metadata": {}, "source": [ "# exampleFunction\n", "Example of using Python functions as inputs to numerical algorithms\n", "using the ROOT Functor class. \n", "\n", "\n", "\n", "\n", "**Author:** Lorenzo Moneta \n", "This notebook tutorial was automatically generated with ROOTBOOK-izer from the macro found in the ROOT repository on Tuesday, May 19, 2026 at 08:24 PM." ] }, { "cell_type": "code", "execution_count": 1, "id": "26842f22", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:24:23.534803Z", "iopub.status.busy": "2026-05-19T20:24:23.534685Z", "iopub.status.idle": "2026-05-19T20:24:24.573906Z", "shell.execute_reply": "2026-05-19T20:24:24.573366Z" } }, "outputs": [], "source": [ "import array\n", "\n", "import ROOT\n", "\n", "try:\n", " import numpy as np\n", "except Exception as e:\n", " print(\"Failed to import numpy:\", e)\n", " exit()" ] }, { "cell_type": "markdown", "id": "5e2a2cf7", "metadata": {}, "source": [ " example 1D function" ] }, { "cell_type": "code", "execution_count": 2, "id": "6f4cace6", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:24:24.576004Z", "iopub.status.busy": "2026-05-19T20:24:24.575809Z", "iopub.status.idle": "2026-05-19T20:24:24.943385Z", "shell.execute_reply": "2026-05-19T20:24:24.942645Z" } }, "outputs": [], "source": [ "def f(x):\n", " return x*x -1\n", "\n", "func = ROOT.Math.Functor1D(f)" ] }, { "cell_type": "markdown", "id": "7fd8b1d4", "metadata": {}, "source": [ "xample of using the integral" ] }, { "cell_type": "code", "execution_count": 3, "id": "b48c5c56", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:24:24.948649Z", "iopub.status.busy": "2026-05-19T20:24:24.948486Z", "iopub.status.idle": "2026-05-19T20:24:25.103642Z", "shell.execute_reply": "2026-05-19T20:24:25.102943Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Use Functor1D for wrapping one-dimensional function and compute integral of f(x) = x^2-1\n", "integral-1D value = 5.999999999999999\n" ] } ], "source": [ "print(\"Use Functor1D for wrapping one-dimensional function and compute integral of f(x) = x^2-1\")\n", "\n", "ig = ROOT.Math.Integrator()\n", "ig.SetFunction(func)\n", "\n", "value = ig.Integral(0, 3)\n", "print(\"integral-1D value = \", value)\n", "expValue = 6\n", "if (not ROOT.TMath.AreEqualRel(value, expValue, 1.E-15)) :\n", " print(\"Error computing integral - computed value - different than expected, diff = \", value - expValue)\n", " " ] }, { "cell_type": "markdown", "id": "44446759", "metadata": {}, "source": [ "example multi-dim function" ] }, { "cell_type": "code", "execution_count": 4, "id": "d595aa6a", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:24:25.105346Z", "iopub.status.busy": "2026-05-19T20:24:25.105213Z", "iopub.status.idle": "2026-05-19T20:24:25.272468Z", "shell.execute_reply": "2026-05-19T20:24:25.271840Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "\n", "Use Functor for wrapping a multi-dimensional function, the Rosenbrock Function r(x,y) and find its minimum\n" ] } ], "source": [ "print(\"\\n\\nUse Functor for wrapping a multi-dimensional function, the Rosenbrock Function r(x,y) and find its minimum\")\n", "\n", "def RosenbrockFunction(xx):\n", " x = xx[0]\n", " y = xx[1]\n", " tmp1 = y-x*x\n", " tmp2 = 1-x\n", " return 100*tmp1*tmp1+tmp2*tmp2\n", "\n", "\n", "func2D = ROOT.Math.Functor(RosenbrockFunction,2)" ] }, { "cell_type": "markdown", "id": "1d26cde1", "metadata": {}, "source": [ "# minimize multi-dim function using fitter class" ] }, { "cell_type": "code", "execution_count": 5, "id": "fe56c501", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:24:25.280485Z", "iopub.status.busy": "2026-05-19T20:24:25.280350Z", "iopub.status.idle": "2026-05-19T20:24:25.402254Z", "shell.execute_reply": "2026-05-19T20:24:25.401405Z" } }, "outputs": [], "source": [ "fitter = ROOT.Fit.Fitter()" ] }, { "cell_type": "markdown", "id": "e439abd1", "metadata": {}, "source": [ "se a numpy array to pass initial parameter array " ] }, { "cell_type": "code", "execution_count": 6, "id": "a161f526", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:24:25.409352Z", "iopub.status.busy": "2026-05-19T20:24:25.409213Z", "iopub.status.idle": "2026-05-19T20:24:25.583727Z", "shell.execute_reply": "2026-05-19T20:24:25.583314Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "****************************************\n", "Minimizer is Minuit2 / Migrad\n", "MinFCN = 1.687e-08\n", "NDf = 0\n", "Edm = 1.68896e-08\n", "NCalls = 146\n", "Par_0 = 0.999952 +/- 1.00372 \n", "Par_1 = 0.999892 +/- 2.00986 \n" ] } ], "source": [ "initialParams = np.array([0.,0.], dtype='d')\n", "fitter.FitFCN(func2D, initialParams)\n", "fitter.Result().Print(ROOT.std.cout)\n", "if (not ROOT.TMath.AreEqualRel(fitter.Result().Parameter(0), 1, 1.E-3) or not ROOT.TMath.AreEqualRel(fitter.Result().Parameter(1), 1, 1.E-3)) :\n", " print(\"Error minimizing Rosenbrock function \")" ] }, { "cell_type": "markdown", "id": "357f1104", "metadata": {}, "source": [ " example 1d grad function\n", " derivative of f(x)= x**2-1" ] }, { "cell_type": "code", "execution_count": 7, "id": "ab89040b", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:24:25.595542Z", "iopub.status.busy": "2026-05-19T20:24:25.595400Z", "iopub.status.idle": "2026-05-19T20:24:25.699118Z", "shell.execute_reply": "2026-05-19T20:24:25.698429Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "\n", "Use GradFunctor1D for making a function object implementing f(x) and f'(x)\n" ] } ], "source": [ "print(\"\\n\\nUse GradFunctor1D for making a function object implementing f(x) and f'(x)\")\n", "\n", "def g(x): return 2 * x" ] }, { "cell_type": "markdown", "id": "cf4fe39e", "metadata": {}, "source": [ "GSL_Newton is part of ROOT's MathMore library, which is not always active.\n", "Let's therefore run this in a try block:" ] }, { "cell_type": "code", "execution_count": 8, "id": "1ae85d72", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:24:25.700678Z", "iopub.status.busy": "2026-05-19T20:24:25.700529Z", "iopub.status.idle": "2026-05-19T20:24:25.961130Z", "shell.execute_reply": "2026-05-19T20:24:25.960345Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Found root value x0 : f(x0) = 0 : 1.0\n", "\n", "\n", "Use GradFunctor for making a function object implementing f(x,y) and df(x,y)/dx and df(x,y)/dy\n" ] } ], "source": [ "try:\n", " gradFunc = ROOT.Math.GradFunctor1D(f, g)\n", " rf = ROOT.Math.RootFinder(ROOT.Math.RootFinder.kGSL_NEWTON)\n", " rf.SetFunction(gradFunc, 3)\n", " rf.Solve()\n", " value = rf.Root()\n", " print(\"Found root value x0 : f(x0) = 0 : \", value)\n", " if value != 1:\n", " print(\"Error finding a ROOT of function f(x)=x^2-1\")\n", "except Exception as e:\n", " print(e)\n", "\n", "\n", "print(\"\\n\\nUse GradFunctor for making a function object implementing f(x,y) and df(x,y)/dx and df(x,y)/dy\")\n", "\n", "def RosenbrockDerivatives(xx, icoord):\n", " x = xx[0]\n", " y = xx[1]\n", " #derivative w.r.t x \n", " if (icoord == 0) :\n", " return 2*(200*x*x*x-200*x*y+x-1)\n", " else : \n", " return 200 * (y - x * x)\n", " \n", "gradFunc2d = ROOT.Math.GradFunctor(RosenbrockFunction, RosenbrockDerivatives, 2)\n", "\n", "fitter = ROOT.Fit.Fitter()" ] }, { "cell_type": "markdown", "id": "087bb3a5", "metadata": {}, "source": [ "ere we use a python array to pass initial parameters" ] }, { "cell_type": "code", "execution_count": 9, "id": "0a0ef6e1", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:24:25.970454Z", "iopub.status.busy": "2026-05-19T20:24:25.970310Z", "iopub.status.idle": "2026-05-19T20:24:26.144479Z", "shell.execute_reply": "2026-05-19T20:24:26.144092Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "****************************************\n", "Minimizer is Minuit2 / Migrad\n", "MinFCN = 2.72222e-08\n", "NDf = 0\n", "Edm = 2.72448e-08\n", "NCalls = 76\n", "Par_0 = 0.999954 +/- 1.00444 \n", "Par_1 = 0.999892 +/- 2.01131 \n" ] } ], "source": [ "initialParams = array.array('d',[0.,0.])\n", "fitter.FitFCN(gradFunc2d, initialParams)\n", "fitter.Result().Print(ROOT.std.cout)\n", "if (not ROOT.TMath.AreEqualRel(fitter.Result().Parameter(0), 1, 1.E-3) or not ROOT.TMath.AreEqualRel(fitter.Result().Parameter(1), 1, 1.E-3)) :\n", " print(\"Error minimizing Rosenbrock function \")" ] }, { "cell_type": "markdown", "id": "e84ff4af", "metadata": {}, "source": [ "Draw all canvases " ] }, { "cell_type": "code", "execution_count": 10, "id": "14fb3a9d", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:24:26.148183Z", "iopub.status.busy": "2026-05-19T20:24:26.148062Z", "iopub.status.idle": "2026-05-19T20:24:26.255877Z", "shell.execute_reply": "2026-05-19T20:24:26.255173Z" } }, "outputs": [], "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 }