{
"cells": [
{
"cell_type": "markdown",
"id": "2d156aaa",
"metadata": {},
"source": [
"# rf111_derivatives\n",
"Basic functionality: numerical 1st,2nd and 3rd order derivatives w.r.t. observables and parameters\n",
"\n",
"```\n",
" pdf = gauss(x,m,s)\n",
"```\n",
"\n",
"\n",
"\n",
"\n",
"**Author:** Wouter Verkerke \n",
"This notebook tutorial was automatically generated with ROOTBOOK-izer from the macro found in the ROOT repository on Tuesday, May 19, 2026 at 08:29 PM."
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "499457a0",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:29:26.090692Z",
"iopub.status.busy": "2026-05-19T20:29:26.090563Z",
"iopub.status.idle": "2026-05-19T20:29:26.104292Z",
"shell.execute_reply": "2026-05-19T20:29:26.103653Z"
}
},
"outputs": [],
"source": [
"%%cpp -d\n",
"#include \"RooDerivative.h\"\n",
"#include \"RooRealVar.h\"\n",
"#include \"RooDataSet.h\"\n",
"#include \"RooGaussian.h\"\n",
"#include \"RooPlot.h\"\n",
"\n",
"#include \"TCanvas.h\"\n",
"#include \"TAxis.h\"\n",
"\n",
"using namespace RooFit;"
]
},
{
"cell_type": "markdown",
"id": "1d33ac62",
"metadata": {},
"source": [
"Setup model\n",
"---------------------"
]
},
{
"cell_type": "markdown",
"id": "54f8dafa",
"metadata": {},
"source": [
"Declare variables x,mean,sigma with associated name, title, initial value and allowed range"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "0080c044",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:29:26.105890Z",
"iopub.status.busy": "2026-05-19T20:29:26.105765Z",
"iopub.status.idle": "2026-05-19T20:29:26.420537Z",
"shell.execute_reply": "2026-05-19T20:29:26.419797Z"
}
},
"outputs": [],
"source": [
"RooRealVar x(\"x\", \"x\", -10, 10);\n",
"RooRealVar mean(\"mean\", \"mean of gaussian\", 1, -10, 10);\n",
"RooRealVar sigma(\"sigma\", \"width of gaussian\", 1, 0.1, 10);"
]
},
{
"cell_type": "markdown",
"id": "09b39a54",
"metadata": {},
"source": [
"Build gaussian pdf in terms of x,mean and sigma"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "8cab8f63",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:29:26.422457Z",
"iopub.status.busy": "2026-05-19T20:29:26.422334Z",
"iopub.status.idle": "2026-05-19T20:29:26.630193Z",
"shell.execute_reply": "2026-05-19T20:29:26.629397Z"
}
},
"outputs": [],
"source": [
"RooGaussian gauss(\"gauss\", \"gaussian PDF\", x, mean, sigma);"
]
},
{
"cell_type": "markdown",
"id": "e7034356",
"metadata": {},
"source": [
"Create and plot derivatives w.r.t. x\n",
"----------------------------------------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "3788f43e",
"metadata": {},
"source": [
"Derivative of normalized gauss(x) w.r.t. observable x"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "0c661bdd",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:29:26.635782Z",
"iopub.status.busy": "2026-05-19T20:29:26.635655Z",
"iopub.status.idle": "2026-05-19T20:29:26.843409Z",
"shell.execute_reply": "2026-05-19T20:29:26.842669Z"
}
},
"outputs": [],
"source": [
"RooAbsReal *dgdx = gauss.derivative(x, 1);"
]
},
{
"cell_type": "markdown",
"id": "acbd88df",
"metadata": {},
"source": [
"Second and third derivative of normalized gauss(x) w.r.t. observable x"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "0f1f96fd",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:29:26.845387Z",
"iopub.status.busy": "2026-05-19T20:29:26.845265Z",
"iopub.status.idle": "2026-05-19T20:29:27.052757Z",
"shell.execute_reply": "2026-05-19T20:29:27.052114Z"
}
},
"outputs": [],
"source": [
"RooAbsReal *d2gdx2 = gauss.derivative(x, 2);\n",
"RooAbsReal *d3gdx3 = gauss.derivative(x, 3);"
]
},
{
"cell_type": "markdown",
"id": "47367af0",
"metadata": {},
"source": [
"Construct plot frame in 'x'"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "e95aca6b",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:29:27.054893Z",
"iopub.status.busy": "2026-05-19T20:29:27.054769Z",
"iopub.status.idle": "2026-05-19T20:29:27.257002Z",
"shell.execute_reply": "2026-05-19T20:29:27.256426Z"
}
},
"outputs": [],
"source": [
"RooPlot *xframe = x.frame(Title(\"d(Gauss)/dx\"));"
]
},
{
"cell_type": "markdown",
"id": "3f83fe26",
"metadata": {},
"source": [
"Plot gauss in frame (i.e. in x)"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "d287493b",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:29:27.259144Z",
"iopub.status.busy": "2026-05-19T20:29:27.259030Z",
"iopub.status.idle": "2026-05-19T20:29:27.466409Z",
"shell.execute_reply": "2026-05-19T20:29:27.465886Z"
}
},
"outputs": [],
"source": [
"gauss.plotOn(xframe);"
]
},
{
"cell_type": "markdown",
"id": "8d4733f0",
"metadata": {},
"source": [
"Plot derivatives in same frame"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "56a6787f",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:29:27.468450Z",
"iopub.status.busy": "2026-05-19T20:29:27.468338Z",
"iopub.status.idle": "2026-05-19T20:29:27.675839Z",
"shell.execute_reply": "2026-05-19T20:29:27.675147Z"
}
},
"outputs": [],
"source": [
"dgdx->plotOn(xframe, LineColor(kMagenta));\n",
"d2gdx2->plotOn(xframe, LineColor(kRed));\n",
"d3gdx3->plotOn(xframe, LineColor(kOrange));"
]
},
{
"cell_type": "markdown",
"id": "10670e8a",
"metadata": {},
"source": [
"Create and plot derivatives w.r.t. sigma\n",
"------------------------------------------------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "8141ac9a",
"metadata": {},
"source": [
"Derivative of normalized gauss(x) w.r.t. parameter sigma"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "035d8008",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:29:27.677788Z",
"iopub.status.busy": "2026-05-19T20:29:27.677676Z",
"iopub.status.idle": "2026-05-19T20:29:27.885137Z",
"shell.execute_reply": "2026-05-19T20:29:27.884473Z"
}
},
"outputs": [],
"source": [
"RooAbsReal *dgds = gauss.derivative(sigma, 1);"
]
},
{
"cell_type": "markdown",
"id": "3af65265",
"metadata": {},
"source": [
"Second and third derivative of normalized gauss(x) w.r.t. parameter sigma"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "82059f6a",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:29:27.888360Z",
"iopub.status.busy": "2026-05-19T20:29:27.888249Z",
"iopub.status.idle": "2026-05-19T20:29:28.095573Z",
"shell.execute_reply": "2026-05-19T20:29:28.095011Z"
}
},
"outputs": [],
"source": [
"RooAbsReal *d2gds2 = gauss.derivative(sigma, 2);\n",
"RooAbsReal *d3gds3 = gauss.derivative(sigma, 3);"
]
},
{
"cell_type": "markdown",
"id": "6acf917a",
"metadata": {},
"source": [
"Construct plot frame in 'sigma'"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "429f5f59",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:29:28.097630Z",
"iopub.status.busy": "2026-05-19T20:29:28.097493Z",
"iopub.status.idle": "2026-05-19T20:29:28.304988Z",
"shell.execute_reply": "2026-05-19T20:29:28.304299Z"
}
},
"outputs": [],
"source": [
"RooPlot *sframe = sigma.frame(Title(\"d(Gauss)/d(sigma)\"), Range(0., 2.));"
]
},
{
"cell_type": "markdown",
"id": "5ad7a47b",
"metadata": {},
"source": [
"Plot gauss in frame (i.e. in x)"
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "7689de48",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:29:28.306856Z",
"iopub.status.busy": "2026-05-19T20:29:28.306744Z",
"iopub.status.idle": "2026-05-19T20:29:28.514434Z",
"shell.execute_reply": "2026-05-19T20:29:28.513731Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[#1] INFO:NumericIntegration -- RooRealIntegral::init(gauss_Int[sigma]) using numeric integrator RooIntegrator1D to calculate Int(sigma)\n"
]
}
],
"source": [
"gauss.plotOn(sframe);"
]
},
{
"cell_type": "markdown",
"id": "1139184f",
"metadata": {},
"source": [
"Plot derivatives in same frame"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "c72d9e72",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:29:28.516131Z",
"iopub.status.busy": "2026-05-19T20:29:28.516018Z",
"iopub.status.idle": "2026-05-19T20:29:28.723972Z",
"shell.execute_reply": "2026-05-19T20:29:28.723509Z"
}
},
"outputs": [],
"source": [
"dgds->plotOn(sframe, LineColor(kMagenta));\n",
"d2gds2->plotOn(sframe, LineColor(kRed));\n",
"d3gds3->plotOn(sframe, LineColor(kOrange));"
]
},
{
"cell_type": "markdown",
"id": "eb6f9a75",
"metadata": {},
"source": [
"Draw all frames on a canvas"
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "824fceac",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:29:28.725414Z",
"iopub.status.busy": "2026-05-19T20:29:28.725307Z",
"iopub.status.idle": "2026-05-19T20:29:28.932559Z",
"shell.execute_reply": "2026-05-19T20:29:28.932085Z"
}
},
"outputs": [],
"source": [
"TCanvas *c = new TCanvas(\"rf111_derivatives\", \"rf111_derivatives\", 800, 400);\n",
"c->Divide(2);\n",
"c->cd(1);\n",
"gPad->SetLeftMargin(0.15);\n",
"xframe->GetYaxis()->SetTitleOffset(1.6);\n",
"xframe->Draw();\n",
"c->cd(2);\n",
"gPad->SetLeftMargin(0.15);\n",
"sframe->GetYaxis()->SetTitleOffset(1.6);\n",
"sframe->Draw();"
]
},
{
"cell_type": "markdown",
"id": "69bdcdf2",
"metadata": {},
"source": [
"Draw all canvases "
]
},
{
"cell_type": "code",
"execution_count": 15,
"id": "cde03116",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:29:28.934152Z",
"iopub.status.busy": "2026-05-19T20:29:28.934045Z",
"iopub.status.idle": "2026-05-19T20:29:29.161701Z",
"shell.execute_reply": "2026-05-19T20:29:29.161249Z"
}
},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"\n",
"
\n",
"\n",
"\n",
"\n"
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"%jsroot on\n",
"gROOT->GetListOfCanvases()->Draw()"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "ROOT C++",
"language": "c++",
"name": "root"
},
"language_info": {
"codemirror_mode": "text/x-c++src",
"file_extension": ".C",
"mimetype": " text/x-c++src",
"name": "c++"
}
},
"nbformat": 4,
"nbformat_minor": 5
}