{
"cells": [
{
"cell_type": "markdown",
"id": "865aa3ba",
"metadata": {},
"source": [
"# rf710_roopoly\n",
"Taylor expansion of RooFit functions using the taylorExpand function with RooPolyFunc\n",
"\n",
"\n",
"\n",
"\n",
"**Author:** Rahul Balasubramanian \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": "9e6a5e07",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:35:02.144839Z",
"iopub.status.busy": "2026-05-19T20:35:02.144733Z",
"iopub.status.idle": "2026-05-19T20:35:02.160446Z",
"shell.execute_reply": "2026-05-19T20:35:02.159870Z"
}
},
"outputs": [],
"source": [
"%%cpp -d\n",
"#include \"RooRealVar.h\"\n",
"#include \"RooPolyFunc.h\"\n",
"#include \"RooAbsCollection.h\"\n",
"#include \"RooPlot.h\"\n",
"#include \"TCanvas.h\"\n",
"\n",
"using namespace RooFit;"
]
},
{
"cell_type": "markdown",
"id": "29b5bfc5",
"metadata": {},
"source": [
"Create polynomial\n",
"function of fourth order\n",
"---------------------------------------------\n",
"x^4 - 5x^3 + 5x^2 + 5x -6\n",
"---------------------------------------------"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "eea14192",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:35:02.162129Z",
"iopub.status.busy": "2026-05-19T20:35:02.162004Z",
"iopub.status.idle": "2026-05-19T20:35:02.560559Z",
"shell.execute_reply": "2026-05-19T20:35:02.559643Z"
}
},
"outputs": [],
"source": [
"RooRealVar x(\"x\", \"x\", 0, -3, 10);\n",
"RooPolyFunc f(\"f\", \"f\", RooArgSet(x));\n",
"f.addTerm(+1, x, 4);\n",
"f.addTerm(-5, x, 3);\n",
"f.addTerm(+5, x, 2);\n",
"f.addTerm(+5, x, 1);\n",
"f.addTerm(-6, x, 0);"
]
},
{
"cell_type": "markdown",
"id": "bff1788c",
"metadata": {},
"source": [
"Create taylor expansion\n",
"---------------------------------------------"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "2940a513",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:35:02.562264Z",
"iopub.status.busy": "2026-05-19T20:35:02.562142Z",
"iopub.status.idle": "2026-05-19T20:35:02.772584Z",
"shell.execute_reply": "2026-05-19T20:35:02.771792Z"
}
},
"outputs": [],
"source": [
"double x0 = 2.0;\n",
"auto taylor_o1 = RooPolyFunc::taylorExpand(\"taylor_o1\", \"taylor expansion order 1\", f, {x}, 1, {x0});\n",
"auto taylor_o2 = RooPolyFunc::taylorExpand(\"taylor_o2\", \"taylor expansion order 2\", f, {x}, 2, {x0});"
]
},
{
"cell_type": "markdown",
"id": "6ad8e2c4",
"metadata": {},
"source": [
"Plot polynomial with first and second order taylor expansion overlaid"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "e32301bc",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:35:02.774217Z",
"iopub.status.busy": "2026-05-19T20:35:02.774097Z",
"iopub.status.idle": "2026-05-19T20:35:02.980327Z",
"shell.execute_reply": "2026-05-19T20:35:02.979627Z"
}
},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"\n",
"
\n",
"\n",
"\n",
"\n"
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"Info in : png file rf710_roopoly.png has been created\n"
]
}
],
"source": [
"auto frame = x.frame(Title(\"x^{4} - 5x^{3} + 5x^{2} + 5x - 6\"));\n",
"auto c = new TCanvas(\"rf710_roopoly\", \"rf710_roopoly\", 400, 400);\n",
"c->cd();\n",
"\n",
"f.plotOn(frame, Name(\"f\"));\n",
"taylor_o1->plotOn(frame, LineColor(kRed), LineStyle(kDashed), Name(\"taylor_o1\"));\n",
"taylor_o2->plotOn(frame, LineColor(kRed - 9), LineStyle(kDotted), Name(\"taylor_o2\"));\n",
"\n",
"frame->SetMinimum(-8.0);\n",
"frame->SetMaximum(+8.0);\n",
"frame->SetYTitle(\"function value\");\n",
"frame->Draw();\n",
"\n",
"auto legend = new TLegend(0.53, 0.7, 0.86, 0.87);\n",
"legend->SetFillColor(kWhite);\n",
"legend->SetLineColor(kWhite);\n",
"legend->SetTextSize(0.02);\n",
"legend->AddEntry(\"taylor_o1\", \"Taylor expansion upto first order\", \"L\");\n",
"legend->AddEntry(\"taylor_o2\", \"Taylor expansion upto second order\", \"L\");\n",
"legend->AddEntry(\"f\", \"Polynomial of fourth order\", \"L\");\n",
"legend->Draw();\n",
"c->Draw();\n",
"c->SaveAs(\"rf710_roopoly.png\");"
]
},
{
"cell_type": "markdown",
"id": "3902599a",
"metadata": {},
"source": [
"Draw all canvases "
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "b580e6b7",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:35:02.981942Z",
"iopub.status.busy": "2026-05-19T20:35:02.981823Z",
"iopub.status.idle": "2026-05-19T20:35:03.197302Z",
"shell.execute_reply": "2026-05-19T20:35:03.196533Z"
}
},
"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
}