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"source": [
"# rf710_roopoly\n",
"Taylor expansion of RooFit functions using the taylorExpand function\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 08:35 PM."
]
},
{
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"source": [
"import ROOT"
]
},
{
"cell_type": "markdown",
"id": "9927c41e",
"metadata": {},
"source": [
"Create functions\n",
"-- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "c23a3304",
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"outputs": [],
"source": [
"x = ROOT.RooRealVar(\"x\", \"x\", 0.0, -3, 10)"
]
},
{
"cell_type": "markdown",
"id": "4940e3d5",
"metadata": {},
"source": [
"RooPolyFunc polynomial\n",
"-- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -\n",
"x ^ 4 - 5x ^ 3 + 5x ^ 2 + 5x - 6\n",
"-- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -"
]
},
{
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"outputs": [],
"source": [
"f = ROOT.RooPolyFunc(\"f\", \"f\", ROOT.RooArgList(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)\n",
"\n",
"f = ROOT.RooFormulaVar(\"f\", \"f\", \"pow(@0,4) -5 * pow(@0,3) +5 * pow(@0,2) + 5 * pow(@0,1) - 6\", [x])"
]
},
{
"cell_type": "markdown",
"id": "3bdd060c",
"metadata": {},
"source": [
"taylor expand around x0 = 0\n",
"-- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -"
]
},
{
"cell_type": "code",
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"id": "597e0f95",
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},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(ELineStyle) (kDashed) : (unsigned int) 2\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"(ELineStyle) (kDotted) : (unsigned int) 3\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"Info in : png file rf710_roopoly.png has been created\n"
]
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"source": [
"x0 = 2.0\n",
"taylor_o1 = ROOT.RooPolyFunc.taylorExpand(\"taylorfunc_o1\", \"taylor expansion order 1\", f, [x], 1, [x0])\n",
"ROOT.SetOwnership(taylor_o1, True)\n",
"taylor_o2 = ROOT.RooPolyFunc.taylorExpand(\"taylorfunc_o2\", \"taylor expansion order 2\", f, [x], 2, [x0])\n",
"ROOT.SetOwnership(taylor_o2, True)\n",
"frame = x.frame(Title=\"x^{4} - 5x^{3} + 5x^{2} + 5x - 6\")\n",
"c = ROOT.TCanvas(\"c\", \"c\", 400, 400)\n",
"\n",
"f.plotOn(frame, Name=\"f\")\n",
"taylor_o1.plotOn(frame, Name=\"taylor_o1\", LineColor=\"kRed\", LineStyle=\"kDashed\")\n",
"taylor_o2.plotOn(frame, Name=\"taylor_o2\", LineColor=\"kRed-9\", LineStyle=\"kDotted\")\n",
"\n",
"c.cd()\n",
"frame.SetMinimum(-8.0)\n",
"frame.SetMaximum(+8.0)\n",
"frame.SetYTitle(\"function value\")\n",
"frame.Draw()\n",
"\n",
"legend = ROOT.TLegend(0.53, 0.73, 0.86, 0.87)\n",
"legend.SetFillColor(\"w\")\n",
"legend.SetLineColor(\"w\")\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",
"\n",
"c.Draw()\n",
"c.SaveAs(\"rf710_roopoly.png\")"
]
},
{
"cell_type": "markdown",
"id": "d7d064be",
"metadata": {},
"source": [
"Draw all canvases "
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "3a59e4f5",
"metadata": {
"collapsed": false,
"execution": {
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"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from ROOT import gROOT \n",
"gROOT.GetListOfCanvases().Draw()"
]
}
],
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"display_name": "Python 3",
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