{
"cells": [
{
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"id": "f50d76d8",
"metadata": {},
"source": [
"# rf111_derivatives\n",
"Basic functionality: numerical 1st, 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:** 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 08:29 PM."
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "bb787282",
"metadata": {
"collapsed": false,
"execution": {
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"shell.execute_reply": "2026-05-19T20:29:30.065186Z"
}
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"outputs": [],
"source": [
"import ROOT"
]
},
{
"cell_type": "markdown",
"id": "a7860c2c",
"metadata": {},
"source": [
"Set up model\n",
"---------------------"
]
},
{
"cell_type": "markdown",
"id": "63c81df8",
"metadata": {},
"source": [
"Declare variables x,mean, with associated name, title, value and allowed\n",
"range"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "f6839361",
"metadata": {
"collapsed": false,
"execution": {
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"shell.execute_reply": "2026-05-19T20:29:30.231285Z"
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},
"outputs": [],
"source": [
"x = ROOT.RooRealVar(\"x\", \"x\", -10, 10)\n",
"mean = ROOT.RooRealVar(\"mean\", \"mean of gaussian\", 1, -10, 10)\n",
"sigma = ROOT.RooRealVar(\"sigma\", \"width of gaussian\", 1, 0.1, 10)"
]
},
{
"cell_type": "markdown",
"id": "6825d68d",
"metadata": {},
"source": [
"Build gaussian pdf in terms of x, and sigma"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "f734c69b",
"metadata": {
"collapsed": false,
"execution": {
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"shell.execute_reply": "2026-05-19T20:29:30.355441Z"
}
},
"outputs": [],
"source": [
"gauss = ROOT.RooGaussian(\"gauss\", \"gaussian PDF\", x, mean, sigma)"
]
},
{
"cell_type": "markdown",
"id": "e50dbf38",
"metadata": {},
"source": [
"Create and plot derivatives w.r.t. x\n",
"----------------------------------------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "b8c726c0",
"metadata": {},
"source": [
"Derivative of normalized gauss(x) w.r.t. observable x"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "9babd67e",
"metadata": {
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"execution": {
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"shell.execute_reply": "2026-05-19T20:29:30.469321Z"
}
},
"outputs": [],
"source": [
"dgdx = gauss.derivative(x, 1)"
]
},
{
"cell_type": "markdown",
"id": "f7f0fd09",
"metadata": {},
"source": [
"Second and third derivative of normalized gauss(x) w.r.t. observable x"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "dc39d32b",
"metadata": {
"collapsed": false,
"execution": {
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}
},
"outputs": [],
"source": [
"d2gdx2 = gauss.derivative(x, 2)\n",
"d3gdx3 = gauss.derivative(x, 3)"
]
},
{
"cell_type": "markdown",
"id": "fa7511f8",
"metadata": {},
"source": [
"Construct plot frame in 'x'"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "41a7bbfe",
"metadata": {
"collapsed": false,
"execution": {
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"shell.execute_reply": "2026-05-19T20:29:30.711471Z"
}
},
"outputs": [],
"source": [
"xframe = x.frame(Title=\"d(Gauss)/dx\")"
]
},
{
"cell_type": "markdown",
"id": "3f46fdea",
"metadata": {},
"source": [
"Plot gauss in frame (i.e. in x)"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "f4a62774",
"metadata": {
"collapsed": false,
"execution": {
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"outputs": [
{
"data": {
"text/plain": [
""
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"gauss.plotOn(xframe)"
]
},
{
"cell_type": "markdown",
"id": "2cb6dd8a",
"metadata": {},
"source": [
"Plot derivatives in same frame"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "32b47e6d",
"metadata": {
"collapsed": false,
"execution": {
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"outputs": [
{
"data": {
"text/plain": [
""
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"dgdx.plotOn(xframe, LineColor=\"m\")\n",
"d2gdx2.plotOn(xframe, LineColor=\"r\")\n",
"d3gdx3.plotOn(xframe, LineColor=\"kOrange\")"
]
},
{
"cell_type": "markdown",
"id": "44af7489",
"metadata": {},
"source": [
"Create and plot derivatives w.r.t. sigma\n",
"------------------------------------------------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "3a094207",
"metadata": {},
"source": [
"Derivative of normalized gauss(x) w.r.t. parameter sigma"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "d0aa0e03",
"metadata": {
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"execution": {
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"shell.execute_reply": "2026-05-19T20:29:31.107795Z"
}
},
"outputs": [],
"source": [
"dgds = gauss.derivative(sigma, 1)"
]
},
{
"cell_type": "markdown",
"id": "d9c0b62d",
"metadata": {},
"source": [
"Second and third derivative of normalized gauss(x) w.r.t. parameter sigma"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "efdebaba",
"metadata": {
"collapsed": false,
"execution": {
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"shell.execute_reply": "2026-05-19T20:29:31.213621Z"
}
},
"outputs": [],
"source": [
"d2gds2 = gauss.derivative(sigma, 2)\n",
"d3gds3 = gauss.derivative(sigma, 3)"
]
},
{
"cell_type": "markdown",
"id": "d74c0ac1",
"metadata": {},
"source": [
"Construct plot frame in 'sigma'"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "4cd59d6b",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:29:31.216235Z",
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"shell.execute_reply": "2026-05-19T20:29:31.325747Z"
}
},
"outputs": [],
"source": [
"sframe = sigma.frame(Title=\"d(Gauss)/d(sigma)\", Range=(0.0, 2.0))"
]
},
{
"cell_type": "markdown",
"id": "8c71db5b",
"metadata": {},
"source": [
"Plot gauss in frame (i.e. in x)"
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "93eb4bf5",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:29:31.328444Z",
"iopub.status.busy": "2026-05-19T20:29:31.328314Z",
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"shell.execute_reply": "2026-05-19T20:29:31.435048Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[#1] INFO:NumericIntegration -- RooRealIntegral::init(gauss_Int[sigma]) using numeric integrator RooIntegrator1D to calculate Int(sigma)\n"
]
},
{
"data": {
"text/plain": [
""
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"gauss.plotOn(sframe)"
]
},
{
"cell_type": "markdown",
"id": "87a6738e",
"metadata": {},
"source": [
"Plot derivatives in same frame"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "290cc262",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:29:31.437665Z",
"iopub.status.busy": "2026-05-19T20:29:31.437514Z",
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"shell.execute_reply": "2026-05-19T20:29:31.542115Z"
}
},
"outputs": [
{
"data": {
"text/plain": [
""
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"dgds.plotOn(sframe, LineColor=\"m\")\n",
"d2gds2.plotOn(sframe, LineColor=\"r\")\n",
"d3gds3.plotOn(sframe, LineColor=\"kOrange\")"
]
},
{
"cell_type": "markdown",
"id": "10600868",
"metadata": {},
"source": [
"Draw all frames on a canvas"
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "7f00cf03",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:29:31.544525Z",
"iopub.status.busy": "2026-05-19T20:29:31.544397Z",
"iopub.status.idle": "2026-05-19T20:29:31.750241Z",
"shell.execute_reply": "2026-05-19T20:29:31.749701Z"
}
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Info in : png file rf111_derivatives.png has been created\n"
]
}
],
"source": [
"c = ROOT.TCanvas(\"rf111_derivatives\", \"rf111_derivatives\", 800, 400)\n",
"c.Divide(2)\n",
"c.cd(1)\n",
"ROOT.gPad.SetLeftMargin(0.15)\n",
"xframe.GetYaxis().SetTitleOffset(1.6)\n",
"xframe.Draw()\n",
"c.cd(2)\n",
"ROOT.gPad.SetLeftMargin(0.15)\n",
"sframe.GetYaxis().SetTitleOffset(1.6)\n",
"sframe.Draw()\n",
"\n",
"c.SaveAs(\"rf111_derivatives.png\")"
]
},
{
"cell_type": "markdown",
"id": "486b8b5f",
"metadata": {},
"source": [
"Draw all canvases "
]
},
{
"cell_type": "code",
"execution_count": 15,
"id": "ecfc0bc5",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:29:31.752561Z",
"iopub.status.busy": "2026-05-19T20:29:31.752435Z",
"iopub.status.idle": "2026-05-19T20:29:31.934476Z",
"shell.execute_reply": "2026-05-19T20:29:31.933810Z"
}
},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"\n",
"
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"\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",
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},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
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