{
"cells": [
{
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"metadata": {},
"source": [
"# rf302_utilfuncs\n",
"Multidimensional models: utility functions classes available for use in tailoring of\n",
"composite (multidimensional) pdfs\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 08:30 PM."
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "82cb5cb8",
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"execution": {
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"source": [
"%%cpp -d\n",
"#include \"RooRealVar.h\"\n",
"#include \"RooDataSet.h\"\n",
"#include \"RooGaussian.h\"\n",
"#include \"TCanvas.h\"\n",
"#include \"TAxis.h\"\n",
"#include \"RooPlot.h\"\n",
"#include \"RooFormulaVar.h\"\n",
"#include \"RooAddition.h\"\n",
"#include \"RooProduct.h\"\n",
"#include \"RooPolyVar.h\"\n",
"#include \"TCanvas.h\"\n",
"#include \"TAxis.h\"\n",
"#include \"TH1.h\"\n",
"\n",
"using namespace RooFit;"
]
},
{
"cell_type": "markdown",
"id": "f0c722c3",
"metadata": {},
"source": [
"Create observables, parameters\n",
"-----------------------------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "a3ce193d",
"metadata": {},
"source": [
"Create observables"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "f404f626",
"metadata": {
"collapsed": false,
"execution": {
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"shell.execute_reply": "2026-05-19T20:30:31.879804Z"
}
},
"outputs": [],
"source": [
"RooRealVar x(\"x\", \"x\", -5, 5);\n",
"RooRealVar y(\"y\", \"y\", -5, 5);"
]
},
{
"cell_type": "markdown",
"id": "82ddc031",
"metadata": {},
"source": [
"Create parameters"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "142be45f",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:31.882444Z",
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"outputs": [],
"source": [
"RooRealVar a0(\"a0\", \"a0\", -1.5, -5, 5);\n",
"RooRealVar a1(\"a1\", \"a1\", -0.5, -1, 1);\n",
"RooRealVar sigma(\"sigma\", \"width of gaussian\", 0.5);"
]
},
{
"cell_type": "markdown",
"id": "d4e22235",
"metadata": {},
"source": [
"Using RooFormulaVar to tailor pdf\n",
"-----------------------------------------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "f229bbbc",
"metadata": {},
"source": [
"Create interpreted function f(y) = a0 - a1*sqrt(10*abs(y))"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "7d23ec0c",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:32.092069Z",
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"shell.execute_reply": "2026-05-19T20:30:32.299064Z"
}
},
"outputs": [],
"source": [
"RooFormulaVar fy_1(\"fy_1\", \"a0-a1*sqrt(10*abs(y))\", RooArgSet(y, a0, a1));"
]
},
{
"cell_type": "markdown",
"id": "d1602c2b",
"metadata": {},
"source": [
"Create gauss(x,f(y),s)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "386d8683",
"metadata": {
"collapsed": false,
"execution": {
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"shell.execute_reply": "2026-05-19T20:30:32.508884Z"
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"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[#0] WARNING:InputArguments -- The parameter 'sigma' with range [-inf, inf] of the RooGaussian 'model_1' exceeds the safe range of (0, inf). Advise to limit its range.\n"
]
}
],
"source": [
"RooGaussian model_1(\"model_1\", \"Gaussian with shifting mean\", x, fy_1, sigma);"
]
},
{
"cell_type": "markdown",
"id": "e04a570b",
"metadata": {},
"source": [
"Using RooPolyVar to tailor pdf\n",
"-----------------------------------------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "280b7ec0",
"metadata": {},
"source": [
"Create polynomial function f(y) = a0 + a1*y"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "17e4da13",
"metadata": {
"collapsed": false,
"execution": {
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"shell.execute_reply": "2026-05-19T20:30:32.718164Z"
}
},
"outputs": [],
"source": [
"RooPolyVar fy_2(\"fy_2\", \"fy_2\", y, RooArgSet(a0, a1));"
]
},
{
"cell_type": "markdown",
"id": "850e0872",
"metadata": {},
"source": [
"Create gauss(x,f(y),s)"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "217f4a70",
"metadata": {
"collapsed": false,
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"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[#0] WARNING:InputArguments -- The parameter 'sigma' with range [-inf, inf] of the RooGaussian 'model_2' exceeds the safe range of (0, inf). Advise to limit its range.\n"
]
}
],
"source": [
"RooGaussian model_2(\"model_2\", \"Gaussian with shifting mean\", x, fy_2, sigma);"
]
},
{
"cell_type": "markdown",
"id": "8af135e4",
"metadata": {},
"source": [
"Using RooAddition to tailor pdf\n",
"-----------------------------------------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "91b21dba",
"metadata": {},
"source": [
"Create sum function f(y) = a0 + y"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "1f3ae99c",
"metadata": {
"collapsed": false,
"execution": {
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"shell.execute_reply": "2026-05-19T20:30:33.137199Z"
}
},
"outputs": [],
"source": [
"RooAddition fy_3(\"fy_3\", \"a0+y\", RooArgSet(a0, y));"
]
},
{
"cell_type": "markdown",
"id": "a417fdd0",
"metadata": {},
"source": [
"Create gauss(x,f(y),s)"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "86158afe",
"metadata": {
"collapsed": false,
"execution": {
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"shell.execute_reply": "2026-05-19T20:30:33.346927Z"
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"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[#0] WARNING:InputArguments -- The parameter 'sigma' with range [-inf, inf] of the RooGaussian 'model_3' exceeds the safe range of (0, inf). Advise to limit its range.\n"
]
}
],
"source": [
"RooGaussian model_3(\"model_3\", \"Gaussian with shifting mean\", x, fy_3, sigma);"
]
},
{
"cell_type": "markdown",
"id": "ab777d5c",
"metadata": {},
"source": [
"Using RooProduct to tailor pdf\n",
"-----------------------------------------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "88931bd5",
"metadata": {},
"source": [
"Create product function f(y) = a1*y"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "f0c153ea",
"metadata": {
"collapsed": false,
"execution": {
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"shell.execute_reply": "2026-05-19T20:30:33.555929Z"
}
},
"outputs": [],
"source": [
"RooProduct fy_4(\"fy_4\", \"a1*y\", RooArgSet(a1, y));"
]
},
{
"cell_type": "markdown",
"id": "553604fd",
"metadata": {},
"source": [
"Create gauss(x,f(y),s)"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "3bc04101",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:33.558642Z",
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"shell.execute_reply": "2026-05-19T20:30:33.765804Z"
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"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[#0] WARNING:InputArguments -- The parameter 'sigma' with range [-inf, inf] of the RooGaussian 'model_4' exceeds the safe range of (0, inf). Advise to limit its range.\n"
]
}
],
"source": [
"RooGaussian model_4(\"model_4\", \"Gaussian with shifting mean\", x, fy_4, sigma);"
]
},
{
"cell_type": "markdown",
"id": "2cec23a5",
"metadata": {},
"source": [
"Plot all pdfs\n",
"----------------------------"
]
},
{
"cell_type": "markdown",
"id": "f804a7ba",
"metadata": {},
"source": [
"Make two-dimensional plots in x vs y"
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "ac6ee0d6",
"metadata": {
"collapsed": false,
"execution": {
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"shell.execute_reply": "2026-05-19T20:30:33.975268Z"
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},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[#1] INFO:NumericIntegration -- RooRealIntegral::init(model_1_Int[x,y]) using numeric integrator RooIntegrator1D to calculate Int(y)\n",
"[#1] INFO:NumericIntegration -- RooRealIntegral::init(model_2_Int[x,y]) using numeric integrator RooIntegrator1D to calculate Int(y)\n",
"[#1] INFO:NumericIntegration -- RooRealIntegral::init(model_3_Int[x,y]) using numeric integrator RooIntegrator1D to calculate Int(y)\n",
"[#1] INFO:NumericIntegration -- RooRealIntegral::init(model_4_Int[x,y]) using numeric integrator RooIntegrator1D to calculate Int(y)\n"
]
}
],
"source": [
"TH1 *hh_model_1 = model_1.createHistogram(\"hh_model_1\", x, Binning(50), YVar(y, Binning(50)));\n",
"TH1 *hh_model_2 = model_2.createHistogram(\"hh_model_2\", x, Binning(50), YVar(y, Binning(50)));\n",
"TH1 *hh_model_3 = model_3.createHistogram(\"hh_model_3\", x, Binning(50), YVar(y, Binning(50)));\n",
"TH1 *hh_model_4 = model_4.createHistogram(\"hh_model_4\", x, Binning(50), YVar(y, Binning(50)));\n",
"hh_model_1->SetLineColor(kBlue);\n",
"hh_model_2->SetLineColor(kBlue);\n",
"hh_model_3->SetLineColor(kBlue);\n",
"hh_model_4->SetLineColor(kBlue);"
]
},
{
"cell_type": "markdown",
"id": "64b4fce0",
"metadata": {},
"source": [
"Make canvas and draw RooPlots"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "11f73acd",
"metadata": {
"collapsed": false,
"execution": {
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"shell.execute_reply": "2026-05-19T20:30:34.181565Z"
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},
"outputs": [],
"source": [
"TCanvas *c = new TCanvas(\"rf302_utilfuncs\", \"rf302_utilfuncs\", 800, 800);\n",
"c->Divide(2, 2);\n",
"c->cd(1);\n",
"gPad->SetLeftMargin(0.20);\n",
"hh_model_1->GetZaxis()->SetTitleOffset(2.5);\n",
"hh_model_1->Draw(\"surf\");\n",
"c->cd(2);\n",
"gPad->SetLeftMargin(0.20);\n",
"hh_model_2->GetZaxis()->SetTitleOffset(2.5);\n",
"hh_model_2->Draw(\"surf\");\n",
"c->cd(3);\n",
"gPad->SetLeftMargin(0.20);\n",
"hh_model_3->GetZaxis()->SetTitleOffset(2.5);\n",
"hh_model_3->Draw(\"surf\");\n",
"c->cd(4);\n",
"gPad->SetLeftMargin(0.20);\n",
"hh_model_4->GetZaxis()->SetTitleOffset(2.5);\n",
"hh_model_4->Draw(\"surf\");"
]
},
{
"cell_type": "markdown",
"id": "5902b95d",
"metadata": {},
"source": [
"Draw all canvases "
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "14a79933",
"metadata": {
"collapsed": false,
"execution": {
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