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"source": [
"# fitNormSum\n",
"Tutorial for normalized sum of two functions\n",
"Here: a background exponential and a crystalball function\n",
"Parameters can be set:\n",
" 1. with the TF1 object before adding the function (for 3) and 4))\n",
" 2. with the TF1NormSum object (first two are the coefficients, then the non constant parameters)\n",
" 3. with the TF1 object after adding the function\n",
"\n",
"Sum can be constructed by:\n",
" 1. by a string containing the names of the functions and/or the coefficient in front\n",
" 2. by a string containg formulas like expo, gaus...\n",
" 3. by the list of functions and coefficients (which are 1 by default)\n",
" 4. by a std::vector for functions and coefficients\n",
"\n",
"\n",
"\n",
"\n",
"**Author:** Lorenzo Moneta \n",
"This notebook tutorial was automatically generated with ROOTBOOK-izer from the macro found in the ROOT repository on Tuesday, May 19, 2026 at 08:24 PM."
]
},
{
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"source": [
"const int nsig = 5.E4;\n",
"const int nbkg = 1.e6;\n",
"int nEvents = nsig + nbkg;\n",
"int nBins = 1e3;\n",
"\n",
"double signal_mean = 3;\n",
"TF1 *f_cb = new TF1(\"MyCrystalBall\", \"crystalball\", -5., 5.);\n",
"TF1 *f_exp = new TF1(\"MyExponential\", \"expo\", -5., 5.);"
]
},
{
"cell_type": "markdown",
"id": "01c02c81",
"metadata": {},
"source": [
"I.:"
]
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"outputs": [],
"source": [
"f_exp->SetParameters(1., -0.3);\n",
"f_cb->SetParameters(1, signal_mean, 0.3, 2, 1.5);"
]
},
{
"cell_type": "markdown",
"id": "4462d04a",
"metadata": {},
"source": [
"CONSTRUCTION OF THE TF1NORMSUM OBJECT ........................................\n",
"1) :"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "5a7df721",
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"outputs": [],
"source": [
"TF1NormSum *fnorm_exp_cb = new TF1NormSum(f_cb, f_exp, nsig, nbkg);"
]
},
{
"cell_type": "markdown",
"id": "691e881a",
"metadata": {},
"source": [
"4) :"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "f5b03a2d",
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"execution": {
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"shell.execute_reply": "2026-05-19T20:25:02.003259Z"
}
},
"outputs": [],
"source": [
"TF1 *f_sum = new TF1(\"fsum\", *fnorm_exp_cb, -5., 5., fnorm_exp_cb->GetNpar());"
]
},
{
"cell_type": "markdown",
"id": "54f323af",
"metadata": {},
"source": [
"III.:"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "c08379c8",
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"source": [
"f_sum->SetParameters(fnorm_exp_cb->GetParameters().data());\n",
"f_sum->SetParName(1, \"NBackground\");\n",
"f_sum->SetParName(0, \"NSignal\");\n",
"for (int i = 2; i < f_sum->GetNpar(); ++i)\n",
" f_sum->SetParName(i, fnorm_exp_cb->GetParName(i));"
]
},
{
"cell_type": "markdown",
"id": "0b5b5a88",
"metadata": {},
"source": [
"GENERATE HISTOGRAM TO FIT .............................................................."
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "6bf6b2af",
"metadata": {
"collapsed": false,
"execution": {
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"shell.execute_reply": "2026-05-19T20:25:02.419227Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Time to generate 1050000 events: Real time 0:00:00, CP time 0.090\n"
]
}
],
"source": [
"TStopwatch w;\n",
"w.Start();\n",
"TH1D *h_sum = new TH1D(\"h_ExpCB\", \"Exponential Bkg + CrystalBall function\", nBins, -5., 5.);\n",
"h_sum->FillRandom(\"fsum\", nEvents);\n",
"printf(\"Time to generate %d events: \", nEvents);\n",
"w.Print();"
]
},
{
"cell_type": "markdown",
"id": "ca706ca8",
"metadata": {},
"source": [
"need to scale histogram with width since we are fitting a density"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "e4619d2a",
"metadata": {
"collapsed": false,
"execution": {
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"shell.execute_reply": "2026-05-19T20:25:02.637601Z"
}
},
"outputs": [],
"source": [
"h_sum->Sumw2();\n",
"h_sum->Scale(1., \"width\");"
]
},
{
"cell_type": "markdown",
"id": "89c3c04c",
"metadata": {},
"source": [
"fit - use Minuit2 if available"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "b5acf9d2",
"metadata": {
"collapsed": false,
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"shell.execute_reply": "2026-05-19T20:25:02.848621Z"
}
},
"outputs": [],
"source": [
"ROOT::Math::MinimizerOptions::SetDefaultMinimizer(\"Minuit2\");\n",
"new TCanvas(\"Fit\", \"Fit\", 800, 1000);"
]
},
{
"cell_type": "markdown",
"id": "131251ee",
"metadata": {},
"source": [
"do a least-square fit of the spectrum"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "dad860e8",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:25:02.851287Z",
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"shell.execute_reply": "2026-05-19T20:25:03.065241Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"****************************************\n",
"Minimizer is Minuit2 / Migrad\n",
"Chi2 = 1018.73\n",
"NDf = 993\n",
"Edm = 9.65559e-06\n",
"NCalls = 233\n",
"NSignal = 50082 +/- 1231.21 \n",
"NBackground = 998899 +/- 1569.86 \n",
"Mean = 2.99896 +/- 0.0022426 \n",
"Sigma = 0.297871 +/- 0.00230279 \n",
"Alpha = 2.12493 +/- 0.1368 \n",
"N = 1.1562 +/- 0.468136 \n",
"Slope = -0.300341 +/- 0.000644187 \n",
"Time to fit using ROOT TF1Normsum: Real time 0:00:00, CP time 0.090\n"
]
}
],
"source": [
"auto result = h_sum->Fit(\"fsum\", \"SQ\");\n",
"result->Print();\n",
"h_sum->Draw();\n",
"printf(\"Time to fit using ROOT TF1Normsum: \");\n",
"w.Print();"
]
},
{
"cell_type": "markdown",
"id": "10d2f799",
"metadata": {},
"source": [
"test if parameters are fine"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "b1dcf868",
"metadata": {
"collapsed": false,
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"std::vector pref = {nsig, nbkg, signal_mean};\n",
"for (unsigned int i = 0; i < pref.size(); ++i) {\n",
" if (!TMath::AreEqualAbs(pref[i], f_sum->GetParameter(i), f_sum->GetParError(i) * 10.))\n",
" Error(\"testFitNormSum\", \"Difference found in fitted %s - difference is %g sigma\", f_sum->GetParName(i),\n",
" (f_sum->GetParameter(i) - pref[i]) / f_sum->GetParError(i));\n",
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"gStyle->SetOptStat(0);"
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{
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"add parameters"
]
},
{
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"outputs": [],
"source": [
"auto t1 = new TLatex(\n",
" -2.5, 300000, TString::Format(\"%s = %8.0f #pm %4.0f\", \"NSignal\", f_sum->GetParameter(0), f_sum->GetParError(0)));\n",
"auto t2 = new TLatex(\n",
" -2.5, 270000, TString::Format(\"%s = %8.0f #pm %4.0f\", \"Nbackgr\", f_sum->GetParameter(1), f_sum->GetParError(1)));\n",
"t1->Draw();\n",
"t2->Draw();"
]
},
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"cell_type": "markdown",
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"metadata": {},
"source": [
"Draw all canvases "
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