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"# fit2a\n",
"Fitting a 2-D histogram (a variant)\n",
"This tutorial illustrates :\n",
" - how to create a 2-d function\n",
" - fill a 2-d histogram randomly from this function\n",
" - fit the histogram\n",
" - display the fitted function on top of the histogram (lego-plot)\n",
" using a surface plot in a sub-range of the histogram.\n",
"\n",
"This example can be executed via the interpreter or/and the compiler\n",
"\n",
"```cpp\n",
" root > .x fit2a.C\n",
" root > .x fit2a.C++\n",
"```\n",
"\n",
"\n",
"\n",
"\n",
"**Author:** Rene Brun \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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" Definition of a helper function: "
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"%%cpp -d\n",
"\n",
"#include \"TF2.h\"\n",
"#include \"TH2.h\"\n",
"#include \"TCutG.h\"\n",
"#include \"TMath.h\"\n",
"#include \"TCanvas.h\"\n",
"#include \"TStyle.h\"\n",
"\n",
"double g2(double *x, double *par) {\n",
" double r1 = double((x[0]-par[1])/par[2]);\n",
" double r2 = double((x[1]-par[3])/par[4]);\n",
" return par[0]*TMath::Exp(-0.5*(r1*r1+r2*r2));\n",
"}"
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"%%cpp -d\n",
"double fun2(double *x, double *par) {\n",
" double *p1 = &par[0];\n",
" double *p2 = &par[5];\n",
" double *p3 = &par[10];\n",
" double result = g2(x,p1) + g2(x,p2) + g2(x,p3);\n",
" return result;\n",
"}"
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"TCanvas *c = new TCanvas();\n",
"gStyle->SetOptStat(true);\n",
"gStyle->SetPalette(57);\n",
"const int npar = 15;\n",
"double f2params[npar] = {100,-3,3,-3,3,160,0,0.8,0,0.9,40,4,0.7,4,0.7};\n",
"auto f2 = new TF2(\"f2\",fun2,-10,10,-10,10, npar);\n",
"f2->SetParameters(f2params);"
]
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{
"cell_type": "markdown",
"id": "71976e37",
"metadata": {},
"source": [
"Create an histogram and fill it randomly with f2"
]
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"auto h2 = new TH2F(\"h2\",\"From f2\",40,-10,10,40,-10,10);\n",
"int nentries = 100000;\n",
"h2->FillRandom(\"f2\",nentries);"
]
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"cell_type": "markdown",
"id": "673e8f4b",
"metadata": {},
"source": [
"Fit h2 with original function f2"
]
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"****************************************\n",
"Minimizer is Minuit2 / Migrad\n",
"Chi2 = 1048.29\n",
"NDf = 1139\n",
"Edm = 3.90056e-06\n",
"NCalls = 519\n",
"p0 = 392.558 +/- 2.07088 \n",
"p1 = -2.99838 +/- 0.0116072 \n",
"p2 = 2.98484 +/- 0.00840711 \n",
"p3 = -3.00201 +/- 0.0115172 \n",
"p4 = 2.97271 +/- 0.00841038 \n",
"p5 = 601.133 +/- 10.5562 \n",
"p6 = 0.00614073 +/- 0.0119548 \n",
"p7 = 0.81626 +/- 0.0107847 \n",
"p8 = -0.000781266 +/- 0.0134062 \n",
"p9 = 0.911288 +/- 0.0119899 \n",
"p10 = 146.899 +/- 5.12261 \n",
"p11 = 3.9882 +/- 0.0182639 \n",
"p12 = 0.727561 +/- 0.0142962 \n",
"p13 = 4.02637 +/- 0.0175896 \n",
"p14 = 0.703077 +/- 0.0140242 \n"
]
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"text": [
"input_line_70:2:2: warning: 'ratio' shadows a declaration with the same name in the 'std' namespace; use '::ratio' to reference this declaration\n",
" float ratio = 4*nentries/100000;\n",
" ^\n"
]
}
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"float ratio = 4*nentries/100000;\n",
"f2params[ 0] *= ratio;\n",
"f2params[ 5] *= ratio;\n",
"f2params[10] *= ratio;\n",
"f2->SetParameters(f2params);\n",
"h2->Fit(\"f2\",\"N\");\n",
"auto cutg = new TCutG(\"cutg\",5);\n",
"cutg->SetPoint(0,-7,-7);\n",
"cutg->SetPoint(1, 2,-7);\n",
"cutg->SetPoint(2, 2, 2);\n",
"cutg->SetPoint(3,-7, 2);\n",
"cutg->SetPoint(4,-7,-7);\n",
"h2->Draw(\"lego2 0\");\n",
"h2->SetFillColor(38);\n",
"f2->SetNpx(80);\n",
"f2->SetNpy(80);\n",
"f2->Draw(\"surf1 same bb [cutg]\");\n",
"return c;"
]
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"source": [
"Draw all canvases "
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