Create, Draw and Fit a TGraph2DErrors¶

---

Create the 2D graph and the function to fit.

In [1]:

const double e = 0.3;
const int nd = 500;

TGraph2DErrors dte(nd);
TF2 f2("f2", "1000*(([0]*sin(x)/x)*([1]*sin(y)/y))+200", -6, 6, -6, 6);
f2.SetParameters(1, 1);

TRandom3 my_random_generator;

Fill the graph.

In [2]:

double rnd, x, y, z, ex, ey, ez;
for (auto i : ROOT::TSeqI(nd)) {
    f2.GetRandom2(x, y);
    
    // A random number in [-e,e]
    rnd = my_random_generator.Uniform(-e,e);
    
    z = f2.Eval(x, y) * (1 + rnd);
    dte.SetPoint(i, x, y, z);
    ex = 0.05 * my_random_generator.Uniform();
    ey = 0.05 * my_random_generator.Uniform();
    ez = fabs(z * rnd);
    dte.SetPointError(i, ex, ey, ez);
}

Warning in <TF2::GetRandom2>: function:f2 has 24 negative values: abs assumed

Fit the function to the generated data.

In [3]:

f2.SetParameters(0.7, 1.5);  // set initial values for fit
f2.SetTitle("Fitted 2D function");
dte.Fit(&f2);

 FCN=517.445 FROM MIGRAD    STATUS=CONVERGED      38 CALLS          39 TOTAL
                     EDM=2.65702e-12    STRATEGY= 1      ERROR MATRIX ACCURATE 
  EXT PARAMETER                                   STEP         FIRST   
  NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE 
   1  p0           6.81725e-01   4.37173e-01   2.40425e-05   8.08231e-04
   2  p1           1.46084e+00   9.36798e-01   5.15197e-05   3.78774e-04

Configure the canvas for plotting the result.

In [4]:

TCanvas c1;
f2.SetLineWidth(1);
f2.SetLineColor(kBlue - 5);
f2.Draw("Surf1");
auto Xaxis = f2.GetXaxis();
auto Yaxis = f2.GetYaxis();
auto Zaxis = f2.GetZaxis();
Xaxis->SetTitle("X Title"); Xaxis->SetTitleOffset(1.5);
Yaxis->SetTitle("Y Title"); Yaxis->SetTitleOffset(1.5);
Zaxis->SetTitle("Z Title"); Zaxis->SetTitleOffset(1.5);
dte.Draw("P0 Same");

Display the 2D graph in the notebook.

In [5]:

c1.Draw();

Make the x and y projections.

In [6]:

gStyle->SetPalette(kBird);
TCanvas c_p("ProjCan", "The Projections", 1000, 400);
c_p.Divide(2,1);
c_p.cd(1);
dte.Project("x")->Draw();
c_p.cd(2);
dte.Project("y")->Draw();

Activate the JavaScript visualisation mode and display the projections in the notebook.

In [7]:

%jsroot on
c_p.Draw();