splines_test.C

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/// \file
/// \ingroup tutorial_graphics
/// \notebook
/// \preview Examples of use of the spline classes.
///
/// \macro_image
/// \macro_code
///
/// \author Federico Carminati
 
void splines_test(Int_t np = 23, Double_t a = -0.5, Double_t b = 31)
{
   const Double_t power = 0.75;
   const Double_t eps = (b - a) * 1.e-5;
 
   // Define the original function
   TF1 *f = new TF1("f", "sin(x)*sin(x/10)", a - 0.05 * (b - a), b + 0.05 * (b - a));
   // Draw function
   f->SetLineColor(kBlue);
   f->Draw("lc");
 
   TSpline3 *spline3 = nullptr;
   TSpline5 *spline5 = nullptr;
   TLegend *legend = nullptr;
 
   for (Int_t nnp = 2; nnp <= np; ++nnp) {
 
      std::vector<Double_t> xx(nnp), yy(nnp);
 
      // Calculate the knots
      for (Int_t i = 0; i < nnp; ++i) {
         xx[i] = a + (b - a) * TMath::Power(i / Double_t(nnp - 1), power);
         yy[i] = f->Eval(xx[i]);
      }
 
      // Evaluate fifth spline coefficients
      delete spline5;
      spline5 = new TSpline5(TString::Format("quintic spline %dknt", nnp),
                             xx.data(), f, nnp, "b1e1b2e2", f->Derivative(a), f->Derivative(b),
                             (f->Derivative(a + eps) - f->Derivative(a)) / eps,
                             (f->Derivative(b) - f->Derivative(b - eps)) / eps);
 
      spline5->SetLineColor(kRed);
      spline5->SetLineWidth(3);
 
      // Draw the quintic spline
      spline5->Draw("lcsame");
 
      // Evaluate third spline coefficients
      delete spline3;
      spline3 = new TSpline3(TString::Format("third spline %dknt", nnp),
                           xx.data(), yy.data(), nnp, "b1e1", f->Derivative(a), f->Derivative(b));
 
      spline3->SetLineColor(kGreen);
      spline3->SetLineWidth(3);
      spline3->SetMarkerColor(kMagenta);
      spline3->SetMarkerStyle(20);
      spline3->SetMarkerSize(1.5);
 
      // Draw the third spline
      spline3->Draw("lcpsame");
 
      delete legend;
      legend = gPad->BuildLegend(0.6, 0.7, 0.88, 0.88);
 
      gPad->Update();
 
      gSystem->Sleep(500);
   }
}