Bessel

Show the different kinds of Bessel functions available in ROOT To execute the macro type in:

root[0] .x Bessel.C

It will create one canvas with the representation of the cylindrical and spherical Bessel functions regular and modified

Author: Magdalena Slawinska
This notebook tutorial was automatically generated with ROOTBOOK-izer from the macro found in the ROOT repository on Wednesday, August 17, 2022 at 09:34 AM.

In [1]:
R__LOAD_LIBRARY(libMathMore);

TCanvas *DistCanvas = new TCanvas("DistCanvas", "Bessel functions example", 10, 10, 800, 600);
DistCanvas->SetFillColor(17);
DistCanvas->Divide(2, 2);
DistCanvas->cd(1);
gPad->SetGrid();
gPad->SetFrameFillColor(19);
TLegend *leg = new TLegend(0.75, 0.7, 0.89, 0.89);

int n = 5; //number of functions in each pad

drawing the set of Bessel J functions

In [2]:
TF1* JBessel[5];
for(int nu = 0; nu < n; nu++)
{
   JBessel[nu]= new TF1("J_0", "ROOT::Math::cyl_bessel_j([0],x)", 0, 10);
   JBessel[nu]->SetParameters(nu, 0.0);
   JBessel[nu]->SetTitle(""); //Bessel J functions");
   JBessel[nu]->SetLineStyle(1);
   JBessel[nu]->SetLineWidth(3);
   JBessel[nu]->SetLineColor(nu+1);
}
JBessel[0]->TF1::GetXaxis()->SetTitle("x");
JBessel[0]->GetXaxis()->SetTitleSize(0.06);
JBessel[0]->GetXaxis()->SetTitleOffset(.7);

//setting the title in a label style
TPaveLabel *p1 = new TPaveLabel(.0,.90 , (.0+.50),(.90+.10) , "Bessel J functions", "NDC");
p1->SetFillColor(0);
p1->SetTextFont(22);
p1->SetTextColor(kBlack);

//setting the legend
leg->AddEntry(JBessel[0]->DrawCopy(), " J_0(x)", "l");
leg->AddEntry(JBessel[1]->DrawCopy("same"), " J_1(x)", "l");
leg->AddEntry(JBessel[2]->DrawCopy("same"), " J_2(x)", "l");
leg->AddEntry(JBessel[3]->DrawCopy("same"), " J_3(x)", "l");
leg->AddEntry(JBessel[4]->DrawCopy("same"), " J_4(x)", "l");

leg->Draw();
p1->Draw();

//------------------------------------------------
DistCanvas->cd(2);
gPad->SetGrid();
gPad->SetFrameFillColor(19);

TLegend *leg2 = new TLegend(0.75, 0.7, 0.89, 0.89);
//------------------------------------------------
//Drawing Bessel k
TF1* KBessel[5];
for(int nu = 0; nu < n; nu++){
   KBessel[nu]= new TF1("J_0", "ROOT::Math::cyl_bessel_k([0],x)", 0, 10);
   KBessel[nu]->SetParameters(nu, 0.0);
   KBessel[nu]->SetTitle("Bessel K functions");
   KBessel[nu]->SetLineStyle(1);
   KBessel[nu]->SetLineWidth(3);
   KBessel[nu]->SetLineColor(nu+1);
}
KBessel[0]->GetXaxis()->SetTitle("x");
KBessel[0]->GetXaxis()->SetTitleSize(0.06);
KBessel[0]->GetXaxis()->SetTitleOffset(.7);

//setting title
TPaveLabel *p2 = new TPaveLabel(.0,.90 , (.0+.50),(.90+.10) , "Bessel K functions", "NDC");
p2->SetFillColor(0);
p2->SetTextFont(22);
p2->SetTextColor(kBlack);

//setting legend
leg2->AddEntry(KBessel[0]->DrawCopy(), " K_0(x)", "l");
leg2->AddEntry(KBessel[1]->DrawCopy("same"), " K_1(x)", "l");
leg2->AddEntry(KBessel[2]->DrawCopy("same"), " K_2(x)", "l");
leg2->AddEntry(KBessel[3]->DrawCopy("same"), " K_3(x)", "l");
leg2->AddEntry(KBessel[4]->DrawCopy("same"), " K_4(x)", "l");
leg2->Draw();
p2->Draw();
//------------------------------------------------
DistCanvas->cd(3);
gPad->SetGrid();
gPad->SetFrameFillColor(19);
TLegend *leg3 = new TLegend(0.75, 0.7, 0.89, 0.89);
//------------------------------------------------
//Drawing Bessel i
TF1* iBessel[5];
for(int nu = 0; nu <= 4; nu++){
   iBessel[nu]= new TF1("J_0", "ROOT::Math::cyl_bessel_i([0],x)", 0, 10);
   iBessel[nu]->SetParameters(nu, 0.0);
   iBessel[nu]->SetTitle("Bessel I functions");
   iBessel[nu]->SetLineStyle(1);
   iBessel[nu]->SetLineWidth(3);
   iBessel[nu]->SetLineColor(nu+1);
}

iBessel[0]->GetXaxis()->SetTitle("x");
iBessel[0]->GetXaxis()->SetTitleSize(0.06);
iBessel[0]->GetXaxis()->SetTitleOffset(.7);

//setting title
TPaveLabel *p3 = new TPaveLabel(.0,.90 , (.0+.50),(.90+.10) ,"Bessel I functions", "NDC");
p3->SetFillColor(0);
p3->SetTextFont(22);
p3->SetTextColor(kBlack);

//setting legend
leg3->AddEntry(iBessel[0]->DrawCopy(), " I_0", "l");
leg3->AddEntry(iBessel[1]->DrawCopy("same"), " I_1(x)", "l");
leg3->AddEntry(iBessel[2]->DrawCopy("same"), " I_2(x)", "l");
leg3->AddEntry(iBessel[3]->DrawCopy("same"), " I_3(x)", "l");
leg3->AddEntry(iBessel[4]->DrawCopy("same"), " I_4(x)", "l");
leg3->Draw();
p3->Draw();
//------------------------------------------------
DistCanvas->cd(4);
gPad->SetGrid();
gPad->SetFrameFillColor(19);
TLegend *leg4 = new TLegend(0.75, 0.7, 0.89, 0.89);
//------------------------------------------------
//Drawing sph_bessel
TF1* jBessel[5];
for(int nu = 0; nu <= 4; nu++){
   jBessel[nu]= new TF1("J_0", "ROOT::Math::sph_bessel([0],x)", 0, 10);
   jBessel[nu]->SetParameters(nu, 0.0);
   jBessel[nu]->SetTitle("Bessel j functions");
   jBessel[nu]->SetLineStyle(1);
   jBessel[nu]->SetLineWidth(3);
   jBessel[nu]->SetLineColor(nu+1);
}
jBessel[0]->GetXaxis()->SetTitle("x");
jBessel[0]->GetXaxis()->SetTitleSize(0.06);
jBessel[0]->GetXaxis()->SetTitleOffset(.7);

//setting title
TPaveLabel *p4 = new TPaveLabel(.0,.90 , (.0+.50),(.90+.10) ,"Bessel j functions", "NDC");
p4->SetFillColor(0);
p4->SetTextFont(22);
p4->SetTextColor(kBlack);

//setting legend

leg4->AddEntry(jBessel[0]->DrawCopy(), " j_0(x)", "l");
leg4->AddEntry(jBessel[1]->DrawCopy("same"), " j_1(x)", "l");
leg4->AddEntry(jBessel[2]->DrawCopy("same"), " j_2(x)", "l");
leg4->AddEntry(jBessel[3]->DrawCopy("same"), " j_3(x)", "l");
leg4->AddEntry(jBessel[4]->DrawCopy("same"), " j_4(x)", "l");

leg4->Draw();
p4->Draw();

DistCanvas->cd();

Draw all canvases

In [3]:
gROOT->GetListOfCanvases()->Draw()