Bessel.C: Show the different kinds of Bessel functions available in ROOT

// 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

#include "TMath.h"
#include "TF1.h"
#include "TCanvas.h"

#include <Riostream.h>
#include "TLegend.h"
#include "TLegendEntry.h"

#include "Math/IFunction.h"
#include <cmath>
#include "TSystem.h"
#include "TAxis.h"
#include "TPaveLabel.h"

void Bessel()
{
  gSystem->Load("libMathMore");

  TCanvas *DistCanvas = new TCanvas("DistCanvas", 
     "Bessel functions example", 10, 10, 1000, 800);  
  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   
  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");
//   for(int nu = 1; nu <= 4; nu++)
//   leg->AddEntry(JBessel[0]->DrawCopy("lsame"), "", "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");
//   for(int nu = 1; nu <= 4; nu++)
//   leg->AddEntry(JBessel[0]->DrawCopy("lsame"), "", "l");
  
    //iBessel[0]->Draw();
    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();
}