pdf009_Bessel.py File Reference

Detailed Description

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

Based on Bessel.C by Magdalena Slawinska

 
import ROOT
from ROOT import TCanvas, TF1, gSystem, gPad, TLegend, TPaveLabel, kBlack
 
 
gSystem.Load("libMathMore")
 
DistCanvas = TCanvas("DistCanvas", "Bessel functions example", 10, 10, 800, 600)
DistCanvas.SetFillColor(17)
DistCanvas.Divide(2, 2)
DistCanvas.cd(1)
gPad.SetGrid()
gPad.SetFrameFillColor(19)
leg = TLegend(0.75, 0.7, 0.89, 0.89)
 
# Drawing the set of Bessel J functions
#
# n is the number of functions in each pad
n = 5
JBessel = []
for nu in range(n):
    jbessel = TF1("J_0", "ROOT::Math::cyl_bessel_j([0],x)", 0, 10)
    jbessel.SetParameters(nu, 0.0)
    jbessel.SetTitle("")
    jbessel.SetLineStyle(ROOT.kSolid)
    jbessel.SetLineWidth(3)
    jbessel.SetLineColor(nu + 1)
    JBessel.append(jbessel)
 
# Setting x axis for JBessel
xaxis = JBessel[0].GetXaxis()
xaxis.SetTitle("x")
xaxis.SetTitleSize(0.06)
xaxis.SetTitleOffset(.7)
 
# setting the title in a label style
p1 = 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()
 
# Set canvas 2
DistCanvas.cd(2)
gPad.SetGrid()
gPad.SetFrameFillColor(19)
leg2 = TLegend(0.75, 0.7, 0.89, 0.89)
 
# Drawing Bessel k
KBessel = []
for nu in range(n):
    kbessel = TF1("J_0", "ROOT::Math::cyl_bessel_k([0],x)", 0, 10)
    kbessel.SetParameters(nu, 0.0)
    kbessel.SetTitle("Bessel K functions")
    kbessel.SetLineStyle(ROOT.kSolid)
    kbessel.SetLineWidth(3)
    kbessel.SetLineColor(nu+1)
    KBessel.append(kbessel)
kxaxis = KBessel[0].GetXaxis()
kxaxis.SetTitle("x")
kxaxis.SetTitleSize(0.06)
kxaxis.SetTitleOffset(.7)
 
# setting title
p2 = 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()
 
# Set canvas 3
DistCanvas.cd(3)
gPad.SetGrid()
gPad.SetFrameFillColor(19)
leg3 = TLegend(0.75, 0.7, 0.89, 0.89)
 
# Drawing Bessel i
iBessel = []
for nu in range(5):
    ibessel = TF1("J_0", "ROOT::Math::cyl_bessel_i([0],x)", 0, 10)
    ibessel.SetParameters(nu, 0.0)
    ibessel.SetTitle("Bessel I functions")
    ibessel.SetLineStyle(ROOT.kSolid)
    ibessel.SetLineWidth(3)
    ibessel.SetLineColor(nu + 1)
    iBessel.append(ibessel)
 
iaxis = iBessel[0].GetXaxis()
iaxis.SetTitle("x")
iaxis.SetTitleSize(0.06)
iaxis.SetTitleOffset(.7)
 
# setting title
p3 = 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()
 
# Set canvas 4
DistCanvas.cd(4)
gPad.SetGrid()
gPad.SetFrameFillColor(19)
leg4 = TLegend(0.75, 0.7, 0.89, 0.89)
 
# Drawing sph_bessel
jBessel = []
for nu in range(5):
    jbessel = TF1("J_0", "ROOT::Math::sph_bessel([0],x)", 0, 10)
    jbessel.SetParameters(nu, 0.0)
    jbessel.SetTitle("Bessel j functions")
    jbessel.SetLineStyle(ROOT.kSolid)
    jbessel.SetLineWidth(3)
    jbessel.SetLineColor(nu+1)
    jBessel.append(jbessel)
jaxis = jBessel[0].GetXaxis()
jaxis.SetTitle("x")
jaxis.SetTitleSize(0.06)
jaxis.SetTitleOffset(.7)
 
# setting title
p4 = 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()

Author

Juan Fernando Jaramillo Botero

Definition in file pdf009_Bessel.py.