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Reference Guide
Bessel.py File Reference

Namespaces

namespace  Bessel
 

Detailed Description

View in nbviewer Open in SWAN Show the different kinds of Bessel functions available in ROOT To execute the macro type in:

root[0] .x Bessel.C
Definition: Bessel.py:1

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

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(1)
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(1)
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(1)
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(1)
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()
The Canvas class.
Definition: TCanvas.h:23
1-Dim function class
Definition: TF1.h:213
This class displays a legend box (TPaveText) containing several legend entries.
Definition: TLegend.h:23
A Pave (see TPave) with a text centered in the Pave.
Definition: TPaveLabel.h:20
Author
Juan Fernando Jaramillo Botero

Definition in file Bessel.py.