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math tutorials translated into Python. #15960

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237 changes: 237 additions & 0 deletions tutorials/pymath/Bessel.py
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## \file
## \ingroup tutorial_math
## \notebook
##
##
## Show different kinds of the Bessel functions available in ROOT
## To execute this macro type:
##
## ~~~{.py}
## IP[1] %run Bessel.py
## ~~~
##
## It will create one canvas with a representation
## of the cylindrical and spherical Bessel functions;
## the so called regular and modified Bessel functions.
## Check-out:
## https://en.wikipedia.org/wiki/Bessel_function
## https://mathworld.wolfram.com/BesselFunction.html

## \macro_image
## \macro_code
##
## \author Magdalena Slawinska
## \translator P. P.


import ROOT

TCanvas = ROOT.TCanvas
TF1 = ROOT.TF1
TMath = ROOT.TMath
TLegend = ROOT.TLegend
TLegendEntry = ROOT.TLegendEntry
##Riostream = ROOT.Riostream #Not implemented in cppyy.
TAxis = ROOT.TAxis
TPaveLabel = ROOT.TPaveLabel
TSystem = ROOT.TSystem
##cmath = ROOT.cmath #Not implemented in cppyy.

#math
Math = ROOT.Math
##IFunction = Math.IFunction #Not implemented in Math.

#constants
kBlack = ROOT.kBlack

#globals
gPad = ROOT.gPad



# void
def Bessel() :
# R__LOAD_LIBRARY(libMathCore.so);
ROOT.gSystem.Load("libMathCore.so")

global DistCanvas
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)
global leg
leg = TLegend(0.75, 0.7, 0.89, 0.89)

n = 5; # number of functions in each pad
# drawing the set of Bessel J functions
#BP: TF1 JBessel[5]
#Not to use:
# JBessel = [ TF1() ] * 5
# because it creates a list with the same object
#Instead:
global JBessel
JBessel = [ TF1() for i in range(5)]
#for (int nu = 0; nu < n; nu++) {
for nu in range(0, n, 1) :
JBessel[nu] = 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].GetXaxis().SetTitle("x")
JBessel[0].GetXaxis().SetTitleSize(0.06)
JBessel[0].GetXaxis().SetTitleOffset(.7)

# setting the title in a label style
global p1
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()

#------------------------------------------------
DistCanvas.cd(2)
gPad.SetGrid()
gPad.SetFrameFillColor(19)

global leg2
leg2 = TLegend(0.75, 0.7, 0.89, 0.89)
#------------------------------------------------
# Drawing Bessel k
global KBessel
KBessel = [ TF1() for i in range(5)]
#for (int nu = 0; nu < n; nu++) {
for nu in range(0, n, 1):
KBessel[nu] = 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].SetTitle("") # doesn't interfere with TPaveLabel title. See below p2.
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
global p2
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()
#------------------------------------------------
DistCanvas.cd(3)
gPad.SetGrid()
gPad.SetFrameFillColor(19)
global leg3
leg3 = TLegend(0.75, 0.7, 0.89, 0.89)
#------------------------------------------------
# Drawing Bessel i
global iBessel
iBessel = [ TF1() for i in range(5)]
#for (int nu = 0; nu <= 4; nu++) {
for nu in range(0, 4+1, 1):
iBessel[nu] = 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].SetTitle("") # Doesn't interfere with TPaveLabel. See below p3.
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
global p3
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()
#------------------------------------------------
DistCanvas.cd(4)
gPad.SetGrid()
gPad.SetFrameFillColor(19)
global leg4
leg4 = TLegend(0.75, 0.7, 0.89, 0.89)
#------------------------------------------------
# Drawing sph_bessel
global jBessel
jBessel = [ TF1() for i in range(5)]
#for (int nu = 0; nu <= 4; nu++) {
for nu in range(0, 4+1, 1):
jBessel[nu] = 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].SetTitle("") # Doesn't interfere with TPaveLabel title. See below p4.
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
global p4
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()



if __name__ == "__main__":
Bessel()
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