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Bessel.py
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1 ## \file
2 ## \ingroup tutorial_math
3 ## \notebook
4 ## Show the different kinds of Bessel functions available in ROOT
5 ## To execute the macro type in:
6 ##
7 ## ~~~{.cpp}
8 ## root[0] .x Bessel.C
9 ## ~~~
10 ##
11 ## It will create one canvas with the representation
12 ## of the cylindrical and spherical Bessel functions
13 ## regular and modified
14 ##
15 ## Based on Bessel.C by Magdalena Slawinska
16 ##
17 ## \macro_image
18 ## \macro_code
19 ##
20 ## \author Juan Fernando Jaramillo Botero
21 
22 from ROOT import TCanvas, TF1, gSystem, gPad, TLegend, TPaveLabel, kBlack
23 
24 
25 gSystem.Load("libMathMore")
26 
27 DistCanvas = TCanvas("DistCanvas", "Bessel functions example", 10, 10, 800, 600)
28 DistCanvas.SetFillColor(17)
29 DistCanvas.Divide(2, 2)
30 DistCanvas.cd(1)
31 gPad.SetGrid()
32 gPad.SetFrameFillColor(19)
33 leg = TLegend(0.75, 0.7, 0.89, 0.89)
34 
35 # Drawing the set of Bessel J functions
36 #
37 # n is the number of functions in each pad
38 n = 5
39 JBessel = []
40 for nu in range(n):
41  jbessel = TF1("J_0", "ROOT::Math::cyl_bessel_j([0],x)", 0, 10)
42  jbessel.SetParameters(nu, 0.0)
43  jbessel.SetTitle("")
44  jbessel.SetLineStyle(1)
45  jbessel.SetLineWidth(3)
46  jbessel.SetLineColor(nu + 1)
47  JBessel.append(jbessel)
48 
49 # Setting x axis for JBessel
50 xaxis = JBessel[0].GetXaxis()
51 xaxis.SetTitle("x")
52 xaxis.SetTitleSize(0.06)
53 xaxis.SetTitleOffset(.7)
54 
55 # setting the title in a label style
56 p1 = TPaveLabel(.0, .90, .0 + .50, .90 + .10, "Bessel J functions", "NDC")
57 p1.SetFillColor(0)
58 p1.SetTextFont(22)
59 p1.SetTextColor(kBlack)
60 
61 # setting the legend
62 leg.AddEntry(JBessel[0].DrawCopy(), " J_0(x)", "l")
63 leg.AddEntry(JBessel[1].DrawCopy("same"), " J_1(x)", "l")
64 leg.AddEntry(JBessel[2].DrawCopy("same"), " J_2(x)", "l")
65 leg.AddEntry(JBessel[3].DrawCopy("same"), " J_3(x)", "l")
66 leg.AddEntry(JBessel[4].DrawCopy("same"), " J_4(x)", "l")
67 
68 leg.Draw()
69 p1.Draw()
70 
71 # Set canvas 2
72 DistCanvas.cd(2)
73 gPad.SetGrid()
74 gPad.SetFrameFillColor(19)
75 leg2 = TLegend(0.75, 0.7, 0.89, 0.89)
76 
77 # Drawing Bessel k
78 KBessel = []
79 for nu in range(n):
80  kbessel = TF1("J_0", "ROOT::Math::cyl_bessel_k([0],x)", 0, 10)
81  kbessel.SetParameters(nu, 0.0)
82  kbessel.SetTitle("Bessel K functions")
83  kbessel.SetLineStyle(1)
84  kbessel.SetLineWidth(3)
85  kbessel.SetLineColor(nu+1)
86  KBessel.append(kbessel)
87 kxaxis = KBessel[0].GetXaxis()
88 kxaxis.SetTitle("x")
89 kxaxis.SetTitleSize(0.06)
90 kxaxis.SetTitleOffset(.7)
91 
92 # setting title
93 p2 = TPaveLabel(.0, .90, .0 + .50, .90 + .10, "Bessel K functions", "NDC")
94 p2.SetFillColor(0)
95 p2.SetTextFont(22)
96 p2.SetTextColor(kBlack)
97 
98 # setting legend
99 leg2.AddEntry(KBessel[0].DrawCopy(), " K_0(x)", "l")
100 leg2.AddEntry(KBessel[1].DrawCopy("same"), " K_1(x)", "l")
101 leg2.AddEntry(KBessel[2].DrawCopy("same"), " K_2(x)", "l")
102 leg2.AddEntry(KBessel[3].DrawCopy("same"), " K_3(x)", "l")
103 leg2.AddEntry(KBessel[4].DrawCopy("same"), " K_4(x)", "l")
104 leg2.Draw()
105 p2.Draw()
106 
107 # Set canvas 3
108 DistCanvas.cd(3)
109 gPad.SetGrid()
110 gPad.SetFrameFillColor(19)
111 leg3 = TLegend(0.75, 0.7, 0.89, 0.89)
112 
113 # Drawing Bessel i
114 iBessel = []
115 for nu in range(5):
116  ibessel = TF1("J_0", "ROOT::Math::cyl_bessel_i([0],x)", 0, 10)
117  ibessel.SetParameters(nu, 0.0)
118  ibessel.SetTitle("Bessel I functions")
119  ibessel.SetLineStyle(1)
120  ibessel.SetLineWidth(3)
121  ibessel.SetLineColor(nu + 1)
122  iBessel.append(ibessel)
123 
124 iaxis = iBessel[0].GetXaxis()
125 iaxis.SetTitle("x")
126 iaxis.SetTitleSize(0.06)
127 iaxis.SetTitleOffset(.7)
128 
129 # setting title
130 p3 = TPaveLabel(.0, .90, .0 + .50, .90 + .10, "Bessel I functions", "NDC")
131 p3.SetFillColor(0)
132 p3.SetTextFont(22)
133 p3.SetTextColor(kBlack)
134 
135 # setting legend
136 leg3.AddEntry(iBessel[0].DrawCopy(), " I_0", "l")
137 leg3.AddEntry(iBessel[1].DrawCopy("same"), " I_1(x)", "l")
138 leg3.AddEntry(iBessel[2].DrawCopy("same"), " I_2(x)", "l")
139 leg3.AddEntry(iBessel[3].DrawCopy("same"), " I_3(x)", "l")
140 leg3.AddEntry(iBessel[4].DrawCopy("same"), " I_4(x)", "l")
141 leg3.Draw()
142 p3.Draw()
143 
144 # Set canvas 4
145 DistCanvas.cd(4)
146 gPad.SetGrid()
147 gPad.SetFrameFillColor(19)
148 leg4 = TLegend(0.75, 0.7, 0.89, 0.89)
149 
150 # Drawing sph_bessel
151 jBessel = []
152 for nu in range(5):
153  jbessel = TF1("J_0", "ROOT::Math::sph_bessel([0],x)", 0, 10)
154  jbessel.SetParameters(nu, 0.0)
155  jbessel.SetTitle("Bessel j functions")
156  jbessel.SetLineStyle(1)
157  jbessel.SetLineWidth(3)
158  jbessel.SetLineColor(nu+1)
159  jBessel.append(jbessel)
160 jaxis = jBessel[0].GetXaxis()
161 jaxis.SetTitle("x")
162 jaxis.SetTitleSize(0.06)
163 jaxis.SetTitleOffset(.7)
164 
165 # setting title
166 p4 = TPaveLabel(.0, .90, .0 + .50, .90 + .10, "Bessel j functions", "NDC")
167 p4.SetFillColor(0)
168 p4.SetTextFont(22)
169 p4.SetTextColor(kBlack)
170 
171 # setting legend
172 leg4.AddEntry(jBessel[0].DrawCopy(), " j_0(x)", "l")
173 leg4.AddEntry(jBessel[1].DrawCopy("same"), " j_1(x)", "l")
174 leg4.AddEntry(jBessel[2].DrawCopy("same"), " j_2(x)", "l")
175 leg4.AddEntry(jBessel[3].DrawCopy("same"), " j_3(x)", "l")
176 leg4.AddEntry(jBessel[4].DrawCopy("same"), " j_4(x)", "l")
177 
178 leg4.Draw()
179 p4.Draw()
180 
181 DistCanvas.cd()