Função de Bessel em Python - Dados completos

Author: Venn

Bessel.py

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+#Feito por Hevenicio Silva
+
+# Importação de biblitecas
+from IPython.display import display, Markdown, Latex
+import matplotlib.pyplot as plt
+import pandas as pd
+import sympy as sym
+import numpy as np
+
+# Entrada de dados
+dados = pd.read_csv("dados.csv")
+df = pd.DataFrame(dados)
+
+# Função Fatorial
+def fatorial(n):
+    if(n == 0):
+        return 1
+    else:
+        return n*fatorial(n - 1)
+
+
+# Formatação dos dados impressos - Latex
+def printmd(string):
+    display(Markdown(string))
+    #display(Latex(string))
+
+f = sym.symbols('$_{0}$')
+g = sym.symbols('$_{1}$')
+h = sym.symbols('$_{2}$')
+
+
+# Definindo as Funções de Bessel
+def J0(x):
+    k = 0
+    soma = 0
+    termo = 1
+    while(1.0e-4 <= termo):
+        termo = pow(x/2, (2*k))/(fatorial(k)*fatorial(k))
+        soma += pow(-1, k)*termo
+        k += 1
+    return soma
+
+def J1(x):
+    k = 0
+    soma = 0
+    termo = 1
+    while(1.0e-4 <= termo):
+        termo = pow(x/2, (2*k + 1))/(fatorial(k)*fatorial(k + 1))
+        soma += pow(-1, k)*termo
+        k += 1
+    return soma
+
+def J2(x):
+    k = 0
+    soma = 0
+    termo = 1
+    while(1.0e-4 <= termo):
+        termo = pow(x/2, (2*k + 2))/(fatorial(k)*fatorial(k + 2))
+        soma += pow(-1, k)*termo
+        k += 1
+    return soma
+
+# Amplitude da função de Bessel
+y = np.sqrt(2/(np.pi*df['entrada']))
+
+z = -np.sqrt(2/(np.pi*df['entrada']))
+
+# Resultados obtidos
+l =[]
+m = []
+n = []
+o = []
+p = [l, m, n, o]
+for i in df['entrada']:
+    l.append(i)
+    m.append(J0(i))
+    n.append(J1(i))
+    o.append(J2(i))
+    #printmd('**$J${}({}):  {: 0.5f} $|$ $J${}({}):  {: 0.5f} $|$ $J${}({}):  {: 0.5f}**'.format(f, i, J0(i), g, i, J1(i), h, i, J2(i)))
+    a = pd.DataFrame(p)
+a = a.rename(index={0:"x", 1:"J0(x)", 2: "J1(x)", 3:"J2(x)"}).T
+print(a)
+
+# Plotando os resultados obtidos
+plt.title('Funções de Bessel - J$_{0}(x)$, J$_{1}(x)$ e J$_{2}(x)$')
+plt.plot(df['entrada'], m, 'g', label = 'J$_{0}(x)$')
+plt.plot(df['entrada'], n, 'limegreen', label = 'J$_{1}(x)$')
+plt.plot(df['entrada'], o, 'lawngreen', label = 'J$_{2}(x)$')
+plt.plot(df['entrada'], y, 'c--', label = '$\sqrt{2 / \pi x}$')
+plt.plot(df['entrada'], z, 'b--', label = '$ - \sqrt{2 / \pi x}$')
+plt.legend(framealpha=1, frameon=True)
+plt.grid(color = 'black')
+plt.style.use('seaborn')
+plt.xlabel('$x$')
+plt.ylabel('$y$')
+plt.show()

dados.csv

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+entrada
+0.0
+0.5
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+1.5
+2.0
+2.5
+3.0
+3.5
+4.0
+4.5
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+5.5
+6.0
+6.5
+7.0
+7.5
+8.0
+8.5
+9.0
+9.5
+10.0
+10.5
+11.0
+11.5
+12.0
+12.5
+13.0
+13.5
+14.0
+14.5
+15.0
+15.5
+16.0
+16.5
+17.0
+17.5
+18.0
+18.5
+19.0
+19.5
+20.0
+20.5
+21.0
+21.5
+22.0
+22.5
+23.0
+23.5
+24.0
+24.5
+25.0
+25.5
+26.0
+26.5
+27.0
+27.5
+28.0
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+29.0
+29.5
+30.0