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import matplotlib.pyplot as plt

from matplotlib import animation

import numpy as np

from scipy.fftpack import rfft, irfft, fftfreq

class Guass_seidel:

 def __init__(self,L,dx,T,e):

 self.L = L

 self.dx = dx

 self.r = 0.25

 self.c = 300

 self.T = T

 self.dt = self.dx/(4*self.c)

 self.e = e 

 pass

 def initialization(self):

 self.string = []

 for i in range(int(self.T/self.dt)):

 self.string.append([])

 for j in range(int(self.L/self.dx)):

 self.string[i].append(0)

 for l in range(1,int(int(self.L/self.dx) - 1)):

 self.string[0][l] = np.e**(-0.1*(l - 30)**2) 

 self.string[0][1] = 0

 self.string[0][-2] = 0

 self.string[0][0] = - self.string[0][2]

 self.string[0][-1] = - self.string[0][-3]

 self.string[1] = self.string[0][:]

 #plt.plot(self.string[1])

 def calculation(self):

 M = int(self.L/self.dx)

 for i in range(2,int(self.T/self.dt)):

 for j in range(2,M-2):

 self.string[i][j] = (2 - 2*self.r**2 - 6*self.e*self.r**2*M**2)*self.string[i - 1][j] - self.string[i - 2][j] + self.r**2*(1 + 4*self.e*M**2)*(self.string[i-1][j+1]+self.string[i-1][j-1]) - self.e*self.r**2*M**2*(self.string[i-1][j+2]+self.string[i-1][j-2])

 #self.string[i][j] = 2*(1-self.r**2)*self.string[i - 1][j] - self.string[i - 2][j] + self.r**2*(self.string[i - 1][j + 1] +self.string[i - 1][j - 1])

 self.string[i][0] = -self.string[i][2]

 self.string[i][-1] = -self.string[i][-3]

 #plt.plot(self.string[-1])

 return self.string

 def fft(self):

 t_plot = np.arange(0,self.T,self.dt)

 amplitude_record = []

 for i in range(int(self.T/self.dt)):

 amplitude_record.append(self.string[i][20])

 freq = fftfreq(len(amplitude_record), d=self.dt)

 freq = np.array(abs(freq))

 f_signal = rfft(amplitude_record)

 f_signal = np.array(f_signal**2)

 #plt.subplot(122)

 plt.title('Power spectra')

 plt.ylabel('Power (arbitrary units)')

 plt.xlabel('Frequency (Hz)')

 plt.xlim(2000,8000)

 plt.plot(freq,f_signal,label = 'epsilon = '+str(self.e))

 return 0

A = Guass_seidel(1,0.01,0.05,0)

A.initialization()

A.calculation()

A.fft() 

# ---- animation ---------------------------------

fig = plt.figure(figsize = (8,6))

ax = plt.axes(xlim=(0, 1),ylim = (-1,1))

line, = ax.plot([], [], 'k')

def init():

 line.set_data([], [])

 return line, 

def animate(i):

 x_plot = np.arange(0.01,0.99,0.01)

 y_plot = []

 for j in range(1, int(A.L/A.dx) - 1):

 y_plot.append(data_record[i][j])

 line.set_data(x_plot,y_plot)

 return line,

anim = animation.FuncAnimation(fig, animate, init_func=init, frames=100, interval=50, blit=True)

anim.save('chapter6_string_guass_e.gif', fps=20, writer='Feng_Chen')

plt.show()