Exponential dataset with hub.sagews

#
# Generate the exponential dataset with minor hub near the saturation.
#
# Author: Chong Zan Kai
# Last update: 7-Feb-2018
#
import matplotlib.pyplot as plt
import numpy as np
from sage.misc.prandom import gauss
import pandas as pd

#
# Create the variables and the equation, i.e. f(t) = 1 - e^(-t) + u(t-delay) + -u(t-delay - pi/2) * sin( (t-delay)*2 ) * 0.3
# for t >= 0.
#
f, t = var('f t')
delay = 3
f(t) = (1  - e^(-t) ) * unit_step(t) + (unit_step(t - delay) + -unit_step(t - delay - pi/2) ) *  - sin((t - delay) *2 )  * 0.3

#
# Building the data points
#
x_arr = np.linspace(0, 10, 200)

y_arr = np.array([ f(x).n() for x in x_arr] )

y_gauss_arr = np.array( [y + gauss(0, 0.2) for y in y_arr] )

#
# Build the dataframe
#
df = pd.DataFrame({'x':x_arr, 'y':y_arr, 'y_gauss': y_gauss_arr})
df.head()


# Write to files
df.to_csv('data.csv', index = False)
# f_x = open('x.txt', 'w')
# f_x.write('%s' % x_arr.tolist())
# f_x.close()

# f_y = open('y.txt', 'w')
# f_y.write('%s' % y_arr.tolist())
# f_y.close()

# f_y_gauss = open('y_gauss.txt', 'w')
# f_y_gauss.write('%s' % y_gauss_arr.tolist())
# f_y_gauss.close()


#
# Plot to graph
#
plt.plot(x_arr, y_arr, 'r-', label = 'Equation'  )
plt.plot(x_arr, y_gauss_arr, 'bo', label = 'With Gaussian noise' )

plt.ylim(-0.2, 1.3)
plt.xlim(0, 8 )

plt.title('Exponential dataset with minor hub')
plt.xlabel('t')
plt.ylabel('f')
plt.legend(loc = 'lower right')
plt.savefig('Graph.png')

plt.show()

x y y_gauss 0 0.000000 0.000000000000000 -0.242034190448092 1 0.050251 0.0490095478443424 -0.305477333152103 2 0.100503 0.0956171599087779 0.223260498701876 3 0.150754 0.139940553979831 -0.266497339883467 4 0.201005 0.182091678548535 0.152274874333325 [<matplotlib.lines.Line2D object at 0x7ff459a24290>] [<matplotlib.lines.Line2D object at 0x7ff459a24710>] (-0.200000000000000, 1.30000000000000) (0, 8) <matplotlib.text.Text object at 0x7ff459ac0790> <matplotlib.text.Text object at 0x7ff459c860d0> <matplotlib.text.Text object at 0x7ff459c20b90> <matplotlib.legend.Legend object at 0x7ff459a24b50>