#!/usr/bin/python3

import matplotlib.pyplot as plt
import numpy as np


def sigmoid(z):
    return 1.0 / (1.0 + np.exp(-z))

z = np.arange(-7, 7, 0.01)
phi_z = sigmoid(z)

plt.plot(z, phi_z)
plt.axvline(0.0, color = 'k')
plt.axhspan(0.0, 1.0, facecolor = '1.0', alpha = 1.0, ls = 'dotted')
plt.axhline(0.5, ls = 'dotted', color = 'k')
plt.yticks([0.0, 0.5, 1.0])
plt.ylim(-0.1, 1.1)
plt.xlabel('z')
plt.ylabel('$\phi (z)$')
plt.show()