import numpy as np import matplotlib.pyplot as plt

1. Initialize variables

ws = [] gamma = 0.01 R = 1

1. Generate random points within the circle of radius R

points = [] while len(points) < 100:

   x, y = np.random.uniform(-R, R, 2)
   if x**2 + y**2 <= R**2:
       points.append((x, y))

1. Remove points with x < gamma

points = [point for point in points if point[0] >= gamma]

1. Initialize w

ws = [] w = np.array([-0.1, 0.0]) ws.append(w.copy())

1. Perceptron learning algorithm

convergence_flag = False while not convergence_flag:

   np.random.shuffle(points)
   convergence_flag = True
   for v in points:
       if np.dot(w, v) <= 0:
           w += v
           ws.append(w.copy())
           convergence_flag = False

1. Plot the items

fig, ax = plt.subplots(figsize=(10,10))

1. Vertical dotted line at x=gamma

ax.axvline(x=gamma, linestyle='--', color='r', label='x=gamma')

1. Circle with radius R centered at (0, 0)

circle = plt.Circle((0, 0), R, fill=False, color='b', linestyle='-', label='Circle') ax.add_artist(circle)

1. Jagged line connecting entries in ws

points = np.array(points) ax.scatter(points[:,0], points[:,1]) ws = np.array(ws) for i in range(1, ws.shape[0]):

   ax.arrow(ws[i-1, 0], ws[i-1, 1], ws[i, 0] - ws[i-1, 0], ws[i, 1] - ws[i-1, 1], color='g', linewidth=0.5,
            head_width=0.03, head_length=0.04, length_includes_head=True)

1. Set axis limits
2. ax.set_xlim(-R, R)
3. ax.set_ylim(-R, R)

ax.set_xlabel('X') ax.set_ylabel('Y') ax.legend()

plt.gca().set_aspect('equal') plt.savefig("perceptron convergence.svg")