problem2.2.py

import numpy as np
import matplotlib.pyplot as plt

y = np.array([2.85, 1.5, .49, 1.57, 1.9, 0.6, 0.38, 2.33, 1.65, 0.3])
x = np.arange(0, 20, 2)
b = np.ones(3) # 3 parameters, b0-b2
eta = .02 # learning rate

g = lambda x: np.array([1, np.sin(x), np.cos(x)])

print(x)
print(y)

X = np.array([g(a) for a in x])
costs = []

num_params = len(b)
for i in range(100):
    # Prediction
    h = np.dot(X, b)
    diff = h - y

    # Update
    rss = np.sum(diff ** 2)
    costs.append(rss)
    gradient = np.dot(X.T, diff)
    b -= eta * gradient

plt.plot(x, y, label='actual')
plt.plot(x, X.dot(b), label='predicted')
plt.legend()
plt.show()

# Make sure error goes down every iteration
plt.plot(costs, label='costs')
plt.legend()
plt.show()

print(' '.join([f'b{i} = {a}' for i, a in enumerate(b)]))