def gradientDescent(X, y, theta, alpha, num_iter):
m, n = len(X), len(X[0])
J_history = np.zeros(num_iter)
J_history[0] = cost(X, y, theta)
for i in range(0, num_iter):
theta = theta - np.sum((X @ theta - y) * X, axis=0).reshape(
(n, 1)) * alpha / m # suan sum de fang shi shi bu dui de
J_history[i] = cost(X, y, theta)
return theta, J_history
def gradientDescent(x, y, theta, alpha, num_iters):
m = np.size(y)
J_history = np.zeros((num_iters, 1))
for iters in range(num_iters):
theta = theta - alpha / m * np.dot(x.T, (np.dot(x, theta) - y))
J_history[iters] = cost(x, y, theta)
return theta, J_history
def visual_J(X, y):
theta0 = np.linspace(-10, 10, 100)
theta1 = np.linspace(-1, 4, 100)
J = np.zeros((len(theta0), len(theta1)))
for i in range(len(theta0)):
for j in range(len(theta1)):
J[i, j] = cost(X, y, [[theta0[i]], [theta1[j]]])
fig = plt.figure()
ax = fig.gca(projection='3d')
ax.plot_surface(theta1, theta0, J)
ax.set_xlabel(r'$\theta0$')
ax.set_ylabel(r'$\theta1$')
plt.figure(0)
plot_data(X, y)
#=================== Part 3: Cost and Gradient descent ===================
m = np.size(y)
X = np.column_stack((np.ones(m), X)) # % Add a column of ones to x
theta = np.zeros((2, 1)) # % initialize fitting parameters
y = y.reshape(m, 1)
#% Some gradient descent settings
iterations = 1500
alpha = 0.01
print('Testing the cost function ...')
#% compute and display initial cost
J = cost(X, y, theta)
print('With theta = [0 ; 0], Cost computed = {:.2f}'.format(
J)) #(approx) 32.07\n
#% further testing of the cost function
J = cost(X, y, [[-1], [2]])
print('\nWith theta = [-1 ; 2], Cost computed = {:.2f}'.format(J))
#(approx) 54.24\n');
print('Running Gradient Descent ...')
#% run gradient descent
theta = gradientDescent(X, y, theta, alpha, iterations)[0]
#% print theta to screen
print('Theta found by gradient descent:', theta)
#(approx):-3.6303 1.1664
# Plot the linear fit
plt.plot(X[:, 1], np.dot(X, theta), '-')