# Initializes parameters "a" and "b" randomly
np.random.seed(42)
a = np.random.randn(1)
b = np.random.randn(1)

print(a, b)

# Sets learning rate
lr = 1e-1
# Defines number of epochs
n_epochs = 1000

for epoch in range(n_epochs):
    # Computes our model's predicted output
    yhat = a + b * x_train
    
    # How wrong is our model? That's the error! 
    error = (y_train - yhat)
    # It is a regression, so it computes mean squared error (MSE)
    loss = (error ** 2).mean()
    
    # Computes gradients for both "a" and "b" parameters
    a_grad = -2 * error.mean()
    b_grad = -2 * (x_train * error).mean()
    
    # Updates parameters using gradients and the learning rate
    a = a - lr * a_grad
    b = b - lr * b_grad
    
print(a, b)

# Sanity Check: do we get the same results as our gradient descent?
from sklearn.linear_model import LinearRegression
linr = LinearRegression()
linr.fit(x_train, y_train)
print(linr.intercept_, linr.coef_[0])