import numpy as np

m = 100
X = np.random.rand(100, 2)
y = (X * 10).sum() + np.random.rand(m)
iter = 100

# calculating the cost function
theta = np.array([[0], [0]])
def h(X, theta):
    return np.matmul(X, theta)

def cost(X, y, theta, m):
    return 1/(2* m) * np.sum((h(X, theta)-y)**2)

print(cost(X, y, theta, m))
# 1-variable gradient decent
cost_vals = []
def grad_decent(X, y, theta, m, alpha):
    theta1 = theta[0, 0]
    theta2 = theta[1, 0]
    for i in range(0, iter):
        cost_vals.append(cost(X, y, np.array([[theta1], [theta2]]), m))
        theta1 = theta1 - alpha/m * np.sum((h(X, theta)-y) * X[:, 0])
        theta2 = theta2 - alpha/m * np.sum((h(X, theta)-y) * X[:, 1])
        # print(f"Iteration {i}: ", theta1, ", ", theta2)

    return np.array([[theta1], [theta2]]), cost_vals

grad_decent(X, y, theta, m, 0.0001)