import numpy as np
import matplotlib.pyplot as plt
from sklearn.model_selection import train_test_split
np.random.seed(123)

# We will use a simple training set
X = 2 * np.random.rand(500, 1)
y = 5 + 3 * X + np.random.randn(500, 1)
fig = plt.figure(figsize=(8,6))
plt.scatter(X, y)
plt.title("Dataset")
plt.xlabel("First feature")
plt.ylabel("Second feature")
plt.show()

# Split the data into a training and test set
X_train, X_test, y_train, y_test = train_test_split(X, y)
print(f'Shape X_train: {X_train.shape}')
print(f'Shape y_train: {y_train.shape}')
print(f'Shape X_test: {X_test.shape}')
print(f'Shape y_test: {y_test.shape}')

class LinearRegression:
    
    def __init__(self):
        pass
    
    def train_gradient_descent(self, X, y, learning_rate=0.01, n_iters=100):
        """
        Trains a linear regression model using gradient descent
        """
        # Step 0: Initialize the parameters
        n_samples, n_features = X.shape
        self.weights = np.zeros(shape=(n_features,1))
        self.bias = 0
        costs = []
        
        for i in range(n_iters):
            # Step 1: Compute a linear combination of the input features and weights
            y_predict = np.dot(X, self.weights) + self.bias
           
            # Step 2: Compute cost over training set
            cost = (1 / n_samples) * np.sum((y_predict - y)**2)
            costs.append(cost)
           
            if i % 100 == 0:
                print(f"Cost at iteration {i}: {cost}")
            
            # Step 3: Compute the gradients
            dJ_dw = (2 / n_samples) * np.dot(X.T, (y_predict - y))
            dJ_db = (2 / n_samples) * np.sum((y_predict - y)) 
            
            # Step 4: Update the parameters
            self.weights = self.weights - learning_rate * dJ_dw
            self.bias = self.bias - learning_rate * dJ_db
        
        return self.weights, self.bias, costs
   
    def train_normal_equation(self, X, y):
        """
        Trains a linear regression model using the normal equation
        """
        self.weights = np.dot(np.dot(np.linalg.inv(np.dot(X.T, X)), X.T), y)
        self.bias = 0
        
        return self.weights, self.bias
        
    def predict(self, X):
        return np.dot(X, self.weights) + self.bias

regressor = LinearRegression()
w_trained, b_trained, costs = regressor.train_gradient_descent(X_train, y_train, learning_rate=0.005, n_iters=600)
fig = plt.figure(figsize=(8,6))
plt.plot(np.arange(n_iters), costs)
plt.title("Development of cost during training")
plt.xlabel("Number of iterations")
plt.ylabel("Cost")
plt.show()

n_samples, _ = X_train.shape
n_samples_test, _ = X_test.shape

y_p_train = regressor.predict(X_train)
y_p_test = regressor.predict(X_test)

error_train =  (1 / n_samples) * np.sum((y_p_train - y_train) ** 2)
error_test =  (1 / n_samples_test) * np.sum((y_p_test - y_test) ** 2)

print(f"Error on training set: {np.round(error_train, 4)}")
print(f"Error on test set: {np.round(error_test)}")

# To compute the parameters using the normal equation, we add a bias value of 1 to each input example
X_b_train = np.c_[np.ones((n_samples)), X_train]
X_b_test = np.c_[np.ones((n_samples_test)), X_test]

reg_normal = LinearRegression()
w_trained = reg_normal.train_normal_equation(X_b_train, y_train)

y_p_train = reg_normal.predict(X_b_train)
y_p_test = reg_normal.predict(X_b_test)

error_train =  (1 / n_samples) * np.sum((y_p_train - y_train) ** 2)
error_test =  (1 / n_samples_test) * np.sum((y_p_test - y_test) ** 2)

print(f"Error on training set: {np.round(error_train, 4)}")
print(f"Error on test set: {np.round(error_test, 4)}")

# Plot the test predictions


fig = plt.figure(figsize=(8,6))
plt.scatter(X_train, y_train)
plt.scatter(X_test, y_p_test)
plt.xlabel("First feature")
plt.ylabel("Second feature")
plt.show()