def initialize_weights(X):
    return np.random.rand(X.shape[1] + 1, 1)


def insert_coeficient_to_weights_matrix(X):
    return np.insert(X, 0, 1, axis=1)


def predict(new_X, B):
    return np.dot(new_X, B)


def calculate_gradient(predictions, new_X, Y):
    return (1/new_X.shape[0]) * multiply_residual_by_features_matrix(predictions, new_X, Y)


def calculate_residual(predictions, real_values):
    return np.subtract(predictions, real_values)


def multiply_residual_by_features_matrix(predictions, new_X, Y):
    return np.dot(np.transpose(new_X), calculate_residual(predictions, Y))


def update_weights(gradient_vector, weights):
    alfa = 0.0001
    new_weights = np.subtract(weights, (alfa * gradient_vector))
    return new_weights