где суммирование при реализации градиентного спуска для линейной регрессии

Question

def gradientDescent(X, y, theta, alpha, num_iters):
    """
    Performs gradient descent to learn `theta`. Updates theta by taking `num_iters`
    gradient steps with learning rate `alpha`.

    Parameters
    ----------
    X : array_like
        The input dataset of shape (m x n+1).

    y : arra_like
        Value at given features. A vector of shape (m, ).

    theta : array_like
        Initial values for the linear regression parameters. 
        A vector of shape (n+1, ).

    alpha : float
        The learning rate.

    num_iters : int
        The number of iterations for gradient descent. 

    Returns
    -------
    theta : array_like
        The learned linear regression parameters. A vector of shape (n+1, ).

    J_history : list
        A python list for the values of the cost function after each iteration.

    Instructions
    ------------
    Peform a single gradient step on the parameter vector theta.

    While debugging, it can be useful to print out the values of 
    the cost function (computeCost) and gradient here.
    """
    # Initialize some useful values
    m = y.shape[0]  # number of training examples

    # make a copy of theta, to avoid changing the original array, since numpy arrays
    # are passed by reference to functions
    theta = theta.copy()

    J_history = [] # Use a python list to save cost in every iteration




             # ================== YOUR CODE HERE =================================

        theta = theta - (alpha / m) * (np.dot(X, theta) - y).dot(X)

        # =====================================================================

        # save the cost J in every iteration
        J_history.append(computeCost(X, y, theta))

    return theta, J_history

Почему они не вычислили сумму ошибки в этой формуле?

Согласно уравнению: '

• theta = theta - (alpha / m) ***np.sum**( (np.dot(X, theta) - y).dot(X)), верно?