Implementing the stochastic gradient descent algorithm of the softmax regression with only NumPy

I am implementing the stochastic gradient descent algorithm. I think there is plenty of room for improvement.

def array2onehot(X_shape, array, start=1):
    """
    transfer a column to a matrix with each row being a onehot
    note that the array index defaults to start with 1 rather than 0
    """
    array += 1 - start if start != 1 else 0
    onehot = np.zeros(X_shape)
    onehot[np.arange(X_shape[0]), array-1] = 1
    return onehot

def stochastic_gradient_descent(self, batch, Y):
    """
    the batch contains both the X's and targets
    Y is the output produced by the forward process using the X's in the batch
    """
    ones = np.ones(batch.shape[0])
    # add the bias to the X's
    X = np.column_stack(ones, batch[:, :-1])
    T = array2onehot(X.shape, batch[:, -1])
    m = self._batch_size
    # batch size is the size of the mini batch

    count = np.zeros(self._class_size)
    # class size is the amount of classes to predict
    delta = np.zeros(self._coefficients.shape)
    for i in range(m):
        k = batch[i, -1] - 1
        count[k] += 1
        delta[:, k] += X[i] * sum(np.multiply(T[i], Y[i]))
    tmp = self._coefficients
    for i in count:
        if i == 0:
            tmp[:, i] = 0
    delta = np.nan_to_num(delta / count) - 2 * self._penalty_rate * tmp
    self._coefficients -= delta