Provides explanations for why the item is liked by the user.

        Parameters
        ---------
        userid : int
            The userid to explain recommendations for
        user_items : csr_matrix
            Sparse matrix containing the liked items for the user
        itemid : int
            The itemid to explain recommendations for
        user_weights : ndarray, optional
            Precomputed Cholesky decomposition of the weighted user liked items.
            Useful for speeding up repeated calls to this function, this value
            is returned
        N : int, optional
            The number of liked items to show the contribution for

        Returns
        -------
        total_score : float
            The total predicted score for this user/item pair
        top_contributions : list
            A list of the top N (itemid, score) contributions for this user/item pair
        user_weights : ndarray
            A factorized representation of the user. Passing this in to
            future 'explain' calls will lead to noticeable speedups

def explain(self, userid, user_items, itemid, user_weights=None, N=10):
        """ Provides explanations for why the item is liked by the user.

        Parameters
        ---------
        userid : int
            The userid to explain recommendations for
        user_items : csr_matrix
            Sparse matrix containing the liked items for the user
        itemid : int
            The itemid to explain recommendations for
        user_weights : ndarray, optional
            Precomputed Cholesky decomposition of the weighted user liked items.
            Useful for speeding up repeated calls to this function, this value
            is returned
        N : int, optional
            The number of liked items to show the contribution for

        Returns
        -------
        total_score : float
            The total predicted score for this user/item pair
        top_contributions : list
            A list of the top N (itemid, score) contributions for this user/item pair
        user_weights : ndarray
            A factorized representation of the user. Passing this in to
            future 'explain' calls will lead to noticeable speedups
        """
        # user_weights = Cholesky decomposition of Wu^-1
        # from section 5 of the paper CF for Implicit Feedback Datasets
        user_items = user_items.tocsr()
        if user_weights is None:
            A, _ = user_linear_equation(self.item_factors, self.YtY,
                                        user_items, userid,
                                        self.regularization, self.factors)
            user_weights = scipy.linalg.cho_factor(A)
        seed_item = self.item_factors[itemid]

        # weighted_item = y_i^t W_u
        weighted_item = scipy.linalg.cho_solve(user_weights, seed_item)

        total_score = 0.0
        h = []
        for i, (itemid, confidence) in enumerate(nonzeros(user_items, userid)):
            if confidence < 0:
                continue

            factor = self.item_factors[itemid]
            # s_u^ij = (y_i^t W^u) y_j
            score = weighted_item.dot(factor) * confidence
            total_score += score
            contribution = (score, itemid)
            if i < N:
                heapq.heappush(h, contribution)
            else:
                heapq.heappushpop(h, contribution)

        items = (heapq.heappop(h) for i in range(len(h)))
        top_contributions = list((i, s) for s, i in items)[::-1]
        return total_score, top_contributions, user_weights