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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def precision_recall_by_user(observed_user_items, recommendations, cutoffs=[10]):
 """ Compute precision and recall at a given cutoff for each user. In information retrieval terms, precision represents the ratio of relevant, retrieved items to the number of relevant items. Recall represents the ratio of relevant, retrieved items to the number of relevant items. Let :math:`p_k` be a vector of the first :math:`k` elements in the recommendations for a particular user, and let :math:`a` be the set of items in ``observed_user_items`` for that user. The "precision at cutoff k" for this user is defined as .. math:: P(k) = \\frac{ | a \cap p_k | }{k}, while "recall at cutoff k" is defined as .. math:: R(k) = \\frac{ | a \cap p_k | }{|a|} The order of the elements in the recommendations affects the returned precision and recall scores. Parameters observed_user_items : SFrame An SFrame containing observed user item pairs, where the first column contains user ids and the second column contains item ids. recommendations : SFrame An SFrame containing columns pertaining to the user id, the item id, the score given to that pair, and the rank of that item among the recommendations made for user id. For example, see the output of recommend() produced by any turicreate.recommender model. cutoffs : list[int], optional The cutoffs to use when computing precision and recall. Returns ------- out : SFrame An SFrame containing columns user id, cutoff, precision, recall, and count where the precision and recall are reported for each user at each requested cutoff, and count is the number of observations for that user id. Notes ----- The corner cases that involve empty lists were chosen to be consistent with the feasible set of precision-recall curves, which start at (precision, recall) = (1,0) and end at (0,1). However, we do not believe there is a well-known consensus on this choice. Examples -------- Given SFrames ``train_data`` and ``test_data`` with columns user_id and item_id: """


    assert type(observed_user_items) == _SFrame
    assert type(recommendations) == _SFrame
    assert type(cutoffs) == list
    assert min(cutoffs) > 0, "All cutoffs must be positive integers."
    assert recommendations.num_columns() >= 2
    user_id = recommendations.column_names()[0]
    item_id = recommendations.column_names()[1]

    assert observed_user_items.num_rows() > 0, \
           "Evaluating precision and recall requires a non-empty " + \
           "observed_user_items."
    assert user_id in observed_user_items.column_names(), \
            "User column required in observed_user_items."
    assert item_id in observed_user_items.column_names(), \
            "Item column required in observed_user_items."
    assert observed_user_items[user_id].dtype == \
           recommendations[user_id].dtype, \
           "The user column in the two provided SFrames must have the same type."
    assert observed_user_items[item_id].dtype == \
           recommendations[item_id].dtype, \
           "The user column in the two provided SFrames must have the same type."

    cutoffs = _array.array('f', cutoffs)

    opts = {'data': observed_user_items,
            'recommendations': recommendations,
            'cutoffs': cutoffs}

    response = _turicreate.toolkits._main.run('evaluation_precision_recall_by_user', opts)
    sf = _SFrame(None, _proxy=response['pr'])
    return sf.sort([user_id, 'cutoff'])