fixed ndcg doc

Author: Daria Tikhonovich

rectools/metrics/ranking.py

@@ -318,24 +318,23 @@ class NDCG(_RankingMetric):
 
     .. math::
         NDCG@k=\frac{1}{|U|}\sum_{u \in U}\frac{DCG_u@k}{IDCG_u@k}
+        DCG_u@k = \sum_{i=1}^{k} \frac{rel_u(i)}{log(i + 1)}
 
     where
-        - :math:`DCG_u@k` is "Discounted Cumulative Gain" at k for user u.
-        - `"Gain"` stands for relevance of item at position i to user. It equals to ``1`` if this item
-          is relevant, ``0`` otherwise
+        - :math:`IDCG_u@k = \sum_{i=1}^{k} \frac{1}{log(i + 1)}` when `divide_by_achievable` is set
+          to ``False`` (default).
+        - :math:`IDCG_u@k = \sum_{i=1}^{\min (|R(u)|, k)} \frac{1}{log(i + 1)}` when
+          `divide_by_achievable` is set to ``True``.
+        - :math:`DCG_u@k` is "Discounted Cumulative Gain" at ``k`` for user ``u``.
+        - :math:`rel_u(i)` is `"Gain"`. Here it is an indicator function, it equals to ``1`` if the
+          item at rank ``i`` is relevant to user ``u``, ``0`` otherwise.
         - `"Discounted Gain"` means that original item relevance is being discounted based on this
           items rank. The closer is item to the top the, the more gain is achieved.
         - `"Discounted Cumulative Gain"` means that discounted gains are summed together.
-        - :math:`IDCG_u@k` is `"Ideal Discounted Cumulative Gain"` at k for user u. This is maximum
-          possible value of `DCG@k`, used as normalization coefficient to ensure that `NDCG@k`
-          values lie in ``[0, 1]``.
-
-    When `divide_by_achievable` is set to ``False`` (default) `IDCG_u@k` is the same value for all
-    users and is equal to:
-    :math:`IDCG_u@k = \sum_{i=1}^{k} \frac{1}{log(i + 1)}`
-    When `divide_by_achievable` is set to ``True``, the formula for IDCG depends
-    on number of each user relevant items in the test set. The formula is:
-    :math:`IDCG_u@k = \sum_{i=1}^{\min (|R(u)|, k)} \frac{1}{log(i + 1)}`
+        - :math:`IDCG_u@k` is `"Ideal Discounted Cumulative Gain"` at ``k`` for user ``u``. This is
+          the maximum possible value of `DCG@k`, used as normalization coefficient to ensure that
+          `NDCG@k` values lie in ``[0, 1]``.
+        - :math:`|R_u|` is number of relevant (ground truth) items for user $u$.
 
     Parameters
     ----------