DOC: #22266 Add examples for tril_indices_from(), triu_indices_from() (#22562)

* DOC: #22266 Add examples for tri[lu]_indices_from()

* DOC: see also for tri[lu]_indices_from()

* DOC: Fix triu_indices_from example and minor updates.
 * incides -> indices
 * Update wording surrounding .

Co-authored-by: Ross Barnowski <rossbar@berkeley.edu>

1 files changed, 69 insertions, 2 deletions

diff --git a/numpy/lib/twodim_base.py b/numpy/lib/twodim_base.py
index 654ee4cf5..dcb4ed46c 100644
--- a/numpy/lib/twodim_base.py
+++ b/numpy/lib/twodim_base.py
@@ -995,9 +995,42 @@ def tril_indices_from(arr, k=0):
     k : int, optional
         Diagonal offset (see `tril` for details).
 
+    Examples
+    --------
+
+    Create a 4 by 4 array.
+
+    >>> a = np.arange(16).reshape(4, 4)
+    >>> a
+    array([[ 0,  1,  2,  3],
+           [ 4,  5,  6,  7],
+           [ 8,  9, 10, 11],
+           [12, 13, 14, 15]])
+
+    Pass the array to get the indices of the lower triangular elements.
+
+    >>> trili = np.tril_indices_from(a)
+    >>> trili
+    (array([0, 1, 1, 2, 2, 2, 3, 3, 3, 3]), array([0, 0, 1, 0, 1, 2, 0, 1, 2, 3]))
+
+    >>> a[trili]
+    array([ 0,  4,  5,  8,  9, 10, 12, 13, 14, 15])
+
+    This is syntactic sugar for tril_indices().
+
+    >>> np.tril_indices(a.shape[0])
+    (array([0, 1, 1, 2, 2, 2, 3, 3, 3, 3]), array([0, 0, 1, 0, 1, 2, 0, 1, 2, 3]))
+
+    Use the `k` parameter to return the indices for the lower triangular array
+    up to the k-th diagonal.
+
+    >>> trili1 = np.tril_indices_from(a, k=1)
+    >>> a[trili1]
+    array([ 0,  1,  4,  5,  6,  8,  9, 10, 11, 12, 13, 14, 15])
+
     See Also
     --------
-    tril_indices, tril
+    tril_indices, tril, triu_indices_from
 
     Notes
     -----
@@ -1114,9 +1147,43 @@ def triu_indices_from(arr, k=0):
     triu_indices_from : tuple, shape(2) of ndarray, shape(N)
         Indices for the upper-triangle of `arr`.
 
+    Examples
+    --------
+
+    Create a 4 by 4 array.
+
+    >>> a = np.arange(16).reshape(4, 4)
+    >>> a
+    array([[ 0,  1,  2,  3],
+           [ 4,  5,  6,  7],
+           [ 8,  9, 10, 11],
+           [12, 13, 14, 15]])
+
+    Pass the array to get the indices of the upper triangular elements.
+
+    >>> triui = np.triu_indices_from(a)
+    >>> triui
+    (array([0, 0, 0, 0, 1, 1, 1, 2, 2, 3]), array([0, 1, 2, 3, 1, 2, 3, 2, 3, 3]))
+
+    >>> a[triui]
+    array([ 0,  1,  2,  3,  5,  6,  7, 10, 11, 15])
+
+    This is syntactic sugar for triu_indices().
+
+    >>> np.triu_indices(a.shape[0])
+    (array([0, 0, 0, 0, 1, 1, 1, 2, 2, 3]), array([0, 1, 2, 3, 1, 2, 3, 2, 3, 3]))
+
+    Use the `k` parameter to return the indices for the upper triangular array
+    from the k-th diagonal.
+
+    >>> triuim1 = np.triu_indices_from(a, k=1)
+    >>> a[triuim1]
+    array([ 1,  2,  3,  6,  7, 11])
+
+
     See Also
     --------
-    triu_indices, triu
+    triu_indices, triu, tril_indices_from
 
     Notes
     -----