DOC: Fix a typo in description and add an example of numpy.tensordot (numpy#23547)

* modify the description of tensordot

* modify the description of tensordot (numpy#174 of numpy-tutorials)

* modify the description of tensordot (numpy#174 of numpy-tutorials)

* Update numeric.py

* Update numpy/core/numeric.py

Co-authored-by: Matti Picus <[email protected]>

* Update numeric.py

* Update numeric.py

* Update numeric.py

* Update numeric.py

* Update numeric.py

* Update numeric.py

* Update numeric.py

* Update numeric.py

* Update numeric.py

add space

* Update numeric.py

* Update numeric.py

* Update numeric.py

* Update numeric.py

* modified:   numpy/_core/numeric.py

---------

Co-authored-by: Matti Picus <[email protected]>

Author: John-Wendell

numpy/_core/numeric.py

@@ -1023,28 +1023,48 @@ def tensordot(a, b, axes=2):
     Notes
     -----
     Three common use cases are:
-
-    * ``axes = 0`` : tensor product :math:`a\\otimes b`
-    * ``axes = 1`` : tensor dot product :math:`a\\cdot b`
-    * ``axes = 2`` : (default) tensor double contraction :math:`a:b`
-
-    When `axes` is a positive integer ``N``, the operation starts with
-    axis ``-N`` of `a` and axis ``0`` of `b`, and it continues through
-    axis ``-1`` of `a` and axis ``N-1`` of `b` (inclusive).
+        * ``axes = 0`` : tensor product :math:`a\\otimes b`
+        * ``axes = 1`` : tensor dot product :math:`a\\cdot b`
+        * ``axes = 2`` : (default) tensor double contraction :math:`a:b`
+
+    When `axes` is integer_like, the sequence of axes for evaluation
+    will be: from the -Nth axis to the -1th axis in `a`,
+    and from the 0th axis to (N-1)th axis in `b`.
+    For example, ``axes = 2`` is the equal to
+    ``axes = [[-2, -1], [0, 1]]``.
+    When N-1 is smaller than 0, or when -N is larger than -1,
+    the element of `a` and `b` are defined as the `axes`.
 
     When there is more than one axis to sum over - and they are not the last
     (first) axes of `a` (`b`) - the argument `axes` should consist of
     two sequences of the same length, with the first axis to sum over given
     first in both sequences, the second axis second, and so forth.
+    The calculation can be referred to ``numpy.einsum``.
 
     The shape of the result consists of the non-contracted axes of the
     first tensor, followed by the non-contracted axes of the second.
 
     Examples
-    --------
-    A "traditional" example:
+    -------- 
+    An example on integer_like:
+
+    >>> a_0 = np.array([[1, 2], [3, 4]])
+    >>> b_0 = np.array([[5, 6], [7, 8]])
+    >>> c_0 = np.tensordot(a_0, b_0, axes=0)
+    >>> c_0.shape
+    (2, 2, 2, 2)
+    >>> c_0
+    array([[[[ 5,  6],
+             [ 7,  8]],
+            [[10, 12],
+             [14, 16]]],
+           [[[15, 18],
+             [21, 24]],
+            [[20, 24],
+             [28, 32]]]])
+
+    An example on array_like:
 
-    >>> import numpy as np
     >>> a = np.arange(60.).reshape(3,4,5)
     >>> b = np.arange(24.).reshape(4,3,2)
     >>> c = np.tensordot(a,b, axes=([1,0],[0,1]))
@@ -1056,7 +1076,9 @@ def tensordot(a, b, axes=2):
            [4664., 5018.],
            [4796., 5162.],
            [4928., 5306.]])
-    >>> # A slower but equivalent way of computing the same...
+           
+    A slower but equivalent way of computing the same...
+    
     >>> d = np.zeros((5,2))
     >>> for i in range(5):
     ...   for j in range(2):