[Array API] Add linalg.vecdot (#70542)

This PR adds the function `linalg.vecdot` specified by the [Array
API](https://data-apis.org/array-api/latest/API_specification/linear_algebra_functions.html#function-vecdot)

For the complex case, it chooses to implement \sum x_i y_i. See the
discussion in https://github.com/data-apis/array-api/issues/356

Edit. When it comes to testing, this function is not quite a binopt, nor a reduction opt. As such, we're this close to be able to get the extra testing, but we don't quite make it. Now, it's such a simple op that I think we'll make it without this.

Resolves https://github.com/pytorch/pytorch/issues/18027.

cc @mruberry @rgommers @pmeier @asmeurer @leofang @AnirudhDagar @asi1024 @emcastillo @kmaehashi
Pull Request resolved: https://github.com/pytorch/pytorch/pull/70542
Approved by: https://github.com/IvanYashchuk, https://github.com/mruberry

torch/_torch_docs.py

@@ -3513,21 +3513,34 @@ add_docstr(torch.vdot,
            r"""
 vdot(input, other, *, out=None) -> Tensor
 
-Computes the dot product of two 1D tensors. The vdot(a, b) function handles complex numbers
-differently than dot(a, b). If the first argument is complex, the complex conjugate of the
-first argument is used for the calculation of the dot product.
+Computes the dot product of two 1D vectors along a dimension.
+
+In symbols, this function computes
+
+.. math::
+
+    \sum_{i=1}^n \overline{x_i}y_i.
+
+where :math:`\overline{x_i}` denotes the conjugate for complex
+vectors, and it is the identity for real vectors.
 
 .. note::
 
     Unlike NumPy's vdot, torch.vdot intentionally only supports computing the dot product
     of two 1D tensors with the same number of elements.
 
+.. seealso::
+
+        :func:`torch.linalg.vecdot` computes the dot product of two batches of vectors along a dimension.
+
 Args:
     input (Tensor): first tensor in the dot product, must be 1D. Its conjugate is used if it's complex.
     other (Tensor): second tensor in the dot product, must be 1D.
 
 Keyword args:
-    {out}
+""" + fr"""
+.. note:: {common_args["out"]}
+""" + r"""
 
 Example::
 
@@ -3539,7 +3552,7 @@ Example::
     tensor([16.+1.j])
     >>> torch.vdot(b, a)
     tensor([16.-1.j])
-""".format(**common_args))
+""")
 
 add_docstr(torch.eig,
            r"""