Remove deprecated torch.eig (#70982)

The time has come to remove deprecated linear algebra related functions. This PR removes `torch.eig`.

cc @jianyuh @nikitaved @pearu @mruberry @walterddr @IvanYashchuk @xwang233 @Lezcano
Pull Request resolved: https://github.com/pytorch/pytorch/pull/70982
Approved by: https://github.com/Lezcano, https://github.com/malfet

torch/_torch_docs.py

@@ -3999,92 +3999,6 @@ Example::
 """,
 )
 
-add_docstr(
-    torch.eig,
-    r"""
-eig(input, eigenvectors=False, *, out=None) -> (Tensor, Tensor)
-
-Computes the eigenvalues and eigenvectors of a real square matrix.
-
-.. note::
-    Since eigenvalues and eigenvectors might be complex, backward pass is supported only
-    if eigenvalues and eigenvectors are all real valued.
-
-    When :attr:`input` is on CUDA, :func:`torch.eig() <torch.eig>` causes
-    host-device synchronization.
-
-.. warning::
-
-    :func:`torch.eig` is deprecated in favor of :func:`torch.linalg.eig`
-    and will be removed in a future PyTorch release.
-    :func:`torch.linalg.eig` returns complex tensors of dtype `cfloat` or `cdouble`
-    rather than real tensors mimicking complex tensors.
-
-    ``L, _ = torch.eig(A)`` should be replaced with
-
-    .. code :: python
-
-        L_complex = torch.linalg.eigvals(A)
-
-    ``L, V = torch.eig(A, eigenvectors=True)`` should be replaced with
-
-    .. code :: python
-
-        L_complex, V_complex = torch.linalg.eig(A)
-
-Args:
-    input (Tensor): the square matrix of shape :math:`(n \times n)` for which the eigenvalues and eigenvectors
-        will be computed
-    eigenvectors (bool): ``True`` to compute both eigenvalues and eigenvectors;
-        otherwise, only eigenvalues will be computed
-
-Keyword args:
-    out (tuple, optional): the output tensors
-
-Returns:
-    (Tensor, Tensor): A namedtuple (eigenvalues, eigenvectors) containing
-
-        - **eigenvalues** (*Tensor*): Shape :math:`(n \times 2)`. Each row is an eigenvalue of ``input``,
-          where the first element is the real part and the second element is the imaginary part.
-          The eigenvalues are not necessarily ordered.
-        - **eigenvectors** (*Tensor*): If ``eigenvectors=False``, it's an empty tensor.
-          Otherwise, this tensor of shape :math:`(n \times n)` can be used to compute normalized (unit length)
-          eigenvectors of corresponding eigenvalues as follows.
-          If the corresponding `eigenvalues[j]` is a real number, column `eigenvectors[:, j]` is the eigenvector
-          corresponding to `eigenvalues[j]`.
-          If the corresponding `eigenvalues[j]` and `eigenvalues[j + 1]` form a complex conjugate pair, then the
-          true eigenvectors can be computed as
-          :math:`\text{true eigenvector}[j] = eigenvectors[:, j] + i \times eigenvectors[:, j + 1]`,
-          :math:`\text{true eigenvector}[j + 1] = eigenvectors[:, j] - i \times eigenvectors[:, j + 1]`.
-
-Example::
-
-    Trivial example with a diagonal matrix. By default, only eigenvalues are computed:
-
-    >>> a = torch.diag(torch.tensor([1, 2, 3], dtype=torch.double))
-    >>> e, v = torch.eig(a)
-    >>> e
-    tensor([[1., 0.],
-            [2., 0.],
-            [3., 0.]], dtype=torch.float64)
-    >>> v
-    tensor([], dtype=torch.float64)
-
-    Compute also the eigenvectors:
-
-    >>> e, v = torch.eig(a, eigenvectors=True)
-    >>> e
-    tensor([[1., 0.],
-            [2., 0.],
-            [3., 0.]], dtype=torch.float64)
-    >>> v
-    tensor([[1., 0., 0.],
-            [0., 1., 0.],
-            [0., 0., 1.]], dtype=torch.float64)
-
-""",
-)
-
 add_docstr(
     torch.eq,
     r"""