Change name for namedtuple return of torch.linalg.svd (#57181)

Summary:
Pull Request resolved: https://github.com/pytorch/pytorch/pull/57181

Documentation for torch.linalg.svd says:
> The returned decomposition is a named tuple `(U, S, Vh)`

The documentation is correct while the implementation was wrong.
Renamed `V` -> `Vh`. `h` stands for hermitian.
This is a BC-breaking change but our linalg module is beta, therefore we can do it without a deprecation notice or aliases.

Test Plan: Imported from OSS

Reviewed By: ngimel

Differential Revision: D28142162

Pulled By: mruberry

fbshipit-source-id: 5e6e0ae5a63300f2db1575ca3259df381f8e1a7e

aten/src/ATen/native/BatchLinearAlgebra.cpp

@@ -2894,7 +2894,7 @@ std::tuple<Tensor&, Tensor&, Tensor&> svd_out(const Tensor& self, bool some, boo
     1. the 2nd parameter is bool some=True, which if effectively the opposite
        of full_matrices=True
 
-    2. svd returns V, while linalg.svd returns VT = V^T (for real inputs) or VT = V^H (for complex inputs).
+    2. svd returns V, while linalg.svd returns Vh = V^T (for real inputs) or Vh = V^H (for complex inputs).
        To accommodate the difference, we transpose() and conj() V upon return
 */
 
@@ -2906,8 +2906,8 @@ std::tuple<Tensor, Tensor, Tensor> linalg_svd(const Tensor& self, bool full_matr
     Tensor U, S, V;
     std::tie(U, S, V) = at::_svd_helper(self, some, /*compute_uv=*/true);
 
-    Tensor VT = V.conj().transpose(-2, -1);
-    return std::make_tuple(U, S, VT);
+    Tensor Vh = V.conj().transpose(-2, -1);
+    return std::make_tuple(U, S, Vh);
 
 }
 
@@ -2917,21 +2917,21 @@ static void svd_resize_and_copy(const char *name, const Tensor& src, Tensor &dst
   dst.copy_(src);
 }
 
-std::tuple<Tensor&, Tensor&, Tensor&> linalg_svd_out(const Tensor& self, bool full_matrices, Tensor& U, Tensor& S, Tensor& VT) {
+std::tuple<Tensor&, Tensor&, Tensor&> linalg_svd_out(const Tensor& self, bool full_matrices, Tensor& U, Tensor& S, Tensor& Vh) {
   checkSameDevice("svd", U, self, "U");
   checkSameDevice("svd", S, self, "S");
-  checkSameDevice("svd", VT, self, "VT");
+  checkSameDevice("svd", Vh, self, "Vh");
   checkLinalgCompatibleDtype("linalg_svd", U, self, "U");
-  checkLinalgCompatibleDtype("linalg_svd", VT, self, "VT");
+  checkLinalgCompatibleDtype("linalg_svd", Vh, self, "Vh");
   // singular values are always real-valued here
   ScalarType real_dtype = toValueType(self.scalar_type());
   checkLinalgCompatibleDtype("linalg_svd", S.scalar_type(), real_dtype, "S");
-  Tensor U_tmp, S_tmp, VT_tmp;
-  std::tie(U_tmp, S_tmp, VT_tmp) = at::native::linalg_svd(self, full_matrices);
+  Tensor U_tmp, S_tmp, Vh_tmp;
+  std::tie(U_tmp, S_tmp, Vh_tmp) = at::native::linalg_svd(self, full_matrices);
   svd_resize_and_copy("U", U_tmp, U);
   svd_resize_and_copy("S", S_tmp, S);
-  svd_resize_and_copy("V", VT_tmp, VT);
-  return std::tuple<Tensor&, Tensor&, Tensor&>(U, S, VT);
+  svd_resize_and_copy("V", Vh_tmp, Vh);
+  return std::tuple<Tensor&, Tensor&, Tensor&>(U, S, Vh);
 }
 
 Tensor linalg_svdvals(const Tensor& input) {

aten/src/ATen/native/native_functions.yaml

@@ -9636,10 +9636,10 @@
   dispatch:
     CPU, CUDA: linalg_vector_norm_out
 
-- func: linalg_svd.U(Tensor self, bool full_matrices=True, *, Tensor(a!) U, Tensor(b!) S, Tensor(c!) V) -> (Tensor(a!) U, Tensor(b!) S, Tensor(c!) V)
+- func: linalg_svd.U(Tensor self, bool full_matrices=True, *, Tensor(a!) U, Tensor(b!) S, Tensor(c!) Vh) -> (Tensor(a!) U, Tensor(b!) S, Tensor(c!) Vh)
   python_module: linalg
 
-- func: linalg_svd(Tensor self, bool full_matrices=True) -> (Tensor U, Tensor S, Tensor V)
+- func: linalg_svd(Tensor self, bool full_matrices=True) -> (Tensor U, Tensor S, Tensor Vh)
   python_module: linalg
   variants: function
 

test/test_linalg.py

@@ -2793,7 +2793,7 @@ class TestLinalg(TestCase):
 
             out_u = torch.empty(0, dtype=dtype, device=device)
             if svd == torch.linalg.svd:
-                msg = "but got VT with dtype Int"
+                msg = "but got Vh with dtype Int"
             else:
                 msg = "but got V with dtype Int"
             with self.assertRaisesRegex(RuntimeError, msg):

test/test_namedtuple_return_api.py

@@ -62,7 +62,8 @@ class TestNamedTupleAPI(TestCase):
                names=('values', 'indices'), hasout=True),
             op(operators=['kthvalue'], input=(1, 0),
                names=('values', 'indices'), hasout=True),
-            op(operators=['svd', '_svd_helper', 'linalg_svd'], input=(), names=('U', 'S', 'V'), hasout=True),
+            op(operators=['svd', '_svd_helper'], input=(), names=('U', 'S', 'V'), hasout=True),
+            op(operators=['linalg_svd'], input=(), names=('U', 'S', 'Vh'), hasout=True),
             op(operators=['slogdet'], input=(), names=('sign', 'logabsdet'), hasout=False),
             op(operators=['qr', 'linalg_qr'], input=(), names=('Q', 'R'), hasout=True),
             op(operators=['solve'], input=(a,), names=('solution', 'LU'), hasout=True),