Improve MVDR stability (#2004)

Summary:
Division first, multiplication second. This helps avoid the value overflow issue. It also helps the ``stv_evd`` solution pass the gradient check.

Pull Request resolved: https://github.com/pytorch/audio/pull/2004

Reviewed By: mthrok

Differential Revision: D32539827

Pulled By: nateanl

fbshipit-source-id: 70a386608324bb6e1b1c7238c78d403698590f22

test/torchaudio_unittest/transforms/autograd_test_impl.py

@@ -276,9 +276,8 @@ class AutogradTestMixin(TestBaseMixin):
 
     @parameterized.expand([
         "ref_channel",
-        # stv_power test time too long, comment for now
+        # stv_power and stv_evd test time too long, comment for now
         # "stv_power",
-        # stv_evd will fail since the eigenvalues are not distinct
         # "stv_evd",
     ])
     def test_mvdr(self, solution):

torchaudio/transforms.py

@@ -1829,7 +1829,7 @@ class MVDR(torch.nn.Module):
             denominator = torch.einsum("...d,...d->...", [stv.conj().squeeze(-1), numerator])
             # normalzie the numerator
             scale = stv.squeeze(-1)[..., self.ref_channel, None].conj()
-            beamform_vector = numerator * scale / (denominator.real.unsqueeze(-1) + eps)
+            beamform_vector = numerator / (denominator.real.unsqueeze(-1) + eps) * scale
 
         return beamform_vector