Add autograd test to T.TimeStretch (and F.phase_vocoder) (#1420)

test/torchaudio_unittest/transforms/autograd_test_impl.py

 from typing import List
+import unittest
 
 from parameterized import parameterized
 import torch
@@ -35,10 +36,16 @@ class AutogradTestMixin(TestBaseMixin):
     ):
         transform = transform.to(dtype=torch.float64, device=self.device)
 
+        # gradcheck and gradgradcheck only pass if the input tensors are of dtype `torch.double` or 
+        # `torch.cdouble`, when the default eps and tolerance values are used.
         inputs_ = []
         for i in inputs:
-            i.requires_grad = True
-            inputs_.append(i.to(dtype=torch.float64, device=self.device))
+            if torch.is_tensor(i):
+                i = i.to(
+                    dtype=torch.cdouble if i.is_complex() else torch.double,
+                    device=self.device)
+                i.requires_grad = True
+            inputs_.append(i)
         assert gradcheck(transform, inputs_)
         assert gradgradcheck(transform, inputs_, nondet_tol=nondet_tol)
 
@@ -129,3 +136,48 @@ class AutogradTestMixin(TestBaseMixin):
         transform = T.AmplitudeToDB()
         waveform = get_whitenoise(sample_rate=sample_rate, duration=0.05, n_channels=2)
         self.assert_grad(transform, [waveform])
+
+    @unittest.expectedFailure
+    def test_timestretch_zeros_fail(self):
+        """Test that ``T.TimeStretch`` fails gradcheck at 0
+
+        This is because ``F.phase_vocoder`` converts data from cartesian to polar coordinate,
+        which performs ``atan2(img, real)``, and gradient is not defined at 0.
+        """
+        n_fft = 16
+        transform = T.TimeStretch(n_freq=n_fft // 2 + 1, fixed_rate=0.99)
+        waveform = torch.zeros(2, 40)
+        spectrogram = get_spectrogram(waveform, n_fft=n_fft, power=None)
+        self.assert_grad(transform, [spectrogram])
+
+    @nested_params(
+        [0.7, 0.8, 0.9, 1.0, 1.3],
+        [False, True],
+    )
+    def test_timestretch_non_zero(self, rate, test_pseudo_complex):
+        """Verify that ``T.TimeStretch`` does not fail if it's not close to 0
+
+        ``T.TimeStrech`` is not differentiable around 0, so this test checks the differentiability
+        for cases where input is not zero.
+
+        As tested above, when spectrogram contains values close to zero, the gradients are unstable
+        and gradcheck fails.
+
+        In this test, we generate spectrogram from random signal, then we push the points around
+        zero away from the origin.
+
+        This process does not reflect the real use-case, and it is not practical for users, but
+        this helps us understand to what degree the function is differentiable and when not.
+        """
+        n_fft = 16
+        transform = T.TimeStretch(n_freq=n_fft // 2 + 1, fixed_rate=rate)
+        waveform = get_whitenoise(sample_rate=40, duration=1, n_channels=2)
+        spectrogram = get_spectrogram(waveform, n_fft=n_fft, power=None)
+
+        # 1e-3 is too small (on CPU)
+        epsilon = 1e-2
+        too_close = spectrogram.abs() < epsilon
+        spectrogram[too_close] = epsilon * spectrogram[too_close] / spectrogram[too_close].abs()
+        if test_pseudo_complex:
+            spectrogram = torch.view_as_real(spectrogram)
+        self.assert_grad(transform, [spectrogram])