Fix nan gradient by using native complex abs op (#1013)

test/torchaudio_unittest/functional/functional_cpu_test.py

 import math
-import unittest
 
 import torch
 import torchaudio
@@ -8,7 +7,7 @@ from parameterized import parameterized
 import pytest
 
 from torchaudio_unittest import common_utils
-from .functional_impl import Lfilter
+from .functional_impl import Lfilter, Spectrogram
 
 
 class TestLFilterFloat32(Lfilter, common_utils.PytorchTestCase):
@@ -21,6 +20,16 @@ class TestLFilterFloat64(Lfilter, common_utils.PytorchTestCase):
     device = torch.device('cpu')
 
 
+class TestSpectrogramFloat32(Spectrogram, common_utils.PytorchTestCase):
+    dtype = torch.float32
+    device = torch.device('cpu')
+
+
+class TestSpectrogramFloat64(Spectrogram, common_utils.PytorchTestCase):
+    dtype = torch.float64
+    device = torch.device('cpu')
+
+
 class TestCreateFBMatrix(common_utils.TorchaudioTestCase):
     def test_no_warning_high_n_freq(self):
         with pytest.warns(None) as w:

test/torchaudio_unittest/functional/functional_cuda_test.py

 import torch
 
 from torchaudio_unittest import common_utils
-from .functional_impl import Lfilter
+from .functional_impl import Lfilter, Spectrogram
 
 
 @common_utils.skipIfNoCuda
@@ -14,3 +14,15 @@ class TestLFilterFloat32(Lfilter, common_utils.PytorchTestCase):
 class TestLFilterFloat64(Lfilter, common_utils.PytorchTestCase):
     dtype = torch.float64
     device = torch.device('cuda')
+
+
+@common_utils.skipIfNoCuda
+class TestSpectrogramFloat32(Spectrogram, common_utils.PytorchTestCase):
+    dtype = torch.float32
+    device = torch.device('cuda')
+
+
+@common_utils.skipIfNoCuda
+class TestSpectrogramFloat64(Spectrogram, common_utils.PytorchTestCase):
+    dtype = torch.float64
+    device = torch.device('cuda')

test/torchaudio_unittest/functional/functional_impl.py

 """Test defintion common to CPU and CUDA"""
 import torch
 import torchaudio.functional as F
+from parameterized import parameterized
 
 from torchaudio_unittest import common_utils
 
@@ -29,3 +30,25 @@ class Lfilter(common_utils.TestBaseMixin):
         assert output_signal.max() <= 1
         output_signal = F.lfilter(input_signal, a_coeffs, b_coeffs, clamp=False)
         assert output_signal.max() > 1
+
+
+class Spectrogram(common_utils.TestBaseMixin):
+    @parameterized.expand([(0., ), (1., ), (2., ), (3., )])
+    def test_grad_at_zero(self, power):
+        """The gradient of power spectrogram should not be nan but zero near x=0
+
+        https://github.com/pytorch/audio/issues/993
+        """
+        x = torch.zeros(1, 22050, requires_grad=True)
+        spec = F.spectrogram(
+            x,
+            pad=0,
+            window=None,
+            n_fft=2048,
+            hop_length=None,
+            win_length=None,
+            power=power,
+            normalized=False,
+        )
+        spec.sum().backward()
+        assert not x.grad.isnan().sum()

torchaudio/functional/functional.py

@@ -70,30 +70,29 @@ def spectrogram(
     waveform = waveform.reshape(-1, shape[-1])
 
     # default values are consistent with librosa.core.spectrum._spectrogram
-    spec_f = torch.view_as_real(
-        torch.stft(
-            input=waveform,
-            n_fft=n_fft,
-            hop_length=hop_length,
-            win_length=win_length,
-            window=window,
-            center=True,
-            pad_mode="reflect",
-            normalized=False,
-            onesided=True,
-            return_complex=True,
-        )
+    spec_f = torch.stft(
+        input=waveform,
+        n_fft=n_fft,
+        hop_length=hop_length,
+        win_length=win_length,
+        window=window,
+        center=True,
+        pad_mode="reflect",
+        normalized=False,
+        onesided=True,
+        return_complex=True,
     )
 
     # unpack batch
-    spec_f = spec_f.reshape(shape[:-1] + spec_f.shape[-3:])
+    spec_f = spec_f.reshape(shape[:-1] + spec_f.shape[-2:])
 
     if normalized:
         spec_f /= window.pow(2.).sum().sqrt()
     if power is not None:
-        spec_f = complex_norm(spec_f, power=power)
-
-    return spec_f
+        if power == 1.0:
+            return spec_f.abs()
+        return spec_f.abs().pow(power)
+    return torch.view_as_real(spec_f)
 
 
 def griffinlim(