Closeness checks in our the test suite, i.e. TestCase.assertEqual, are performed component wise meaning closeness is computed for the real and imaginary components separately.

The recently introduced torch.testing.assert_close inherited the behavior:

The componentwise checking was introduced in #34258 but no public explanation was provided on the reason behind it.

Pros:

• Since complex64 is comprised of two float32, we can reuse the testing tolerances. Of course the same is true for complex128 and complex32.

Cons:

• torch.testing.assert_close and torch.isclose diverge for complex tensors:

  >>> rtol, atol = 0.1, 0.3
  >>> expected = torch.tensor(1 + 1j)
  >>> actual1 = torch.tensor(1 + 1.43j)
  >>> torch.testing.assert_close(actual1, expected, rtol=rtol, atol=atol)
  AssertionError: Scalars are not close!
  >>> torch.isclose(actual1, expected, rtol=rtol, atol=atol)
  tensor(True)
  >>> actual2 = torch.tensor(0.6 + 1.3j)
  >>> torch.testing.assert_close(actual2, expected, rtol=rtol, atol=atol)
  >>> torch.isclose(actual2, expected, rtol=rtol, atol=atol)
  tensor(False)

  torch.isclose follows the implementation of numpy and partially cmath by comparing the absolute values of the difference of the two values. torch.testing.assert_close on the other hand compares the absolute values of the difference of the individual components. To be exact, torch.isclose as well as numpy evaluate the closeness inequality abs(a - b) <= atol + rtol * abs(b) the same way for complex as for real numbers. torch.testing.assert_close evaluates it twice for the real and imaginary component and checks the logical and of the results.

• The implementation is more messy and introduces more edgecases:

  • Is complex(inf, 0) close to complex(inf, 1)?
  • Is complex(0, NaN) close to complex(NaN, 0)?

  The second case led to equal_nan="relaxed" in TestCase.assertEqual which accepts these comparisons while they will be rejected for equal_nan=True. torch.isclose currently bails out for complex values and equal_nan=True

  pytorch/aten/src/ATen/native/TensorCompare.cpp

  Lines 101 to 102 in a26a9f8

  	TORCH_CHECK(!(self.is_complex() && equal_nan),
  	"isclose with equal_nan=True is not supported for complex inputs.");

Regions of closeness

By checking the components individually we are forming a rectangle region of closeness around the expected value. Despite the divergence on the tolerance definition, torch.isclose, numpy, and cmath form a circle around the expected values. Thus is impossible to convert the old tolerances to achieve the same behavior if we go for this change.

RFC

Since in most cases the specific values of the tolerances hardly matter, IMHO the cons severly outweigh the pros. Thus, the current plan is to retire the componentwise checking and merge the complex behavior of our internal and public testing functions with torch.isclose and in turn with numpy. If you disagree with that plan, please let us know in this issue.

cc @ezyang @anjali411 @dylanbespalko @mruberry @lezcano @nikitaved @VitalyFedyunin @walterddr