BUG: np.testing.assert_allclose does not work if argument is empty iterable

[unalmis]

Describe the issue:

title

Reproduce the code example:

a = 3 # make this anything you want
np.testing.assert_allclose(a, [])

Error message:

No response

Python and NumPy Versions:

See #27413

Runtime Environment:

See #27413

Context for the issue:

This is misleading for this to pass.

This is docstring

Raises an AssertionError if two objects are not equal up to desired tolerance. Given two array_like objects, check that their shapes and all elements are equal (but see the Notes for the special handling of a scalar). An exception is raised if the shapes mismatch or any values conflict. In contrast to the standard usage in numpy, NaNs are compared like numbers, no assertion is raised if both objects have NaNs in the same positions.

[WarrenWeckesser]

a is a scalar, and the quoted docstring says but see the Notes for the special handling of a scalar. In the Notes (with Numpy version >= 2.0.0), it is explained that

    When one of `actual` and `desired` is a scalar and the other is
    array_like, the function performs the comparison as if the scalar were
    broadcasted to the shape of the array.
    This behaviour can be disabled with the `strict` parameter.

The second argument in your example, [], is "array_like", and when a scalar (shape ()) is broadcast with an array with shape (0,), the result is an array with shape (0,). So nothing is actually tested, and the assertion is trivially true.

I wouldn't mind if we deprecated and eventually removed this handling of scalars, but for now, this is an API wart that users need to be aware of. Use the parameter strict=True to avoid it (if you are using NumPy 2.0 or later).

[unalmis]

Ok thanks. I'd suggest either change this or emphasize this example in the docstring.