Added a UserWarning when using torch.{std,var,std_mean,std_var} with dof<=0

[tringwald]

Fixes #109696.

This PR adds a UserWarning when calling

• torch.var
• torch.var_mean
• torch.std
• torch.std_mean

with an effective dof<=0. Until now, only torch.cov warned about this. The code also handles edge cases, such as torch.empty

>>> import torch; torch.std_mean(torch.empty(0), correction=0)
<stdin>:1: UserWarning: std_mean(): degrees of freedom is <= 0 (Triggered internally at /app/aten/src/ATen/native/ReduceOps.cpp:1671.)
(tensor(nan), tensor(nan))

multi-dim reductions

>>> import torch; torch.std_mean(torch.empty(10, 30, 20, 50), correction=600, dim=(1, 2))
<stdin>:1: UserWarning: std_mean(): degrees of freedom is <= 0 (Triggered internally at /app/aten/src/ATen/native/ReduceOps.cpp:1671.)
[... snip ...]

and a negative correction.

>>> import torch; torch.std_mean(torch.randn(0), correction=-5)
(tensor(nan), tensor(nan))

[pytorch-bot]

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✅ You can merge normally! (1 Unrelated Failure)

As of commit d8c410d with merge base 6ca964b ():

UNSTABLE - The following job failed but was likely due to flakiness present on trunk and has been marked as unstable:

• trunk / linux-focal-rocm5.6-py3.8 / test (default, 3, 3, linux.rocm.gpu, unstable) (gh)

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[albanD]

Will let @soulitzer review this one

[soulitzer]

Thanks!
Could we add a small test in test/test_reductions.py?

 with warnings.catch_warnings(record=True) as w:
        # stuff

self.assertIn('blah', str(w[0].message))

[soulitzer]

Looks great, thanks for the update!

[soulitzer]

@pytorchbot merge

[pytorchmergebot]

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