Std of single element tensor is nan

1

The std computed on a tensor containing single element is nan.
Precisely:
`

v = th.randn(1, 128, 4, 4)
v.std(dim=0)
tensor([[[nan., nan., nan., nan.],
[nan., nan., nan., nan.],
[nan., nan., nan., nan.],
[nan., nan., nan., nan.]],

    [[nan., nan., nan., nan.],
     [nan., nan., nan., nan.],
     [nan., nan., nan., nan.],
     [nan., nan., nan., nan.]],

    [[nan., nan., nan., nan.],
     [nan., nan., nan., nan.],
     [nan., nan., nan., nan.],
     [nan., nan., nan., nan.]],

    ...,

    [[nan., nan., nan., nan.],
     [nan., nan., nan., nan.],
     [nan., nan., nan., nan.],
     [nan., nan., nan., nan.]],

    [[nan., nan., nan., nan.],
     [nan., nan., nan., nan.],
     [nan., nan., nan., nan.],
     [nan., nan., nan., nan.]],

    [[nan., nan., nan., nan.],
     [nan., nan., nan., nan.],
     [nan., nan., nan., nan.],
     [nan., nan., nan., nan.]]])

`

In fact, just one element is:
`

v = th.randn(1)
v.std()
tensor(nan.)
`

Theoretically speaking, shouldn’t the std of a single element be 0? Please help me to clear this confusion

2

Have you checked the documentation for std?
PyTorch uses the unbiased estimate of std by default and that is not well-defined for a single element. If you set unbiased=False, you’ll get what I would suppose is what you expect.

Best regards

Thomas

3

Hi Thomas,

Thank you for the response. Oh yes, bessel’s correction uses (n - 1) instead of (n) for calculating the std. This would cause a ‘divide by 0’ case resulting in nan. I actually got caught up in searching for the source of this function. Thanks again.

Best regards,
Animesh