[Numpy-discussion] numpy.pad -- problem?

[Andras Deak]

> mean(y):  -1.3778013372117948e-16
> ypad:
>  [-1.37780134e-16 -1.37780134e-16 -1.37780134e-16  0.00000000e+00
>   3.09016994e+00  5.87785252e+00  8.09016994e+00  9.51056516e+00
>   1.00000000e+01  9.51056516e+00  8.09016994e+00  5.87785252e+00
>   3.09016994e+00  1.22464680e-15 -3.09016994e+00 -5.87785252e+00
>  -8.09016994e+00 -9.51056516e+00 -1.00000000e+01 -9.51056516e+00
>  -8.09016994e+00 -5.87785252e+00 -3.09016994e+00 -2.44929360e-15
>  -7.40148683e-17 -7.40148683e-17]
>
> The left pad is correct, but the right pad is different and not the mean of
> y)  --- why?

This is how np.pad computes mean padding:
https://github.com/numpy/numpy/blob/01541f2822d0d4b37b96f6b42e35963b132f1947/numpy/lib/arraypad.py#L1396-L1400
elif mode == 'mean':
    for axis, ((pad_before, pad_after), (chunk_before, chunk_after)) \
    in enumerate(zip(pad_width, kwargs['stat_length'])):
    newmat = _prepend_mean(newmat, pad_before, chunk_before, axis)
    newmat = _append_mean(newmat, pad_after, chunk_after, axis)

That is, first the mean is prepended, then appended, and in the latter
step the updates (front-padded) array is used for computing the mean
again. Note that with arbitrary precision this is fine, since
appending n*`mean` to an array with mean `mean` should preserve the
mean. But with doubles you can get errors on the order of the machine
epsilon, which is what happens here:

In [16]: ypad[3:-2].mean()
Out[16]: -1.1663302849022412e-16

In [17]: ypad[:-2].mean()
Out[17]: -3.700743415417188e-17

So the prepended values are `y.mean()`, but the appended values are
`ypad[:-2].mean()` which includes the near-zero padding values. I
don't think this error should be a problem in practice, but I agree
it's surprising.

András