Hi all,
I have a possibly naive question. I don't really understand this
particular set of output:
In [1]: import numpy
In [2]: a1 = numpy.random.random((512,512,512)).astype("float32")
In [3]: a1.sum(axis=0).sum(axis=0).sum(axis=0)
Out[3]: 67110312.0
In [4]: a1.sum()
Out[4]: 16777216.0
I recognize that the intermediate sums may accumulate error
differently than a single call to .sum(), but I guess my concern is
that it's accumulating a lot faster than I anticipated. (Interesting
to note that a1.sum() returns 0.5*512^3, down to the decimal; is it
summing up the mean, which should be ~0.5?) However, with a 256^3
array:
In [1]: import numpy
In [2]: a1 = numpy.random.random((256,256,256)).astype("float32")
In [3]: a1.sum(axis=0).sum(axis=0).sum(axis=0)
Out[3]: 8389703.0
In [4]: a1.sum()
Out[4]: 8389245.0
The errors are much more reasonable. Is there an overflow or
something that occurs with the 512^3? These problems all go
completely away with a float64 array, but the issue originally showed
up when trying to normalize an on-disk float32 array of size 512^3,
where the normalization factor was off by a substantial factor (>2x)
depending on the mechanism used to sum. My suspicion is that perhaps
I have a naive misconception about intermediate steps in summations,
or there is a subtlety I'm missing here.
I placed a sample script I used to test this here:
http://pastebin.com/dGbHwFPK
Thanks for any insight anybody can provide,
Matt
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