[SciPy-User] down-sampling an array by averaging - vectorized form?

Andrew Giessel andrew_giessel@hms.harvard....
Sat Feb 11 14:14:54 CST 2012

Heya Zach-

On Sat, Feb 11, 2012 at 14:56, Zachary Pincus <zachary.pincus@yale.edu>wrote:

> Hi Andrew,
> > None of them are 'vectorized' persay but all are more clever or
> effeicent ways of getting at the same problem.  I thought I'd write a
> couple of quick comments.
> It depends what you mean by "vectorized" -- none are using SIMD
> instructions on the chip, but from the Matlab/numpy perspective I think
> people often mean "vectorized" as "multiple data elements acted on by a
> single command" such as C = A + B, where A and B are matrices.
> In any case, the reshaping approach is "vectorized" according to the
> latter definition, which obviously really just means "the loops are pushed
> down into C"...

Yes, I guess that's more precisely what I mean- I would call the reshaping
approach vectorized as well.

> > The binning followed by scalar division is wicked fast and yields
> results that are very close to my original algorithm.  The reshaping seems
> very clever and I am going to read it more carefully to learn some lessons
> there, I think.
> For more information on reshaping to do decimation, see the "avoiding
> loops when downsampling arrays" thread on the numpy-discussion list from
> last week:
> https://groups.google.com/forum/#!topic/numpy/qyDKJTj5jx4
> There's a bit more discussion about how this works, and some memory-layout
> caveats to be aware of.
> Also, instead of doing the reshaping, you could see if hard-coding the
> averaging is faster. Here's how to do it for the 2x2 case:
> B = (A[::2,::2] + A[1::2,::2] + A[::2,1::2] + A[1::2,::2])/4.0

Wow, last week?  Guess that's what I get for not searching archives.  I
just joined both numpy-discussion and scipy-user this week.  I will check
that thread.

> The ndimage.zoom approach is a very general approach (and roughly as
> quick as the others).  As far as I can tell, that function uses spline
> interpolation for zoom factors > 1, and I'm unsure how it deals with zoom
> factors < 1.  It might do nearest neighbor or something like that, I wasn't
> able to quickly determine from glancing at the source.  If anyone knows, it
> would be cool to hear.
> I'm pretty certain that the zoom function doesn't do anything smart for
> image decimation/minification -- it just uses the requested interpolation
> order to take a point-sample of the image at the calculated coordinates.
> Lack of good decimation is a limitation of ndimage. I know that there are
> decimation routines in scipy.signal, but I'm not sure if they're just 1D.
> In general, for integer-factor downsampling, I either do it with slicing
> like the above example, or use convolution (like ndimage.gaussian_filter
> with the appropriate bandwidth, which is quite fast) to prefilter followed
> by taking a view such as A[::3,::3] to downsample by a factor of three.

Cheers, it's great to know what other people do.


Andrew Giessel, PhD

Department of Neurobiology, Harvard Medical School
220 Longwood Ave Boston, MA 02115
ph: 617.432.7971 email: andrew_giessel@hms.harvard.edu
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