[Numpy-discussion] A faster median (Wirth's method)

Charles R Harris charlesr.harris@gmail....
Wed Sep 2 18:21:29 CDT 2009

On Wed, Sep 2, 2009 at 1:25 PM, Chad Netzer <chad.netzer@gmail.com> wrote:

> On Mon, Aug 31, 2009 at 9:06 PM, Sturla Molden<sturla@molden.no> wrote:
> >
> > We recently has a discussion regarding an optimization of NumPy's median
> > to average O(n) complexity. After some searching, I found out there is a
> > selection algorithm competitive in speed with Hoare's quick select. It
> > has the advantage of being a lot simpler to implement. In plain Python:
> > Chad, you can continue to write quick select using NumPy's C quick sort
> > in numpy/core/src/_sortmodule.c.src.  When you are done, it might be
> > about 10% faster than this. :-)
> I was sick for a bit last week, so got stalled on my version, but I'll
> be working on it this weekend.  I'm going for a more general partition
> function, that could have slightly more general use cases than just a
> median.  Nevertheless, its good to see there could be several options,
> hopefully at least one of which can be put into numpy.
> By the way, as far as I can tell, the above algorithm is exactly the
> same idea as a non-recursive Hoare (ie. quicksort) selection:  Do the
> partition, then only proceed to the sub-partition that must contain
> the nth element.    My version is a bit more general, allowing
> partitioning on a range of elements rather than just one, but the
> concept is the same.  The numpy quicksort already does non recursive
> sorting.
> I'd also like to, if possible, have a specialized 2D version, since
> image media filtering is one of my interests, and the C version works
> on 1D (raveled) arrays only.
There are special hardwired medians for 2,3,5,9 elements, which covers a lot
of image processing. They aren't in numpy, though ;) David has implemented a
NeighborhoodIter that could help extract the elements if you want to deal
with images.

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