[Numpy-discussion] Slicing/selection in multiple dimensions simultaneously

[Timothy Hochberg]

On 9/11/07, Robert Kern <robert.kern at gmail.com> wrote:
>
> Mike Ressler wrote:
> > The following seems to be a wart: is it expected?
> >
> > Set up a 10x10 array and some indexing arrays:
> >
> > a=arange(100)
> > a.shape=(10,10)
> > q=array([0,2,4,6,8])
> > r=array([0,5])
> >
> > Suppose I want to extract only the "even" numbered rows from a - then
> >
> > print a[q,:]
> >
> > <works - output deleted>
> >
> > Every fifth column:
> >
> > print a[:,r]
> >
> > <works - output deleted>
> >
> > Only the even rows of every fifth column:
> >
> > print a[q,r]
> >
> >
> ---------------------------------------------------------------------------
> > <type 'exceptions.ValueError'>            Traceback (most recent call
> last)
> >
> > /.../.../.../<ipython console> in <module>()
> >
> > <type 'exceptions.ValueError'>: shape mismatch: objects cannot be
> > broadcast to a single shape
> >
> > But, this works:
> >
> > print a[q,:][:,r]
> >
> > [[ 0  5]
> >  [20 25]
> >  [40 45]
> >  [60 65]
> >  [80 85]]
> >
> > So why does the a[q,r] form have problems? Thanks for your insights.
>
> It is intended that the form a[q,r] be the general case: q and r are
> broadcasted
> against each other to a single shape. The result of the indexing is an
> array of
> that broadcasted shape with elements found by using each pair of elements
> in the
> broadcasted q and r arrays as indices.
>
> There are operations you can express with this form that you couldn't if
> the
> behavior that you expected were the case whereas you can get the result
> you want
> relatively straightforwardly.
>
> In [6]: a[q[:,newaxis], r]
> Out[6]:
> array([[ 0,  5],
>        [20, 25],
>        [40, 45],
>        [60, 65],
>        [80, 85]])



At the risk of making Robert grumpy: while it is true the form we ended up
with is more general I've come to the conclusion that it was a bit of a
mistake. In the spirit of making simple things simple and complex things
possible, I suspect that having fancy-indexing do the obvious thing here[1]
and delegating the more powerful but also more difficult to understand case
to a function or method would have been overall more useful. Cases where the
multidimensional features of fancy-indexing get used are messy enough that
they don't benefit much from the conciseness of the indexing notation, at
least in my experience.

-- 
.  __
.   |-\
.
.  tim.hochberg at ieee.org

[1] Just in case the 'obvious' thing isn't all that obvious: I mean restrict
index-arrays to one dimension and have them simply select the given values
along the axis. Hmmm. Without giving examples, which I have not time for
right now, that's probably not any clearer than saying nothing. Ah well.
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