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

[Travis E. Oliphant]

Timothy Hochberg wrote:
>
>
> On 9/11/07, *Robert Kern* <robert.kern at gmail.com 
> <mailto: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.
This is a reasonable argument.    It is reasonable enough that I 
intentionally made an ix_ function to do what you want.

a[ix_(q,r)]

does as originally expected if a bit more line-noise.

-Travis