[Numpy-discussion] rank-0 arrays

[eric jones]

Hey Konrad,

> 
> "eric jones" <eric at enthought.com> writes:
> 
> > Reductions and indexing return different types based on the number
of
> > dimensions of the input array:
> >
> > >>> b = sum(a)
> > >>> l = len(b) # or whatever
> >
> > This code works happily if "a" is 2 or more dimensions, but will
fail if
> > it is 1d because the sum(a) will return a scalar in this case.  To
write
> 
> And it should fail, because a rank-0 array is not a sequence, so it
> doesn't have a length.
> 

I disagree. You should not have to write special code to check for a
specific case.  It breaks one of the beauties of Numeric -- i.e. you can
write generic code that handles arrays of any size and type.  Any method
that works on a 1 or more d array should also work on 0d arrays.  If you
ask for its shape, it returns a tuple.  If you ask for its size it
returns its length along its "first" axis.  This will always be 1.  It
allows for generic code.

On this note:
I do not see the benefit of making a scalar type object that is separate
for 0d arrays.  It seems to remove instead of enhance capabilities.
What does a scalar object buy that simply using 0d arrays for that
purpose does not?

> 
> But there are valid examples in which it would be nice if scalars
> were arrays (but probably if  *all* scalars supported array
operations,
> not just those that were generated by indexing from arrays):
> 
> - a.shape  should return () for a scalar (and (len(a),) for any
>            sequence type)
> 
> - a.astype(N.Float) should also work for scalars
> 
> Similarly, it would be nice if complex operations (real/imaginary
> part) would work on integers and floats.

Yes, this is needed.  And I think the argument for it is similar as
having len() work on 0d arrays.  It allows for generic code.

> 
> There's one more annoying difference between scalars and arrays of
> any rank which I think should be removed in numarray:
> 
>   >>> 3 % -2
>   -1
>   >>> array(3) % 2
>   1
>   >>> fmod(3, -2)
>   1.0
> 
> I.e. the mod operation uses fmod() for arrays, but different rules
> for standard Python numbers.

I think you meant, 

>   >>> array(3) % -2
>   1

That is unfortunate.  It would be nice to clean this up.

eric