[Numpy-discussion] rank-0 arrays are mutable scalars

[Huaiyu Zhu]

On Tue, 17 Sep 2002, Travis Oliphant wrote:

> > 	len(d) == Exception == d.shape[0]
> >
> > 	# Currently the last is wrong?
> 
> Agreed, but this is because d is an integer and out of Numerics control.
> This is a case for returning 0d arrays rather than Python scalars.

That is one problem.  It can be removed by using shape(d).  

More fundamentally, though, len(d) == shape(d)[0] == ()[0] => IndexError.
I think Konrad made this point a few days back.

> > 	size(d) == 1 == product(d.shape)
> >
> > 	# Currently the last is wrong
> 
> I disagree that this is wrong.  This works as described for me.

Right.  Change d.shape to shape(d) here (and in several other places).

> Why is this?  I thought you argued the other way for len(scalar).  Of
> course, one solution is that we could overwrite the len() function and
> allow it to work for scalars.

Raising exception is the correct behavior, not a problem to be solved.

> >
> > Conclusion 5: rank-0 int arrays should be allowed to act as indices.
> > 	See property 5.
> 
> Can't do this for lists and other builtin sequences.

If numarray defines a consistent set of behaviors for integer types that
is intuitively understandable, it might not be difficult to persuade core
Python to check against an abstract integer type.

> >   - Is there substantial difference in overhead between rank-0 arrays and
> >     scalars?
> 
> Yes.

That would be one major problem.  


However, after giving this some more thoughts, I'm starting to doubt the 
analogy I made.  The problem is that in the end there is still a need to 
index an array and obtain a good old immutable scalar.  So

- What notation should be used for this purpose?  We can use c[0] to get
  immutable scalars and c[0,] for rank-0 arrays / mutable scalars.  But 
  what about other ranks?  Python does not allow distinctions based on  
  a[1,1,1] versus a[(1,1,1)] or d[] versus d[()].

- This weakens the argument that rank-0 arrays are scalars, since that 
  argument is essentially based on sum(c) and c[0] being of the same type.

Huaiyu