Some languages and at least one (old) version of
APL identify atoms with 1-element vectors. This
treatment has consequences such as muddling the
treatment of unit axes. An example demonstrates what I mean:
If i is an array of integers and m is a matrix,
then i{m has shape ($i),(}.$m).
m=: 3 4$'abcdefghijkl'
m
abcd
efgh
ijkl
i=: 2 1 2 2 0
i{m
ijkl
efgh
ijkl
ijkl
$ i{m
5 4
($i),}.$m
5 4
Now consider the case when the index array is
an atom vs. when it is a one element vector:
$ 2{m
4
$ (,2){m
1 4
$ 2{"1 m
3
$ (,2){"1 m
3 1
If you identify atoms with 1-element lists, you
would be forced to identify 1-row matrices,
1-column matrices, and vectors. And on it goes.
----- Original Message -----
From: Terrence Brannon <[EMAIL PROTECTED]>
Date: Sunday, April 1, 2007 12:38 pm
Subject: [Jgeneral] "J for C Programmers" - atoms versus degenerate arrays
> On this page we see:
>
> <quote href="http://www.jsoftware.com/help/jforc/declarations.htm";>
> An atom is defined to have rank 0; therefore, its shape is an
> array with 0
> items, i. e. an empty array of rank 1.
> </quote>
>
> My question about this quote is: why wouldn't an atom be a rank-1
> array with
> 1 item of shape 1?
>
> An array with 0 items would have no data. An atom has data. I
> think an atom
> is more similar to a rank-1 array with shape 1 than a rank-1 array
> of shape
> 0.
>
> Continuing the the "Cells" section we see:
>
> <quote href="http://www.jsoftware.com/help/jforc/declarations.htm";>
> A rank-3 array of shape 4 5, 6 such as the one defined in C by the
> declaration
>
> int q[4][5][6];
>
> can be thought of as an array of 4 elements, each with rank 2 and
> shape 5 6,
> or as a 4x5 array of elements, each with rank 1 and shape 6, or as
> a 4x5x6
> array of rank-0 atoms.
> </quote>
>
> And my question is: on the bolded part: why not a 4x5x6 of rank-1
> atoms? But
> I think I know the answer to this. It is because a 4x5x6 array
> already has
> "boxes" for data on each axis and we simply need to pop "boxless"
> atoms in.
>
> But understanding my second question does not make my first
> question any
> clearer.
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