[Jprogramming] Fwd: Axis specification in APL2

[Roy A. Crabtree]

Normally, I would normalize into a broader view of the topic:  Shift into
fully associative arrays/relational model,
then "map" the sequence: look for broadly general patterns, and then fold
back in to the operational functors available
as a subset.

Whether or not bracket notation has any use in the face of any other axis
functoring becomes crystal clear at that point.

It is amazing how long the original APL spec stood up under such pressures
... and how well it serves as a basis
for the _differing_ "generalizations" of it.

Perhaps a single unifying generalization would help ...

On 6/22/06, Rob Hodgkinson <rhodgkin at bigpond.net.au> wrote:
>
> In your example below of non-applicable shapes, the transpose is required
> by
> the APL axis operator also as you point out, as in:
>    TX=. |:X
>    TX ; Y : TX+"1 Y
> +--------+-----+-------+
> |  0 300 | 0  1|  0 301|
> |100 400 | 2  3|  2 303|
> |200 500 | 4  5|  4 305|
> |        | 6  7|  6 307|
> |        |     |       |
> |        | 8  9|108 409|
> |        |10 11|110 411|
> |        |12 13|112 413|
> |        |14 15|114 415|
> |        |     |       |
> |        |16 17|216 517|
> |        |18 19|218 519|
> |        |20 21|220 521|
> |        |22 23|222 523|
> +--------+-----+-------+
> visually the data above is 'aligned' to add as we want - and now this is
> the
> same model as the original example.
>
> This is an example where I would stop and ask if X has been created with
> the
> wrong shape and it might be better to set it up originally as shape 3 2,
> then the transpose would never have been necessary.
>
> I can't see how the axis operator could have done the above without the
> transpose either, but better to review/revise the data model to avoid it
> in
> both cases.
>
> Note re your last example referring to this same data:
>    (X+"0 3 Y) -: (X+/Y)
> 1
>
> and your more complicated examples in your message, such as:
>    $(i.5 4,3   6) +"1"2 3 i.5,3 2   6
> 5 4 3 2 6
> ... I don't believe are possible with the Axis Operator, but would
> likewise
> be glad to be shown a solution, as also for an Axis example that can not
> be
> reproduced using Rank with no transpose.  I can't think of one.
>
> Regards, Rob Hodgkinson
>
> -----Original Message-----
> From: programming-bounces at jsoftware.com
> [mailto:programming-bounces at jsoftware.com] On Behalf Of Oleg Kobchenko
> Sent: Thursday, 22 June 2006 6:45 PM
> To: Programming forum
> Subject: Re: [Jprogramming] Fwd: Axis specification in APL2
>
> <...snip>
>
> Here's an example of non-applicable shapes:
>
>    X=. 100*i.2 3
>    Y=. i.3 4 2
>    X ; Y ; (|:X) +"1 Y
> +-----------+-----+-------+
> |  0 100 200| 0  1|  0 301|
> |300 400 500| 2  3|  2 303|
> |           | 4  5|  4 305|
> |           | 6  7|  6 307|
> |           |     |       |
> |           | 8  9|108 409|
> |           |10 11|110 411|
> |           |12 13|112 413|
> |           |14 15|114 415|
> |           |     |       |
> |           |16 17|216 517|
> |           |18 19|218 519|
> |           |20 21|220 521|
> |           |22 23|222 523|
> +-----------+-----+-------+
>
> it not possible to get the result above with
> rank only without transpose,
> although, it is possible to match + in a way
>    $X +"0 3 Y
> 2 3 3 4 2
> Can either of the two examples above be done
> with axis +[? ?]  without transpose?
>
> Can somebody provide an axis example,
> that really cannot be done with rank alone?
>
> <snip>
>
>
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