Roger wrote:
> "Empty frame" made sense when a frame was the axes of an array left over
> after you've accounted for the cell.
I don’t remember who introduced me to the idea, but I was first encountered
them, enchanted by the definitions:
- Axis: index in the shape of an array
- Dimension: Value at that index
So the noun A=:i.5 7 11 has three axes, and the dimensions 5x7x11. You can
box along the first axis with 1 <;.1 A, you can box along the second axis with
(‘’;1) <;.1 A and you can box along the third axis with (‘’;’’;1) <;.1 A .
Or you can move axes around with |: (both monad and dyad) and then use the
normal rank mechanisms to address the leading axes of the array*.
Some other primitive which allow you to address non-leading axes of an array
are:
- ;. NB. as seen above
- |. NB. the LHA can be a vector of length #$y; each atom in the vector
determines how much the corresponding axis of y is rotated
- {. NB. similar to |. except each atom of x determines the corresponding
dimension of y . Similarly for }. .
- |: NB. Sorta. Any use changes all axes; some uses change rank too.
- } NB. Sorta; arbitrary amendments; doesn’t require that leading axes be
addressed, but all amendments must be rectangular. Cannot alter dimensions.
Sometimes I’ve wished A. followed the model of |. but currently its left rank
is 0 instead of 1 .
It would be an interesting exercise to imagine a J less heavily weighted
towards leading axes and “items”. Being able to easily address and manipulate
arbitrary axes would move J closer to an RDBMS or BI tool (think of a cube of
sales x month x customer x region x product).
Sometimes you want sales by month, sometimes you want customer by region,
sometimes you want product by customer, sometimes you want sales by product by
customer … . These differing perspectives account for e.g. why not all empty
arrays are the same: depending on which dimension is 0 (i.e. at which axis),
you might have no sales, or no customers, or no months …
-Dan
* Sometimes, after doing that, you’ll also have to reverse the effects of the
transpose (due to rank changes and/or boxing, sadly this often can not be
expressed with an elegant &. ).
----------------------------------------------------------------------
For information about J forums see http://www.jsoftware.com/forums.htm
