Axis: Difference between revisions

In the APL [[array model]], an '''axis''' is one dimension along which the [[element]]s of an array are organized. The [[rank]] of an array is the number of axes it has, and the [[shape]] is the list of their lengths. The [[index]] of a single element of an array is composed of a one index along each axis. An index [[Index#Index along an axis|along one axis]] is a single number; in this sense, axes are one-dimensional.

The choice to give leading axes lower indices and trailing axes higher indices is related to the choice to put lower-order places at higher indices in the base representation functions [[Decode]] and [[Encode]]. This is known in the wider programming world as a [[wikipedia:Endianness|big-endian]] order. Because the base representation and axis ordering are in alignment, [[selection]] of an single element from an array satisfies the clean identity <source lang=apl inline>i⌷A</source> {{←→}} <source lang=apl inline>((⍴A)⊥i)⌷,A</source>. If base representation used the opposite order, both of Decode's arguments would need to be reversed.