Axis Operator

A number of primitive functions and operators can be applied to a particular axis (or dimension) of an array. The [ ] brackets are used to indicate the axis being specified.

The highest dimension of a data item is considered to be the first dimension and the lowest dimension the last . Thus the first dimension of a matrix is the rows and the last dimension is the columns. In the case of a three-dimensional object, the first dimension is the planes followed by the rows and columns.

Axis numbers are governed by the Index Origin, ⎕IO, and in Index Origin 1, (the default), the first dimension is represented by [1], the second by [2] and so on. In Index Origin 0 the first dimension would be [0], the second [1] and so on. The number used to represent the axis is always a whole number, except for the ravel and laminate functions.

The primitive functions and operators which will accept an axis operator include the dyadic forms of the primitive scalar functions :

     + - × ÷ | ⌈ ⌊ * ⍟ ○ ! ^ ∨ ⍲ ⍱ < ≤ = ≥ > ≠

and some primitive mixed functions :

     , ⍪       Ravel/Catenate/Laminate       (note first axis variant)
     ⌽ ⊖       Reverse/Rotate                (note first axis variant)
     ⊂         Enclose/Partition
     ⊃         Disclose
     ↑         Take
     ↓         Drop
     ⌷         Index

as well as the operators:

     / ⌿       Compress/Replicate            (note first axis variant)
     / ⌿       Reduce                        (note first axis variant)
     \ ⍀       Scan                          (note first axis variant)
     \ ⍀       Expand                        (note first axis variant)

See the reference section entry for Axis ([]) for more details, as well as the reference entries for individual mixed functions and operators listed above.