f must be a dyadic primitive scalar function, or a dyadic primitive mixed function taken from Table 15 below. B must be a numeric scalar or vector. X and Y may be any arrays whose items are appropriate to function f. Axis does not follow the normal syntax of an operator.
Table 15: Primitive dyadic mixed functions with optional axis.
| Function | Name | Range of B |
|---|---|---|
| / or ⌿ | Replicate | B∊⍳⍴⍴Y |
| \ or ⍀ | Expand | B∊⍳⍴⍴Y |
| ⊂ | Partitioned Enclose | B∊⍳⍴⍴Y |
| ⌽ or ⊖ | Rotate | B∊⍳⍴⍴Y |
| , or ⍪ | Catenate | B∊⍳⍴⍴Y |
| , or ⍪ | Laminate | (0≠1|B)^(B>⎕IO-1)^(B<⎕IO+(⍴⍴X)⌈⍴⍴Y) |
| ↑ | Take | one or more axes of Y |
| ↓ | Drop | one or more axes of Y |
| ⌷ | Index | one or more axes of Y |
In most cases, B must be an integer value identifying the axis of X and Y along which function f is to be applied.
Exceptionally, B must be a fractional value for the Laminate function (,) whose upper and lower integer bounds identify a pair of axes or an extreme axis of X and Y. For Take (↑) and Drop (↓), B can be a vector of two or more axes.
⎕IO is an implicit argument of the derived function which determines the meaning of B.
Examples
1 4 5 =[1] 3 2⍴⍳6 1 0 0 1 1 0 2 ¯2 1/[2]2 3⍴'ABCDEF' AA C DD F 'ABC',[1.1]'=' A= B= C= 'ABC',[0.1]'=' ABC === ⎕IO←O 'ABC',[¯0.5]'=' ABC ===
Axis with Scalar Dyadic Functions
The axis operator [X] can take a scalar dyadic function as operand. This has the effect of "stretching" a lower rank array to fit a higher rank one. The arguments must be conformable along the specified axis (or axes) with elements of the lower rank array being replicated along the other axes.
For example, if H is the higher rank array, L the lower rank one, X is an axis specification, and f a scalar dyadic function, then the expressions Hf[X]L and Lf[X]H are conformable if (⍴L)←→(⍴H)[X]. Each element of L is replicated along the remaining (⍴H)~X axes of H.
In the special case where both arguments have the same rank, the right one will play the role of the higher rank array. If R is the right argument, L the left argument, X is an axis specification and f a scalar dyadic function, then the expression Lf[X]R is conformable if (⍴L)←→(⍴R)[X].
Examples
mat 10 20 30 40 50 60 mat+[1]1 2 ⍝ add along first axis 11 21 31 42 52 62 mat+[2]1 2 3 ⍝ add along last axis 11 22 33 41 52 63 cube 100 200 300 400 500 600 700 800 900 1000 1100 1200 cube+[1]1 2 101 201 301 401 501 601 702 802 902 1002 1102 1202 cube+[3]1 2 3 101 202 303 401 502 603 701 802 903 1001 1102 1203 cube+[2 3]mat 110 220 330 440 550 660 710 820 930 1040 1150 1260
cube+[1 3]mat 110 220 330 410 520 630 740 850 960 1040 1150 1260