Function axis (
[ax]) is a special syntax which modifies the behavior of a function, for example
⌽ to Rotate along the second axis. Axis specification was a feature of Iverson notation and was ubiquitous in early APLs; many newer APLs which adhere to leading axis theory reject the use of axis specification in favor of the Rank operator because it is a fully general operator while the behavior of functions with axis must be defined for each function separately.
The following monads may allow an axis:
- Mix accepts a list of axes to specify where the axes of argument elements will be placed in the result.
- Ravel accepts a list of axes which are combined, or a single fractional number to add a length-1 axis.
- Enclose accepts a list of axes. Each subarray along these axes is enclosed.
- Split accepts a single axis, and encloses each vector along that axis.
- Reverse reverses along the specified axis.
The following dyads may allow one:
- Scalar dyadics accept a list of axes to override conformability rules: it specifies , for each axis in the lower-rank (or left, in case of a tie) argument, which axis in the other argument it is paired with.
- Catenate combines along the selected axis, adding a new axis if a non-integer axis is given.
- Rotate rotates the right argument along the selected axis.
- Replicate and Expand work on the specified right argument axis.
- Take and Drop modify the selected right argument axes.
- Squish takes axes to specify which axis of the right argument corresponds to each left argument element.
- Partition and Partitioned Enclose have complicated and different behavior.
The following operators may admit axis specification:
- Reduction removes the specified right argument axis.
- Scan works on the specified right argument axis.
Axis specification always modifies the derived function obtained from an operator, and not the operator itself. The exact syntax may vary: in most cases a set of brackets is parsed like a monadic operator and applies directly to the derived function; sometimes brackets can be applied directly to an operator, in which case the derived function produced by this operator is modified. In Dyalog APL, a slash with axis retains its function-operator overloading: it can be applied as an operator or as a dyadic function (Replicate or Expand).
|APL syntax |
|Overview||Comparison with traditional mathematics ∙ Precedence|
|Array||Numeric literal ∙ String ∙ Strand notation ∙ Object literal ∙ Array notation|
|Function||Argument ∙ Function valence ∙ Derived function ∙ Function train ∙ Monadic function ∙ Dyadic function ∙ Ambivalent function|
|Operator||Operand ∙ Operator valence ∙ Derived function ∙ Derived operator|
|Assignment||Multiple ∙ Indexed ∙ Selective ∙ Modified|
|User definition||Tradfn ∙ Dfn ∙ Tacit|
|Other||Function axis ∙ Branching ∙ System command ∙ User command ∙ Keyword ∙ Dot notation|