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Function axis: Difference between revisions
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Miraheze>Marshall m (Marshall moved page Bracket axis to Function axis over redirect: Eh, axis applies to the derived function (even if it was initially attached to an operator). We should name things after the functionality and not the syntax unless there is a really strong reason to do so.) |
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{{Built-in| | {{Built-in|Function axis|[ax]}} is a special syntax which modifies the behavior of a function, for example <source lang=apl inline>⌽[2]</source> 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. | ||
== Functions == | == Functions == | ||
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=== Dyadic functions === | === Dyadic functions === | ||
The following [[Dyadic function|dyads]] may allow one: | The following [[Dyadic function|dyads]] may allow one: | ||
* [[Scalar | * [[Scalar function|Scalar]] [[dyadic]]s 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. | * [[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. | * [[Rotate]] rotates the right argument along the selected axis. | ||
* [[Replicate]] and [[Expand]] work on the specified right argument axis. | * [[Replicate]] and [[Expand]] work on the specified right argument axis. | ||
* [[Take]] and [[Drop]] modify the selected right argument axes. | * [[Take]] and [[Drop]] modify the selected right argument axes. | ||
* [[ | * [[Squad indexing]] 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. | * [[Partition]] and [[Partitioned Enclose]] have complicated and different behavior. | ||
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* [[Scan]] works on the specified right argument axis. | * [[Scan]] works on the specified right argument axis. | ||
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]]). | In [[SHARP APL]], [[Replicate]] and [[Expand]] are also included in this category as they are operators and not functions. | ||
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]]). | |||
== External links == | == External links == | ||
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* [https://chat.stackexchange.com/rooms/52405/conversation/lesson-3-some-apl-operators-----#message-40898783 APL Cultivation] | * [https://chat.stackexchange.com/rooms/52405/conversation/lesson-3-some-apl-operators-----#message-40898783 APL Cultivation] | ||
{{APL | {{APL syntax}} | ||