Function axis: Difference between revisions
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{{Built-in|Bracket axis|[ax]}} or '''function axis''' is the a special syntax whereby many APLs allow the behavior of a function to be modified, 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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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 [[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 == | |||
=== Documentation === | |||
* [https://help.dyalog.com/latest/index.htm#Language/Primitive%20Operators/Operators%20Summarised.htm Dyalog] | |||
* [http://microapl.com/apl_help/ch_020_010_020.htm APLX] | |||
=== Lesson === | |||
* [https://chat.stackexchange.com/rooms/52405/conversation/lesson-3-some-apl-operators-----#message-40898783 APL Cultivation] | |||
{{APL programming language}} | {{APL programming language}} | ||
Revision as of 02:31, 4 November 2019
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Bracket axis ([ax]) or function axis is the a special syntax whereby many APLs allow the behavior of a function to be modified, for example ⌽[2] 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
Monadic functions
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.
Dyadic functions
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.
Operators
The following operators may admit axis specification:
- Reduction removes 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).