Difference between revisions of "Function axis"

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Miraheze>Adám Brudzewsky
Miraheze>Adám Brudzewsky
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In many APLs the behavior of a function may be modified using bracket notation, 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.
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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]]).
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== External links ==
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=== Documentation ===
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* [https://help.dyalog.com/latest/index.htm#Language/Primitive%20Operators/Operators%20Summarised.htm Dyalog]
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* [http://microapl.com/apl_help/ch_020_010_020.htm APLX]
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=== Lesson ===
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* [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

[ax]

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).

External links

Documentation

Lesson

Template:APL programming language