Difference between revisions of "Function axis"

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Miraheze>Adám Brudzewsky
m (Adám Brudzewsky moved page Function axis to Bracket axis: New name covers ops too)
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.
 
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.
  
== Functions with Axis ==
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== Functions ==
 
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=== Monadic functions ===
 
The following [[Monadic function|monads]] may allow an axis:
 
The following [[Monadic function|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.
 
* [[Mix]] accepts a list of axes to specify where the axes of argument elements will be placed in the result.
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* [[Split]] accepts a single axis, and encloses each [[vector]] along that axis.
 
* [[Split]] accepts a single axis, and encloses each [[vector]] along that axis.
 
* [[Reverse]] reverses along the specified axis.
 
* [[Reverse]] reverses along the specified axis.
 
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=== Dyadic functions ===
 
The following [[Dyadic function|dyads]] may allow one:
 
The following [[Dyadic function|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.
 
* [[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.
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* [[Partition]] and [[Partitioned Enclose]] have complicated and different behavior.
 
* [[Partition]] and [[Partitioned Enclose]] have complicated and different behavior.
  
Additionally, [[reduction]] and [[scan]] operators may admit axis specification. 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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== Operators ==
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The following [[operator]]s may admit axis specification:
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* [[Reduction]] removes the specified right argument axis.
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* [[Scan]] works on the specified right argument axis.
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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]]).
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{{APL programming language}}
 
{{APL programming language}}

Revision as of 02:20, 4 November 2019

In many APLs the behavior of a function may be modified using bracket notation, 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).

Template:APL programming language