Function axis: Difference between revisions
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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 | == Functions == | ||
=== 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. | ||
=== 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. | ||
== Operators == | |||
The following [[operator]]s 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]]). | |||
{{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).