Difference between revisions of "Function axis"
Miraheze>Marshall (Created page with "In many APLs the behavior of a function may be modified using bracket notation, for example <code>⌽[2]</code> to Rotate along the second axis. Axis specification was...") 

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−  +  {{BuiltinFunction 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 == 
−  +  === Monadic functions ===  
−  The following [[monads]] may allow an axis:  +  The following [[Monadic functionmonads]] 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.  
* [[Ravel]] accepts a list of axes which are combined, or a single fractional number to add a length1 axis.  * [[Ravel]] accepts a list of axes which are combined, or a single fractional number to add a length1 axis.  
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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 [[dyads]] may allow one:  +  The following [[Dyadic functiondyads]] may allow one: 
−  * [[Scalar  +  * [[Scalar functionScalar]] [[dyadic]]s accept a list of axes to override [[conformability]] rules: it specifies , for each axis in the lowerrank (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 noninteger axis is given.  * [[Catenate]] combines along the selected axis, adding a new axis if a noninteger 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.  
−  +  == 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 [[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 [[functionoperator 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/lesson3someaploperators#message40898783 APL Cultivation]  
+  
+  {{APL syntax}} 
Revision as of 16:22, 9 January 2020
[ax]

Function axis ([ax]
) is a special syntax which modifies the behavior of a function, 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.
Contents
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 length1 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 lowerrank (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 noninteger 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.
 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.
Operators
The following operators may admit axis specification:
 Reduction removes the specified right argument axis.
 Scan works on the specified right argument axis.
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 functionoperator overloading: it can be applied as an operator or as a dyadic function (Replicate or Expand).
External links
Documentation
Lesson