Difference between revisions of "Key"

From APL Wiki
Jump to navigation Jump to search
(wp link)
Line 2: Line 2:
  
 
== Description ==
 
== Description ==
Monadically, key will group identical major cells together and applies the [[function]] operand f to each unique key, and the indices of the elements matching that key.
+
[[Monadic]]ally, Key will group identical [[major cell]]s together and applies the [[function]] operand once for each unique major cell. The function is applied with the unique major cell as left argument, while the right argument is the indices of major cells that match it:
  
 
<source lang=apl>
 
<source lang=apl>
Line 17: Line 17:
 
</source>
 
</source>
  
In the dyadic case, key applies f to the elements of the right argument corresponding to the unique elements of the left.
+
In the [[dyadic]] case, Key applies the function to collections of major cells from the right argument corresponding to unique elements of the left argument:
  
 
<source lang=apl>
 
<source lang=apl>
Line 32: Line 32:
 
</source>
 
</source>
  
In fact, the monadic case <source lang=apl inline>f⌸⍵</source> is equivalent to <source lang=apl inline>f⌸ ⍳≢⍵</source>
+
The monadic case, <source lang=apl inline>f⌸Y</source> is equivalent to <source lang=apl inline>Y f⌸ ⍳≢Y</source>.
  
 
== External links ==
 
== External links ==

Revision as of 08:37, 16 January 2022

Key () is a primitive monadic operator which takes a dyadic function operand where specified keys group the indices or major cells of an argument. It was introduced in Dyalog APL version 14.0 and is commonly compared to SQL's GROUP BY statement.

Description

Monadically, Key will group identical major cells together and applies the function operand once for each unique major cell. The function is applied with the unique major cell as left argument, while the right argument is the indices of major cells that match it:

      {⍺⍵}'Mississippi'
┌─┬────────┐
M1       
├─┼────────┤
i2 5 8 11
├─┼────────┤
s3 4 6 7 
├─┼────────┤
p9 10    
└─┴────────┘

In the dyadic case, Key applies the function to collections of major cells from the right argument corresponding to unique elements of the left argument:

      'Mississippi'{⍺⍵}'ABCDEFGHIJK' 
┌─┬────┐
MA   
├─┼────┤
iBEHK
├─┼────┤
sCDFG
├─┼────┤
pIJ  
└─┴────┘

The monadic case, fY is equivalent to Y f ⍳≢Y.

External links

Lessons

Documentation


APL built-ins [edit]
Primitive functions
Scalar
Monadic ConjugateNegateSignumReciprocalMagnitudeExponentialNatural LogarithmFloorCeilingFactorialNotPi TimesRollTypeImaginarySquare Root
Dyadic AddSubtractTimesDivideResiduePowerLogarithmMinimumMaximumBinomialComparison functionsBoolean functions (And, Or, Nand, Nor) ∙ GCDLCMCircularComplexRoot
Non-Scalar
Structural ShapeReshapeTallyDepthRavelEnlistTableCatenateReverseRotateTransposeRazeMixSplitEncloseNestCut (K)PairLinkPartitioned EnclosePartition
Selection FirstPickTakeDropUniqueIdentitySelectReplicateExpandSet functions (IntersectionUnionWithout) ∙ Bracket indexingIndex
Selector Index generatorGradeIndex OfInterval IndexIndicesDeal
Computational MatchNot MatchMembershipFindNub SieveEncodeDecodeMatrix InverseMatrix DivideFormatExecuteMaterialiseRange
Primitive operators Monadic EachCommuteConstantReplicateExpandReduceWindowed ReduceScanOuter ProductKeyI-beamSpawnFunction axis
Dyadic BindCompositions (Compose, Reverse Compose, Beside, Withe, Atop, Over) ∙ Inner ProductPowerAtUnderRankDepthVariantStencilCut (J)
Quad names
Arrays Index originMigration levelAtomic vector
Functions Name classCase convertUnicode convert
Operators SearchReplace