Expand

From APL Wiki
(Redirected from Expand First)
Jump to navigation Jump to search
\

Expand (\, ) is a dyadic function or monadic operator that copies each element of the right argument a given number of times and inserts prototype elements, ordering the copies along a specified axis. Typically \ is called Expand while is called "Expand First" or an equivalent.

Expand is usually associated with Replicate (/), and the two functions are related to Mesh and Mask. It shares a glyph with Scan even though Expand is naturally a function and Scan must be an operator. This incongruity is sometimes resolved by making Expand an operator itself, and sometimes by function-operator overloading allowing both syntactic elements to coexist.

Examples

If the right argument is a vector, the number of positive values in the left argument must match the length of the right argument. Each positive value produces copies of the corresponding item on the right argument; a zero or negative value produces one or more prototype elements.

      1 0 3 ¯2 2\'abc'
a bbb  cc

For Boolean left argument, Expand is the right inverse of Replicate, as Expand inserts prototype elements at the exact places which Replicate will remove:

      1 0 0 1 0 1\'abc'
a  b c
      1 0 0 1 0 1/'a  b c'
abc

High-rank arrays

Expand works along a particular axis, which can be specified in languages with function axis and otherwise is the first axis for , and the last axis for \.

      A3 4⎕A
ABCD
EFGH
IJKL
      1 0 3 2 ¯2 1\A
A BBBCC  D
E FFFGG  H
I JJJKK  L
      3 1 ¯1 2A
ABCD
ABCD
ABCD
EFGH
    
IJKL
IJKL

Some implementations allow the right argument to have length 1 along the expansion axis even if other axes have lengths not equal to 1.

      1 ¯2 3 \ 'abc'
a  aaa
b  bbb
c  ccc

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