Expand

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\ ⍀

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 \. 

      ⎕←A←3 4⍴⎕A
ABCD
EFGH
IJKL
      1 0 3 2 ¯2 1\A
A BBBCC  D
E FFFGG  H
I JJJKK  L
      3 1 ¯1 2⍀A
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]
Primitives (Timeline) Functions
Scalar
Monadic Conjugate ∙ Negate ∙ Signum ∙ Reciprocal ∙ Magnitude ∙ Exponential ∙ Natural Logarithm ∙ Floor ∙ Ceiling ∙ Factorial ∙ Not ∙ Pi Times ∙ Roll ∙ Type ∙ Imaginary ∙ Square Root ∙ Round
Dyadic Add ∙ Subtract ∙ Times ∙ Divide ∙ Residue ∙ Power ∙ Logarithm ∙ Minimum ∙ Maximum ∙ Binomial ∙ Comparison functions ∙ Boolean functions (And, Or, Nand, Nor) ∙ GCD ∙ LCM ∙ Circular ∙ Complex ∙ Root
Non-Scalar
Structural Shape ∙ Reshape ∙ Tally ∙ Depth ∙ Ravel ∙ Enlist ∙ Table ∙ Catenate ∙ Reverse ∙ Rotate ∙ Transpose ∙ Raze ∙ Mix ∙ Split ∙ Enclose ∙ Nest ∙ Cut (K) ∙ Pair ∙ Link ∙ Partitioned Enclose ∙ Partition
Selection First ∙ Pick ∙ Take ∙ Drop ∙ Unique ∙ Identity ∙ Stop ∙ Select ∙ Replicate ∙ Expand ∙ Set functions (Intersection ∙ Union ∙ Without) ∙ Bracket indexing ∙ Index ∙ Cartesian Product ∙ Sort
Selector Index generator ∙ Grade ∙ Index Of ∙ Interval Index ∙ Indices ∙ Deal ∙ Prefix and suffix vectors
Computational Match ∙ Not Match ∙ Membership ∙ Find ∙ Nub Sieve ∙ Encode ∙ Decode ∙ Matrix Inverse ∙ Matrix Divide ∙ Format ∙ Execute ∙ Materialise ∙ Range
Operators Monadic Each ∙ Commute ∙ Constant ∙ Replicate ∙ Expand ∙ Reduce ∙ Windowed Reduce ∙ Scan ∙ Outer Product ∙ Key ∙ I-Beam ∙ Spawn ∙ Function axis ∙ Identity (Null, Ident)
Dyadic Bind ∙ Compositions (Compose, Reverse Compose, Beside, Withe, Atop, Over) ∙ Inner Product ∙ Determinant ∙ Power ∙ At ∙ Under ∙ Rank ∙ Depth ∙ Variant ∙ Stencil ∙ Cut ∙ Direct definition (operator) ∙ Identity (Lev, Dex)
Quad names Index origin ∙ Comparison tolerance ∙ Migration level ∙ Atomic vector
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