Enclose

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⊂ <

Enclose (⊂, <), or Box, is a monadic primitive function which creates a nested scalar by wrapping its argument under one level of nesting. When used with function axis, only the selected axes of the given array are enclosed. This can be seen as a more general form of Split, which can only enclose (or split) one selected axis.

Examples

An enclosed array is a scalar, which is subject to scalar extension. This can be used to simulate outer product by a scalar function or one-sided Each (pair the entire right argument with each element of the left argument, or vice versa). A notable application of this behavior is the "chipmunk idiom" X⊃¨⊂Y, which simulates Y[X] for (possibly nested) vector Y and simple X. 

      1 2 3+⊂4 5 6  ⍝ Computes (1+4 5 6)(2+4 5 6)(3+4 5 6)
┌─────┬─────┬─────┐
│5 6 7│6 7 8│7 8 9│
└─────┴─────┴─────┘
      1 2 3,¨⊂4 5 6  ⍝ Computes (1,4 5 6)(2,4 5 6)(3,4 5 6)
┌───────┬───────┬───────┐
│1 4 5 6│2 4 5 6│3 4 5 6│
└───────┴───────┴───────┘
      (2 2⍴1 2 2 1)⊃¨⊂(1 2)(3 4)(5 6)  ⍝ "chipmunk" idiom
┌───┬───┐
│1 2│3 4│
├───┼───┤
│3 4│1 2│
└───┴───┘

Enclose with function axis can be used to move one or more axes to an extra level of nesting. 

      ⎕←M←2 3 4⍴⎕A
ABCD
EFGH
IJKL
    
MNOP
QRST
UVWX
      ⊂[3]M  ⍝ Enclose last axis; same as ↓M
┌────┬────┬────┐
│ABCD│EFGH│IJKL│
├────┼────┼────┤
│MNOP│QRST│UVWX│
└────┴────┴────┘
      ⊂[2 3]M  ⍝ Enclose two axes at once
┌────┬────┐
│ABCD│MNOP│
│EFGH│QRST│
│IJKL│UVWX│
└────┴────┘

      N←2 3 4 5⍴⎕A
      ⍴⊂[1 3]N  ⍝ Shape of the array is enclosed axes removed
3 5
      ⍴⊃⊂[1 3]N  ⍝ Shape of each element is the enclosed axes
2 4
Works in: Dyalog APL

Description

With no function axis, Enclose returns a scalar array whose only element is the argument. In the flat array model this means that the argument is placed in a box, and the result is this box as a scalar. In the nested array model it can simply be viewed as creating a new array. However, if the argument is a simple scalar, then the result will match the argument because nested array theory dicatates that simple scalars float.

Properties

Enclose (without axis) is the inverse of both Mix and First in the sense that either of these undoes the additional nesting introduced by Enclose.

External links

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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