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The shape of an array is a [[vector]] of lengths of the array along each [[axis]]. The Shape function <code class="apl">⍴</code> is a [[monadic function]] which returns the shape of its argument array. The [[dyadic function]] [[Reshape]] (<code class="apl">⍴</code>) produces an array of the shape specified by its left argument.
{{Built-in|Shape|⍴}} is a [[monadic function]] which returns the ''shape'' of its argument array, namely a [[vector]] of lengths of the array along each [[axis]]. The [[dyadic function]] using the same symbol is [[Reshape]] which produces an array of the shape specified by its left argument.


An array's shape may be any vector of nonnegative integers with length less than or equal to the [[maximum rank]]. The length of an array's shape is the array's [[rank]], and the product of the shape is its [[bound]]. If the shape is [[Empty array]] then the array is a [[scalar]].
An array's shape may be any vector of nonnegative integers with length less than or equal to the [[maximum rank]]. The length of an array's shape is the array's [[rank]], and the product of the shape is its [[bound]]. If the shape is [[Empty array|empty]] then the array is a [[scalar]].


An array's shape, along with the [[index origin]], determine the possible values which can be used as an [[index]] into the array. A complete index is a vector of integers with the same length as the shape. When the index origin is subtracted from the index each element must be at least 0 and less than the corresponding element of the shape. In languages with [[negative indexing]] it may be greater than or equal to the negative of the shape rather than 0.
An array's shape, along with the [[index origin]], determine the possible values which can be used as an [[index]] into the array. A complete index is a vector of integers with the same length as the shape. When the index origin is subtracted from the index each element must be at least 0 and less than the corresponding element of the shape. In languages with [[negative indexing]] it may be greater than or equal to the negative of the shape rather than 0.
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== Examples ==
== Examples ==


<source class="apl">
<syntaxhighlight lang="apl">
       (⍬≡⍴)¨1 'A'                ⍝ The shape of a scalar is the empty numeric vector ⍬
       (⍬≡⍴)¨1 'A'                ⍝ The shape of a scalar is the empty numeric vector ⍬
1 1
1 1
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       ⍴'ABC'∘.,1 2 3 4∘.×0J1 1J2  ⍝ Two consecutive outer products result in a cuboid
       ⍴'ABC'∘.,1 2 3 4∘.×0J1 1J2  ⍝ Two consecutive outer products result in a cuboid
3 4 2
3 4 2
</source>
</syntaxhighlight>


{{APL programming language}}
== See also ==
* [[Tally]]
* [[Index generator]]
== External links ==
 
=== Lessons ===
 
* [https://chat.stackexchange.com/rooms/52405/conversation/lesson-10-apl-functions-- APL Cultivation]
* [https://www.sacrideo.us/apl-a-day-3-arrays-have-shape/ Arrays have Shape] (from [https://www.sacrideo.us/tag/apl-a-day/ APL a Day])
 
=== Documentation ===
 
* [https://help.dyalog.com/latest/index.htm#Language/Primitive%20Functions/Shape.htm Dyalog]
* [http://wiki.nars2000.org/index.php/Rho NARS2000]
* [http://microapl.com/apl_help/ch_020_020_460.htm APLX]
* [https://www.jsoftware.com/help/dictionary/d210.htm J Dictionary], [https://code.jsoftware.com/wiki/Vocabulary/dollar J NuVoc] (as <syntaxhighlight lang=apl inline>$</syntaxhighlight> "Shape Of")
* [https://mlochbaum.github.io/BQN/doc/shape.html BQN]
 
{{APL features}}
{{APL built-ins}}[[Category:Primitive functions]][[Category:Array characteristics]]

Latest revision as of 22:05, 10 September 2022

⍴

Shape (⍴) is a monadic function which returns the shape of its argument array, namely a vector of lengths of the array along each axis. The dyadic function using the same symbol is Reshape which produces an array of the shape specified by its left argument.

An array's shape may be any vector of nonnegative integers with length less than or equal to the maximum rank. The length of an array's shape is the array's rank, and the product of the shape is its bound. If the shape is empty then the array is a scalar.

An array's shape, along with the index origin, determine the possible values which can be used as an index into the array. A complete index is a vector of integers with the same length as the shape. When the index origin is subtracted from the index each element must be at least 0 and less than the corresponding element of the shape. In languages with negative indexing it may be greater than or equal to the negative of the shape rather than 0.

Examples

      (⍬≡⍴)¨1 'A'                 ⍝ The shape of a scalar is the empty numeric vector ⍬
1 1
      ⍴'ABCDE'                    ⍝ The shape of a vector is a length-1 vector
5
      ⍴'ABC'∘.,1 2 3 4            ⍝ The shape of the matrix result of an outer product
3 4
      ⍴'ABC'∘.,1 2 3 4∘.×0J1 1J2  ⍝ Two consecutive outer products result in a cuboid
3 4 2

See also

External links

Lessons

Documentation


APL features [edit]
Built-ins Primitives (functions, operators) ∙ Quad name
Array model Shape ∙ Rank ∙ Depth ∙ Bound ∙ Index (Indexing) ∙ Axis ∙ Ravel ∙ Ravel order ∙ Element ∙ Scalar ∙ Vector ∙ Matrix ∙ Simple scalar ∙ Simple array ∙ Nested array ∙ Cell ∙ Major cell ∙ Subarray ∙ Empty array ∙ Prototype
Data types Number (Boolean, Complex number) ∙ Character (String) ∙ Box ∙ Namespace ∙ Function array
Concepts and paradigms Conformability (Scalar extension, Leading axis agreement) ∙ Scalar function (Pervasion) ∙ Identity element ∙ Complex floor ∙ Array ordering (Total) ∙ Tacit programming (Function composition, Close composition) ∙ Glyph ∙ Leading axis theory ∙ Major cell search ∙ First-class function
Errors LIMIT ERROR ∙ RANK ERROR ∙ SYNTAX ERROR ∙ DOMAIN ERROR ∙ LENGTH ERROR ∙ INDEX ERROR ∙ VALUE ERROR ∙ EVOLUTION ERROR
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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