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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.


      (≡⍴)¨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
      '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

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APL features [edit]
Built-ins Primitive functionPrimitive operatorQuad name
Array model ShapeRankDepthBoundIndexAxisRavelRavel orderElementScalarVectorMatrixSimple scalarSimple arrayNested arrayBoxCellMajor cellSubarrayEmpty arrayPrototype
Concepts and paradigms Leading axis theoryScalar extensionConformabilityScalar functionGlyphIdentity element
APL built-ins [edit]
Primitive functions
Monadic ConjugateNotRollType
Dyadic AddSubtractEqual to (Xnor) ∙ Not Equal to (Xor)
Structural ShapeReshapeTallyDepthRavelReverseRazeMixCut (K)
Selection TakeDropUniqueIdentity
Selector Interval Index
Computational MatchNot MatchNub Sieve
Primitive operators Each
Quad names
Arrays Index originMigration level
Other ZildeHigh minusFunction axis