Difference between revisions of "Rank"

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:''This page is about array rank, a number associated with every array. For numbers associated with a function specifying its argument rank, see [[function rank]]. For the operator that applies a function at a given rank, see [[Rank (operator)]].''
 
:''This page is about array rank, a number associated with every array. For numbers associated with a function specifying its argument rank, see [[function rank]]. For the operator that applies a function at a given rank, see [[Rank (operator)]].''
  
In the APL [[array model]], the '''rank''' of an array is the number of dimensions or [[Axis|axes]] in its structure, or the length of its [[shape]]. The traditional expression for the rank of an array <source lang=apl inline>A</source> is <source lang=apl inline>⍴⍴A</source>. Because this expression results in a one-element [[vector]] rather than a [[scalar]], it is idiomatic in languages with a [[Tally]] function to write <source lang=apl inline>≢⍴A</source> instead.
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In the APL [[array model]], the '''rank''' of an [[array]] is the number of dimensions or [[Axis|axes]] in its structure, or the length of its [[shape]]. The traditional expression for the rank of an array <source lang=apl inline>A</source> is <source lang=apl inline>⍴⍴A</source>. Because this expression results in a one-element [[vector]] rather than a [[scalar]], it is idiomatic in languages with a [[Tally]] function to write <source lang=apl inline>≢⍴A</source> instead.
  
 
Arrays are given names based on their rank:
 
Arrays are given names based on their rank:

Latest revision as of 08:21, 18 February 2021

This page is about array rank, a number associated with every array. For numbers associated with a function specifying its argument rank, see function rank. For the operator that applies a function at a given rank, see Rank (operator).

In the APL array model, the rank of an array is the number of dimensions or axes in its structure, or the length of its shape. The traditional expression for the rank of an array A is ⍴⍴A. Because this expression results in a one-element vector rather than a scalar, it is idiomatic in languages with a Tally function to write ≢⍴A instead.

Arrays are given names based on their rank:

Rank Name
0 scalar
1 vector
2 matrix

Many APLs have a maximum rank. A function that would produce an array with rank greater than this maximum typically gives a LIMIT ERROR.

External Links

APL features [edit]
Built-ins Primitive functionPrimitive operatorQuad name
Array model ShapeRankDepthBoundIndex (Indexing) ∙ AxisRavelRavel orderElementScalarVectorMatrixSimple scalarSimple arrayNested arrayCellMajor cellSubarrayEmpty arrayPrototype
Data types Number (Boolean, Complex number) ∙ Character (String) ∙ BoxNamespace
Concepts and paradigms Leading axis theoryScalar extensionConformabilityLeading axis agreementScalar functionPervasionGlyphIdentity elementComplex floorTotal array ordering
Errors LIMIT ERRORRANK ERRORSYNTAX ERRORDOMAIN ERRORLENGTH ERRORINDEX ERRORVALUE ERROR