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]].''
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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)]].''
  
 
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.
 
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.

Latest revision as of 12:38, 24 March 2020

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

Wikipedia

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 elementTotal array ordering
Errors LIMIT ERRORRANK ERRORSYNTAX ERROR