Rank

From APL Wiki
Jump to navigation Jump to search
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]
Syntax ArrayFunctionOperatorAssignment
Built-ins Primitive functionPrimitive operatorQuad name
Array model ShapeRankDepthBoundIndexAxisRavelRavel orderElementScalarVectorMatrixSimple scalarSimple arrayNested arrayBoxCellMajor cellSubarrayEmpty arrayPrototype
User definition TradfnDfnTacit
Concepts and paradigms Leading axis theoryScalar extensionConformabilityScalar functionGlyphIdentity element
Errors LIMIT ERRORRANK ERROR