Major cell

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In the APL array model and leading axis theory, a major cell, or item, is a cell of an array which has rank one smaller than the rank of the array, or equal to it if the array is a scalar. The number of major cells in an array is its Tally, and a function can be called on the major cells of an array individually by applying it with rank <syntaxhighlight lang=apl inline>¯1</source> using the Rank operator. Functions designed to follow leading axis theory often manipulate the major cells of an array. For example, Reverse First (<syntaxhighlight lang=apl inline>⊖</source>) is considered the primary form of Reverse in leading-axis languages because it can be interpreted as reversing the major cells of its argument; J removes last-axis Reverse entirely.

Examples

<syntaxhighlight lang=apl inline>A</source> is an array with shape <syntaxhighlight lang=apl inline>3 4</source>. Using Tally we see that the number of major cells in <syntaxhighlight lang=apl inline>A</source> is the first element of the shape, <syntaxhighlight lang=apl inline>3</source>: <syntaxhighlight lang=apl>

     ⎕←A ← 5 3 1 ∘.∧ 2 3 4 5

10 15 20 5

6  3 12 15
2  3  4  5
     ≢A

3 </source> We can separate <syntaxhighlight lang=apl inline>A</source>'s major cells using Enclose with rank <syntaxhighlight lang=apl inline>¯1</source>: <syntaxhighlight lang=apl>

     ⊂⍤¯1 ⊢A

┌──────────┬─────────┬───────┐ │10 15 20 5│6 3 12 15│2 3 4 5│ └──────────┴─────────┴───────┘ </source> Given another array <syntaxhighlight lang=apl inline>B</source> we can search for cells of <syntaxhighlight lang=apl inline>B</source> which match major cells of <syntaxhighlight lang=apl inline>B</source>. High-rank Index-of always searches for right argument cells whose rank matches the rank of a left argument major cell: if the right argument is a vector and not a matrix then it searches for the entire vector rather than its major cells (which are scalars). <syntaxhighlight lang=apl>

     ⎕←B ← ↑ 4,/⍳6

1 2 3 4 2 3 4 5 3 4 5 6

     A ⍳ B

4 3 4

     A ⍳ 2 3 4 5

3 </source>


APL features [edit]
Built-ins Primitives (functions, operators) ∙ Quad name
Array model ShapeRankDepthBoundIndex (Indexing) ∙ AxisRavelRavel orderElementScalarVectorMatrixSimple scalarSimple arrayNested arrayCellMajor cellSubarrayEmpty arrayPrototype
Data types Number (Boolean, Complex number) ∙ Character (String) ∙ BoxNamespaceFunction array
Concepts and paradigms Conformability (Scalar extension, Leading axis agreement) ∙ Scalar function (Pervasion) ∙ Identity elementComplex floorArray ordering (Total) ∙ Tacit programming (Function composition, Close composition) ∙ GlyphLeading axis theoryMajor cell searchFirst-class function
Errors LIMIT ERRORRANK ERRORSYNTAX ERRORDOMAIN ERRORLENGTH ERRORINDEX ERRORVALUE ERROREVOLUTION ERROR