Major cell
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 | Shape ∙ Rank ∙ Depth ∙ Bound ∙ Index (Indexing) ∙ Axis ∙ Ravel ∙ Ravel order ∙ Element ∙ Scalar ∙ Vector ∙ Matrix ∙ Simple scalar ∙ Simple array ∙ Nested array ∙ Cell ∙ Major cell ∙ Subarray ∙ Empty array ∙ Prototype |
| Data types | Number (Boolean, Complex number) ∙ Character (String) ∙ Box ∙ Namespace ∙ Function array |
| Concepts and paradigms | Conformability (Scalar extension, Leading axis agreement) ∙ Scalar function (Pervasion) ∙ Identity element ∙ Complex floor ∙ Array ordering (Total) ∙ Tacit programming (Function composition, Close composition) ∙ Glyph ∙ Leading axis theory ∙ Major cell search ∙ First-class function |
| Errors | LIMIT ERROR ∙ RANK ERROR ∙ SYNTAX ERROR ∙ DOMAIN ERROR ∙ LENGTH ERROR ∙ INDEX ERROR ∙ VALUE ERROR ∙ EVOLUTION ERROR |