Major cell: Difference between revisions
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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 < | 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 == | == 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 | ⎕←A ← 5 3 1 ∘.∧ 2 3 4 5 | ||
10 15 20 5 | 10 15 20 5 | ||
| Line 12: | Line 12: | ||
3 | 3 | ||
</source> | </source> | ||
We can separate < | We can separate <syntaxhighlight lang=apl inline>A</source>'s major cells using [[Enclose]] with [[Rank operator|rank]] <syntaxhighlight lang=apl inline>¯1</source>: | ||
< | <syntaxhighlight lang=apl> | ||
⊂⍤¯1 ⊢A | ⊂⍤¯1 ⊢A | ||
┌──────────┬─────────┬───────┐ | ┌──────────┬─────────┬───────┐ | ||
| Line 19: | Line 19: | ||
└──────────┴─────────┴───────┘ | └──────────┴─────────┴───────┘ | ||
</source> | </source> | ||
Given another array < | 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 set functions|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 [[scalar]]s). | ||
< | <syntaxhighlight lang=apl> | ||
⎕←B ← ↑ 4,/⍳6 | ⎕←B ← ↑ 4,/⍳6 | ||
1 2 3 4 | 1 2 3 4 | ||
Revision as of 21:12, 10 September 2022
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 |