4,493
edits
Major cell: Difference between revisions
Jump to navigation
Jump to search
m
Text replacement - "</source>" to "</syntaxhighlight>"
m (Text replacement - " ⊢( *[^∘])" to " ⎕←$1") |
m (Text replacement - "</source>" to "</syntaxhighlight>") |
||
| (One intermediate revision by the same user not shown) | |||
| Line 1: | Line 1: | ||
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</syntaxhighlight> 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>⊖</syntaxhighlight>) 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</syntaxhighlight> is an array with [[shape]] <syntaxhighlight lang=apl inline>3 4</syntaxhighlight>. Using [[Tally]] we see that the number of major cells in <syntaxhighlight lang=apl inline>A</syntaxhighlight> is the first element of the shape, <syntaxhighlight lang=apl inline>3</syntaxhighlight>: | ||
< | <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 11: | Line 11: | ||
≢A | ≢A | ||
3 | 3 | ||
</ | </syntaxhighlight> | ||
We can separate < | We can separate <syntaxhighlight lang=apl inline>A</syntaxhighlight>'s major cells using [[Enclose]] with [[Rank operator|rank]] <syntaxhighlight lang=apl inline>¯1</syntaxhighlight>: | ||
< | <syntaxhighlight lang=apl> | ||
⊂⍤¯1 ⊢A | ⊂⍤¯1 ⊢A | ||
┌──────────┬─────────┬───────┐ | ┌──────────┬─────────┬───────┐ | ||
│10 15 20 5│6 3 12 15│2 3 4 5│ | │10 15 20 5│6 3 12 15│2 3 4 5│ | ||
└──────────┴─────────┴───────┘ | └──────────┴─────────┴───────┘ | ||
</ | </syntaxhighlight> | ||
Given another array < | Given another array <syntaxhighlight lang=apl inline>B</syntaxhighlight> we can search for cells of <syntaxhighlight lang=apl inline>B</syntaxhighlight> which [[match]] major cells of <syntaxhighlight lang=apl inline>B</syntaxhighlight>. [[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 | ||
| Line 29: | Line 29: | ||
A ⍳ 2 3 4 5 | A ⍳ 2 3 4 5 | ||
3 | 3 | ||
</ | </syntaxhighlight> | ||
{{APL features}}[[Category:Array relationships]] | {{APL features}}[[Category:Array relationships]] | ||