Singleton: Difference between revisions
Jump to navigation
Jump to search
m (4 revisions imported: Migrate from miraheze) |
No edit summary |
||
| Line 1: | Line 1: | ||
A '''singleton''' is an array with [[bound]] 1. Equivalently, its [[shape]] consists entirely of 1s. It may have any [[rank]]. | A '''singleton''' is an [[array]] with [[bound]] 1. Equivalently, its [[shape]] consists entirely of 1s. It may have any [[rank]]. For example, all the following are singletons: | ||
* The [[scalar]] <source lang=apl inline>42</source> | |||
* The [[vector]] <source lang=apl inline>,42</source> | |||
* The [[matrix]] <source lang=apl inline>⍪42</source> | |||
* The three-[[dimension]]al array <source lang=apl inline>1 1 1⍴42</source> | |||
* The [[nested]] scalar <source lang=apl inline>⊂4 2</source> | |||
Whether an array <source lang=apl inline>X</source> is a singleton can be determined with <source lang=apl inline>1=×/⍴X</source> or, less efficiently, with <source lang=apl inline>1=≢,X</source>. | |||
Every scalar <source lang=apl inline>X</source> is a singleton, because <source lang=apl inline>1=×/⍴X</source>, or alternatively <source lang=apl inline>1=≢,X</source>. | |||
Singletons may be subject to [[singleton extension]]. | Singletons may be subject to [[singleton extension]]. | ||
{{APL features}} | |||
Revision as of 11:07, 26 December 2019
A singleton is an array with bound 1. Equivalently, its shape consists entirely of 1s. It may have any rank. For example, all the following are singletons:
- The scalar
42 - The vector
,42 - The matrix
⍪42 - The three-dimensional array
1 1 1⍴42 - The nested scalar
⊂4 2
Whether an array X is a singleton can be determined with 1=×/⍴X or, less efficiently, with 1=≢,X.
Every scalar X is a singleton, because 1=×/⍴X, or alternatively 1=≢,X.
Singletons may be subject to singleton extension.
| 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 |