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|<code>⊇</code> <code>@</code> | |<code>⊇</code> <code>@</code> | ||
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'''From''' (<code>⊇</code> or <code>@</code> and also called '''Select''', or, [[humour]]ously, ''Sane Indexing'') is a [[primitive function]] that selects multiple [[major cell]]s of its right argument using an array of [[index|indices]] given by its left. The primitive often offers additional functionality for a [[nested]] left argument, which varies from one language to another. It appears in [[SAX]] (as < | '''From''' (<code>⊇</code> or <code>@</code> and also called '''Select''', or, [[humour]]ously, ''Sane Indexing'') is a [[primitive function]] that selects multiple [[major cell]]s of its right argument using an array of [[index|indices]] given by its left. The primitive often offers additional functionality for a [[nested]] left argument, which varies from one language to another. It appears in [[SAX]] (as <syntaxhighlight lang=apl inline>@</source>), [[Extended Dyalog APL]], [[dzaima/APL]], and [[KAP]] (as <syntaxhighlight lang=apl inline>⊇</source>), [[J]] (as <syntaxhighlight lang=j inline>{</source>), and [[BQN]] (as <code>⊏</code>). | ||
== Common usage == | == Common usage == | ||
Select is commonly used to reorder the major cells of an array. For example, the following shuffles any array into random order: | Select is commonly used to reorder the major cells of an array. For example, the following shuffles any array into random order: | ||
[https://tio.run/##SyzI0U2pTMzJT9dNrShJzUtJTfn/PzijNC0tJ/VR2wT7R70rHnXMeNS56FFX@6OuRVyP@qYChaEKFNQTk5JTUtPU//8HAA Try it online!]< | [https://tio.run/##SyzI0U2pTMzJT9dNrShJzUtJTfn/PzijNC0tJ/VR2wT7R70rHnXMeNS56FFX@6OuRVyP@qYChaEKFNQTk5JTUtPU//8HAA Try it online!]<syntaxhighlight lang=apl> | ||
Shuffle←?⍨∘≢⊇⊢ | Shuffle←?⍨∘≢⊇⊢ | ||
Shuffle 'abcdef' | Shuffle 'abcdef' | ||
fbdcea | fbdcea | ||
</source>{{Works in|[[dzaima/APL]], [[Extended Dyalog APL]]}} | </source>{{Works in|[[dzaima/APL]], [[Extended Dyalog APL]]}} | ||
Without Select, one would have to write < | Without Select, one would have to write <syntaxhighlight lang=apl inline>Shuffle←⊢⌷⍨∘⊂?⍨∘≢</source>. In this meaning, Select might be written as <syntaxhighlight lang=apl inline>⌷⍨∘⊂⍨</source> or <syntaxhighlight lang=apl inline>⌷⍤0 99</source> in [[Dyalog APL]] (where 99 exceeds the system's maximum array [[rank]]). | ||
In a case where the left argument is a permutation vector for the right argument, the functionality can rightfully be called ''Permute''. | In a case where the left argument is a permutation vector for the right argument, the functionality can rightfully be called ''Permute''. | ||
Select especially cleans up expressions for reordering. An ascending sort can be represented as < | Select especially cleans up expressions for reordering. An ascending sort can be represented as <syntaxhighlight lang=apl inline>⍋⊇⊢</source> and "sort by" can be written as <syntaxhighlight lang=apl inline>⊇⍨∘⍋</source>: | ||
[https://tio.run/##SyzI0U2pTMzJT9dNrShJzUtJTfn//1Hf1EdtE9QTk5JTUtUVHnW1P@pd8ahjxqPebgVjBUMFEyA2/f8fAA Try it online!]< | [https://tio.run/##SyzI0U2pTMzJT9dNrShJzUtJTfn//1Hf1EdtE9QTk5JTUtUVHnW1P@pd8ahjxqPebgVjBUMFEyA2/f8fAA Try it online!]<syntaxhighlight lang=apl> | ||
'abcde' ⊇⍨∘⍋ 3 1 4 1 5 | 'abcde' ⊇⍨∘⍋ 3 1 4 1 5 | ||
bdace | bdace | ||
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== Extensions == | == Extensions == | ||
=== Scatter-point === | === Scatter-point === | ||
In [[A Dictionary of APL]], [[J]], and [[SAX]], a boxed left argument indicates that each [[element]] will be used independently to select a [[cell]] of the argument. The behavior on a single element is very similar to APL's [[Index (function)|Index]] function. < | In [[A Dictionary of APL]], [[J]], and [[SAX]], a boxed left argument indicates that each [[element]] will be used independently to select a [[cell]] of the argument. The behavior on a single element is very similar to APL's [[Index (function)|Index]] function. <syntaxhighlight lang=j inline>{</source> has a left [[Function rank|rank]] of 0, so that results are [[mix]]ed together and those with different shapes may be padded with [[fill]]s. | ||
< | <syntaxhighlight lang=j> | ||
]a =. 4 4$(a.i.'A')}.a. | ]a =. 4 4$(a.i.'A')}.a. | ||
ABCD | ABCD | ||
| Line 38: | Line 38: | ||
APL | APL | ||
</source>{{Works in|[[J]]}} | </source>{{Works in|[[J]]}} | ||
In APL this extension can be defined as < | In APL this extension can be defined as <syntaxhighlight lang=apl inline>⌷⍨∘⊃⍨⍤0 ∞</source> thus allowing both the above usage and "scatter point indexing":<ref>[[Richard Park]]. [https://dyalog.tv/Webinar/?v=AgYDvSF2FfU Selecting from Arrays]. [[Dyalog Webinar]]. 16 Apr 2020. (Presented in the form <syntaxhighlight lang=apl inline>((⊃⊣)⌷⊢)⍤0 99</source>.)</ref> | ||
== History == | == History == | ||