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{{Built-in|Bracket indexing|<nowiki>[]</nowiki>}}, or simply '''Indexing''', is a special [[primitive function]] which uses the | {{Built-in|Bracket indexing|<nowiki>[]</nowiki>}}, or simply '''Indexing''', is a special [[primitive function]] which uses the postcircumfix notation <syntaxhighlight lang=apl inline>X[Y]</syntaxhighlight> instead of a normal prefix function. The result of <syntaxhighlight lang=apl inline>X[Y]</syntaxhighlight> is an array formed with items of X extracted by the [[index]] specification Y. | ||
== Indexing modes == | == Indexing modes == | ||
| Line 5: | Line 5: | ||
=== Simple indexing === | === Simple indexing === | ||
Most APL implementations support only this mode of indexing. In its simplest form, < | Most APL implementations support only this mode of indexing. In its simplest form, <syntaxhighlight lang=apl inline>X[Y]</syntaxhighlight> on vector X and scalar Y extracts the item of X at index Y. In general, Y can be an array of any shape, with each item being a valid index in X; then <syntaxhighlight lang=apl inline>X[Y]</syntaxhighlight> is a Y-shaped array which contains the indexed results. | ||
< | <syntaxhighlight lang=apl> | ||
'ABCDE'[2] | 'ABCDE'[2] | ||
B | B | ||
| Line 13: | Line 13: | ||
ABC | ABC | ||
DEA | DEA | ||
</ | </syntaxhighlight> | ||
For higher-[[rank]] array X with rank n, the notation < | For higher-[[rank]] array X with rank n, the notation <syntaxhighlight lang=apl inline>X[Y1;Y2;...;Yn]</syntaxhighlight> selects the indexes of X over each axis. If some <syntaxhighlight lang=apl inline>Yk</syntaxhighlight> is omitted, it implies all indices of k-th axis is selected, which is equivalent to specifying <syntaxhighlight lang=apl inline>⍳(⍴X)[k]</syntaxhighlight>. The resulting shape is the concatenation of shapes of Y1, Y2, ..., Yn. | ||
< | <syntaxhighlight lang=apl> | ||
⎕←A←2 3 4⍴10×⍳24 | |||
10 20 30 40 | 10 20 30 40 | ||
50 60 70 80 | 50 60 70 80 | ||
| Line 37: | Line 37: | ||
50 60 70 80 | 50 60 70 80 | ||
170 180 190 200 | 170 180 190 200 | ||
</ | </syntaxhighlight> | ||
The major limitation of this indexing mode is that it only supports rectangular selection. For example, it is not possible to form < | The major limitation of this indexing mode is that it only supports rectangular selection. For example, it is not possible to form <syntaxhighlight lang=apl inline>X[1;1],X[2;2]</syntaxhighlight> from a matrix X by single indexing. | ||
=== Choose indexing === | === Choose indexing === | ||
| Line 45: | Line 45: | ||
In this mode, the index specification Y is a [[depth]]-2 [[nested array]]. Each item of Y is a vector whose length is the rank of X, and the result is a collection of items of X selected by each item of Y. | In this mode, the index specification Y is a [[depth]]-2 [[nested array]]. Each item of Y is a vector whose length is the rank of X, and the result is a collection of items of X selected by each item of Y. | ||
< | <syntaxhighlight lang=apl> | ||
M | M | ||
10 20 30 40 | 10 20 30 40 | ||
| Line 62: | Line 62: | ||
'Z'[3⍴⊂⍬] ⍝ Scalar X can be indexed using enclosed empty vector | 'Z'[3⍴⊂⍬] ⍝ Scalar X can be indexed using enclosed empty vector | ||
ZZZ | ZZZ | ||
</ | </syntaxhighlight> | ||
=== Reach indexing === | === Reach indexing === | ||
| Line 68: | Line 68: | ||
In this mode, Y is a depth-3 nested array. Each item of Y is a vector of nested vectors which specify the index at each level of nesting (which is equivalent to the indexing by [[Pick]]). This allows to extract multiple items from a deeply nested array with a single indexing operation. | In this mode, Y is a depth-3 nested array. Each item of Y is a vector of nested vectors which specify the index at each level of nesting (which is equivalent to the indexing by [[Pick]]). This allows to extract multiple items from a deeply nested array with a single indexing operation. | ||
< | <syntaxhighlight lang=apl> | ||
G←('ABC' 1)('DEF' 2)('GHI' 3)('JKL' 4) | G←('ABC' 1)('DEF' 2)('GHI' 3)('JKL' 4) | ||
G←2 3⍴G,('MNO' 5)('PQR' 6) | G←2 3⍴G,('MNO' 5)('PQR' 6) | ||
| Line 96: | Line 96: | ||
│└───┴─┘│ | │└───┴─┘│ | ||
└───────┘ | └───────┘ | ||
</ | </syntaxhighlight> | ||
== Implementation support == | == Implementation support == | ||
[[Dyalog APL]] and [[NARS2000]] support all three modes of indexing. [[NARS2000]] even supports mixing Choose and Reach indexing modes. [[J]] does not have this notation at all. | [[Dyalog APL]] and [[NARS2000]] support all three modes of indexing. [[NARS2000]] even supports mixing Choose and Reach indexing modes. [[J]] does not have this notation at all. | ||
== See also == | |||
* [[Index (function)]] | |||
* [[Select]] | |||
== External links == | == External links == | ||
| Line 106: | Line 110: | ||
=== Documentation === | === Documentation === | ||
* [ | * [https://help.dyalog.com/latest/#Language/Primitive%20Functions/Indexing.htm Dyalog] | ||
* [http://wiki.nars2000.org/index.php/Indexing NARS2000] | * [http://wiki.nars2000.org/index.php/Indexing NARS2000] | ||
* [http://microapl.com/apl_help/ch_020_010_040.htm APLX] | * [http://microapl.com/apl_help/ch_020_010_040.htm APLX] | ||
{{APL built-ins}}[[Category:Primitive functions]] | {{APL built-ins}}[[Category:Primitive functions]] | ||