Bracket indexing
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Bracket indexing ([]), or simply Indexing, is a special primitive function which uses the postcircumfix notation <syntaxhighlight lang=apl inline>X[Y]</source> instead of a normal prefix function. The result of <syntaxhighlight lang=apl inline>X[Y]</source> is an array formed with items of X extracted by the index specification Y.
Indexing modes
Simple indexing
Most APL implementations support only this mode of indexing. In its simplest form, <syntaxhighlight lang=apl inline>X[Y]</source> 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]</source> is a Y-shaped array which contains the indexed results.
<syntaxhighlight lang=apl>
'ABCDE'[2]
B
'ABCDE'[2 3⍴1 2 3 4 5 1]
ABC DEA </source>
For higher-rank array X with rank n, the notation <syntaxhighlight lang=apl inline>X[Y1;Y2;...;Yn]</source> selects the indexes of X over each axis. If some <syntaxhighlight lang=apl inline>Yk</source> is omitted, it implies all indices of k-th axis is selected, which is equivalent to specifying <syntaxhighlight lang=apl inline>⍳(⍴X)[k]</source>. 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 50 60 70 80 90 100 110 120
130 140 150 160 170 180 190 200 210 220 230 240
A[1;1;1]
10
A[2;3 2;4 1]
240 210 200 170
A[;2;] 50 60 70 80
170 180 190 200 </source>
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]</source> from a matrix X by single indexing.
Choose indexing
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
10 20 30 40 50 60 70 80
M[⊂1 2]
20
M[2 2⍴⊂2 4]
80 80 80 80
M[(2 1)(1 2)]
50 20
'Z'[3⍴⊂⍬] ⍝ Scalar X can be indexed using enclosed empty vector
ZZZ </source>
Reach indexing
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←2 3⍴G,('MNO' 5)('PQR' 6)
G
┌───────┬───────┬───────┐ │┌───┬─┐│┌───┬─┐│┌───┬─┐│ ││ABC│1│││DEF│2│││GHI│3││ │└───┴─┘│└───┴─┘│└───┴─┘│ ├───────┼───────┼───────┤ │┌───┬─┐│┌───┬─┐│┌───┬─┐│ ││JKL│4│││MNO│5│││PQR│6││ │└───┴─┘│└───┴─┘│└───┴─┘│ └───────┴───────┴───────┘
G[((1 2)1)((2 3)2)]
┌───┬─┐ │DEF│6│ └───┴─┘
G[2 2⍴⊂(2 2)2]
5 5 5 5
G[⊂⊂1 1]
┌───────┐ │┌───┬─┐│ ││ABC│1││ │└───┴─┘│ └───────┘ </source>
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.
See also
External links
Documentation