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Bracket indexing: Difference between revisions
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{{Built-in|Bracket indexing|<nowiki>[]</nowiki>}}, or simply '''Indexing''', is a special [[primitive function]] which uses the postcircumfix notation < | {{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]</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 == | == Indexing modes == | ||
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=== 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]</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] | 'ABCDE'[2] | ||
B | B | ||
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</source> | </source> | ||
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]</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 | ⎕←A←2 3 4⍴10×⍳24 | ||
10 20 30 40 | 10 20 30 40 | ||
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</source> | </source> | ||
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]</source> from a matrix X by single indexing. | ||
=== Choose indexing === | === Choose indexing === | ||
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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 | ||
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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) | ||