{ encompasses everything performed by bracket indexing in other languages. The ranks are 0 _ , that is, x{y can be considered individually for each scalar in x and for y in toto, with the overall result constructed from the individual results in the same way as for all other functions. For scalar x then: >x is a scalar or a list, and r=:>j{,>x are the indices for axis j. r may be integers in the range i.&.(+&n)n=:j{$y, which selects cells n|r, or r may be boxed integers in that range, in which case the selected cells are all except those in n|r. Thus: |
z=: 0{y=: 3 3 3$'ABCDEFGHIJKLMNOPQRSTUVWXYZ]' ibbb=: <ibb=: <ib=: <i=: 1 _1 jbbb=: <jbb=: <jb=: <j=: 2 1 ijbbb=: <ijbb=: <ijb=: <ij=: 2 2$i,j (] ; i&{ ; ib&{ ; ibb&{ ; ibbb&{) z +-----------------+ ¦ABC¦DEF¦F¦DEF¦ABC¦ ¦DEF¦GHI¦ ¦GHI¦ ¦ ¦GHI¦ ¦ ¦ ¦ ¦ +-----------------+ ijb{y ¦rank error ¦ ijb {y (] ; i&{ ; ijbb&{ ; ijbbb&{) z +---------------+ ¦ABC¦DEF¦DEF¦ABC¦ ¦DEF¦GHI¦GHI¦ ¦ ¦GHI¦ ¦ ¦ ¦ ¦ ¦ ¦GHI¦ ¦ ¦ ¦ ¦DEF¦ ¦ +---------------+
The amend adverb } applied to an index produces a function that replaces the selected part of the right argument by the left argument. For example: |
'*' ib} z ABC DE* GHI ('def',:'ghi') i} z ABC def ghi (] ; i&{ ; ib&{ ; ibb&{ ; ibbb&{)"2 y +-----------------+ ¦ABC¦DEF¦F¦DEF¦ABC¦ ¦DEF¦GHI¦ ¦GHI¦ ¦ ¦GHI¦ ¦ ¦ ¦ ¦ +---+---+-+---+---¦ ¦JKL¦MNO¦O¦MNO¦JKL¦ ¦MNO¦PQR¦ ¦PQR¦ ¦ ¦PQR¦ ¦ ¦ ¦ ¦ +---+---+-+---+---¦ ¦STU¦VWX¦X¦VWX¦STU¦ ¦VWX¦YZ]¦ ¦YZ]¦ ¦ ¦YZ]¦ ¦ ¦ ¦ ¦ +-----------------+ $(<<'') { z 0 3 $(<a:) { z 0 3
Indexing on higher-rank arrays may be illustrated by the argument y: |
]k=: <1 2;a:;0 2 +------------+ ¦+----------+¦ ¦¦1 2¦++¦0 2¦¦ ¦¦ ¦¦¦¦ ¦¦ ¦¦ ¦++¦ ¦¦ ¦+----------+¦ +------------+ y ; k{y +------+ ¦ABC¦JL¦ ¦DEF¦MO¦ ¦GHI¦PR¦ ¦ ¦ ¦ ¦JKL¦SU¦ ¦MNO¦VX¦ ¦PQR¦Y]¦ ¦ ¦ ¦ ¦STU¦ ¦ ¦VWX¦ ¦ ¦YZ]¦ ¦ +------+
The following examples further illustrate the use of the indexing function. For each example, it may be instructive to plug the values into the expression r=:>j{,>x and work out the result.
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