3A. Indexing

{ 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.