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{ 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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