Mastering Array Selection and Indexing in Data Processing
Selecting from Arrays
Richard Park (16/04/2020)
What? Indexing? Pfffft…
Selecting from Arrays: Audience
Mainly beginners
Experienced APLers also
Simple
Choose
Reach
The rank operator
⍤
Sane
Select
Choose
Cells
Simple
Choose
Reach
Indexed assignment
Modified assignment
Optimised
A←'YEAST'
⋄
A[3 4]←'E'
A←1 9
⋄
A[1]+←5
Cells, subarrays and elements
A←2 3 4
⍴⎕
A
Cells, subarrays and elements
⎕
←A←2 3 4
⍴⎕
A
ABCD
EFGH
IJKL
MNOP
QRST
UVWX
3D array
A ←
2
3 4
⍴⎕
A
3D Array
Major cell
: Matrix
Cells, subarrays and elements
Dimensions / Axes
A ← 2 3 4
⍴⎕
A
A ←
2
3 4
⍴⎕
A
A ← 2
3
4
⍴⎕
A
A ← 2 3
4
⍴⎕
A
I
J
E
K
F
G
A
B
C
L
H
D
M
N
O
P
A ← 2
3
4
⍴⎕
A
3D Array
Major cell
: Matrix
1-cell
:
Vector
Cells, subarrays and elements
M
N
O
U
V
W
X
Q
R
S
T
P
A ← 2 3
4
⍴⎕
A
3D Array
Major cell
: Matrix
1-cell
:
Vector
0-cell:
Scalar
I
J
K
L
E
F
G
H
A
B
C
D
Cells, subarrays and elements
I
J
K
E
F
G
A
B
C
L
H
D
A ← 2 3 4
⍴⎕
A
A[1;;]
ABCD
EFGH
IJKL
Simple indexing
I
J
K
E
F
G
A
B
C
L
H
D
A ← 2 3 4
⍴⎕
A
1
⌷
A
ABCD
EFGH
IJKL
Simple indexing
E
F
G
H
A ← 2 3 4
⍴⎕
A
A[1;2;]
EFGH
Simple indexing
E
F
G
H
A ← 2 3 4
⍴⎕
A
1 2
⌷
A
EFGH
Simple indexing
G
A ← 2 3 4
⍴⎕
A
A[1;2;3]
G
Simple indexing
G
A ← 2 3 4
⍴⎕
A
1 2 3
⌷
A
G
Simple indexing
Simple indexing
cat ← 'ABCD'
qty ← 1 10 100 1000
(cat
∊
'AD')
⌿
qty
1 1000
Simple indexing
cat ← 'ABCD'
qty ← 1 10 100 1000
qty[
⍸
cat
∊
'AD']
1 1000
U
V
W
Q
R
S
M
N
O
X
T
P
I
J
K
E
F
G
A
B
C
L
H
D
A ← 2 3 4
⍴⎕
A
A[1 2;2 3;3 4] (1 2)(2 3)(3 4)
⌷
A
GH
KL
ST
WX
Simple indexing
I
J
K
E
F
G
A
B
C
L
H
D
A ← 2 3 4
⍴⎕
A
A[1 2;1 3;1 4] (1 2)(1 3)(1 4)
⌷
A
AD
IL
MP
UX
Simple indexing
A ← 2 3 4
⍴⎕
A
ABCD
EFGH
IJKL
MNOP
QRST
UVWX
A[1 2;1 3;1 4] (1 2)(1 3)(1 4)
⌷
A
AD
IL
MP
UX
Simple indexing
A ← 2 3 4
⍴⎕
A
ABCD
EFGH
IJKL
MNOP
QRST
UVWX
A[
1
2;1 3;1 4] (1 2)(1 3)(1 4)
⌷
A
AD
IL
MP
UX
Simple indexing
A ← 2 3 4
⍴⎕
A
ABCD
EFGH
IJKL
MNOP
QRST
UVWX
A[1
2
;1 3;1 4] (1 2)(1 3)(1 4)
⌷
A
AD
IL
MP
UX
Simple indexing
A ← 2 3 4
⍴⎕
A
ABCD
EFGH
IJKL
MNOP
QRST
UVWX
A[1 2;1 3;1 4] (1 2)(1 3)(1 4)
⌷
A
AD
IL
MP
UX
Simple indexing
A ← 2 3 4
⍴⎕
A
ABCD
EFGH
IJKL
MNOP
QRST
UVWX
A[(1 1 1)(2 1 4)(1 3 4)]
APL
Choose indexing
A ← 2 3 4
⍴⎕
A
A
BCD
EFGH
IJK
L
MNO
P
QRST
UVWX
A[(
1 1 1
)(
2 1 4
)(
1 3 4
)]
APL
Choose indexing
nest←2 2 2
⍴
(2 2
⍴
'DYAL') 1 2 3 (2 2
⍴
'ABCD') ('AE' 'IO' 'U') 'NT' 4┌──
┬
─────────┐
│DY│1 │
│AL│ │
├
──
┼
─────────
┤
│2 │3 │
└──
┴
─────────┘
┌──
┬
─────────┐
│AB│┌──
┬
──
┬
─┐│
│CD││AE│IO│U││
│ │└──
┴
──
┴
─┘│
├
──
┼
─────────
┤
│NT│4 │
└──
┴
─────────┘
Reach indexing
nest[
⊂
2 1 2
]
┌─────────┐
│┌──
┬
──
┬
─┐│
││AE│IO│U││
│└──
┴
──
┴
─┘│
└─────────┘
⊂
2 1 2
┌─────┐
│2 1 2│
└─────┘
Reach indexing
nest
┌──
┬
─────────┐
│DY│1 │
│AL│ │
├
──
┼
─────────
┤
│2 │3 │
└──
┴
─────────┘
┌──
┬
─────────┐
│AB│
┌──
┬
──
┬
─┐
│
│CD│
│AE│IO│U│
│
│ │
└──
┴
──
┴
─┘
│
├
──
┼
─────────
┤
│NT│4 │
└──
┴
─────────┘
nest[
⊂
(
2 1 2
)
2
]
┌──┐
│IO│
└──┘
⊂
(2 1 2)2
┌─────────┐
│┌─────
┬
─┐│
││2 1 2│2││
│└─────
┴
─┘│
└─────────┘
Reach indexing
nest
┌──
┬
─────────┐
│DY│1 │
│AL│ │
├
──
┼
─────────
┤
│2 │3 │
└──
┴
─────────┘
┌──
┬
─────────┐
│AB│
┌──
┬
──
┬
─┐
│
│CD│
│AE│
IO
│U│
│
│ │
└──
┴
──
┴
─┘
│
├
──
┼
─────────
┤
│NT│4 │
└──
┴
─────────┘
nest[
⊂
(
2 1 2
)
2
(
2
)]
O
⊂
(2 1 2)2(2)
┌───────────┐
│┌─────
┬
─
┬
─┐│
││2 1 2│2│2││
│└─────
┴
─
┴
─┘│
└───────────┘
Reach indexing
nest
┌──
┬
─────────┐
│DY│1 │
│AL│ │
├
──
┼
─────────
┤
│2 │3 │
└──
┴
─────────┘
┌──
┬
─────────┐
│AB│
┌──
┬
──
┬
─┐
│
│CD│
│AE│
I
O
│U│
│
│ │
└──
┴
──
┴
─┘
│
├
──
┼
─────────
┤
│NT│4 │
└──
┴
─────────┘
DOMAIN ERROR
(
⊂
(2 1 2)2(2))
⌷
nest
∧
⊂
(2 1 2)2(2)
┌───────────┐
│┌─────
┬
─
┬
─┐│
││2 1 2│2│2││
│└─────
┴
─
┴
─┘│
└───────────┘
Reach indexing
nest
┌──
┬
─────────┐
│DY│1 │
│AL│ │
├
──
┼
─────────
┤
│2 │3 │
└──
┴
─────────┘
┌──
┬
─────────┐
│AB│
┌──
┬
──
┬
─┐
│
│CD│
│AE│
I
O
│U│
│
│ │
└──
┴
──
┴
─┘
│
├
──
┼
─────────
┤
│NT│4 │
└──
┴
─────────┘
((
2 1 2
))
2
(
2
)
⊃
nest
O
(2 1 2)2(2)
┌─────
┬
─
┬
─┐
│2 1 2│2│2│
└─────
┴
─
┴
─┘
Pick
Reach indexing
nest
┌──
┬
─────────┐
│DY│1 │
│AL│ │
├
──
┼
─────────
┤
│2 │3 │
└──
┴
─────────┘
┌──
┬
─────────┐
│AB│
┌──
┬
──
┬
─┐
│
│CD│
│AE│
I
O
│U│
│
│ │
└──
┴
──
┴
─┘
│
├
──
┼
─────────
┤
│NT│4 │
└──
┴
─────────┘
Pick
Reach indexing
⎕
←'this' 'that' 'the other thing'
┌────
┬
────
┬
───────────────┐
│this│that│the other thing│
└────
┴
────
┴
───────────────┘
3
⊃
'this' 'that' 'the other thing'
the other thing
Simple
Choose
Reach
Subarrays
0-cells
AKA
Scalars
Nested arrays
Indexing as a function
∴
you can use operators
Squad
⌷
A←2 3 4
⍴⎕
A
ABCD
EFGH
IJKL
MNOP
QRST
UVWX
2
⌷⍤
2
⊢
A 2
⌷
[2]A
EFGH
QRST
I
J
K
F
G
L
H
E
D
C
B
A
A ← 2 3 4
⍴⎕
A
2
⌷
[1]A
GH
KL
ST
WX
2
I
J
K
L
E
F
G
H
A
B
C
D
A ←
2
3 4
⍴⎕
A
2
⌷
[
1
]A
MNOP
QRST
UVWX
Squad with axis
⌷
[]
I
J
K
L
E
F
G
H
A
B
C
D
A ←
2 3 4
⍴⎕
A
2
⌷⍤
3
⊢
A
MNOP
QRST
UVWX
Squad with rank
⌷⍤
I
J
K
E
F
G
L
H
A
B
C
D
A ← 2
3
4
⍴⎕
A
2
⌷
[
2
]A
EFGH
QRST
Squad with axis
⌷
[]
I
J
K
E
F
G
L
H
A
B
C
D
A ←
2
3 4
⍴⎕
A
2
⌷⍤
2
⊢
A
EFGH
QRST
Squad with rank
⌷⍤
U
V
W
Q
R
S
M
N
O
X
T
P
I
J
K
E
F
G
L
H
A
B
C
D
A ←
2
3 4
⍴⎕
A
2
⌷⍤
2
⊢
A
EFGH
QRST
Squad with rank
⌷⍤
I
J
K
L
E
F
G
H
A
B
C
D
A ← 2 3
4
⍴⎕
A
2
⌷
[
3
]A
BFJ
NRV
Squad with axis
⌷
[]
I
J
K
L
E
F
G
H
A
B
C
D
A ← 2 3
4
⍴⎕
A
2
⌷⍤
1
⊢
A
BFJ
NRV
Squad with rank
⌷⍤
I
J
K
L
E
F
G
H
A
B
C
D
A ← 2 3
4
⍴⎕
A
2
⌷⍤
1
⊢
A
BFJ
NRV
Squad with rank
⌷⍤
I
J
K
L
E
F
G
H
A
B
C
D
A ← 2 3
4
⍴⎕
A
2
⌷⍤
1
⊢
A
BFJ
NRV
Squad with rank
⌷⍤
U
V
W
Q
R
S
M
N
O
X
T
P
I
J
K
L
E
F
G
H
A
B
C
D
A ← 2 3
4
⍴⎕
A
2
⌷⍤
1
⊢
A
BFJ
NRV
Squad with rank
⌷⍤
U
V
W
Q
R
S
M
N
O
X
T
P
I
J
K
L
E
F
G
H
A
B
C
D
A ← 2 3
4
⍴⎕
A
2
⌷⍤
1
⊢
A
BFJ
NRV
Squad with rank
⌷⍤
U
V
W
Q
R
S
M
N
O
X
T
P
I
J
K
L
E
F
G
H
A
B
C
D
A ← 2 3
4
⍴⎕
A
2
⌷⍤
1
⊢
A
BFJ
NRV
Squad with rank
⌷⍤
Indexing as a function → you can use operators
Squad
⌷
A
←
2
3
4
⍴
⎕
A
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
2
⌷
⍤
1
⊢
A
B
F
J
N
R
V
2
⌷
[
3
]
A
Indexing as a function → you can use operators
Squad
⌷
A
←
2
3
4
⍴
⎕
A
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
2
⌷⍤
2
⊢
A
2
⌷
[2]A
EFGH
QRST
⎕
←n←
⍉
3 5
⍴⍳
15
1 6 11
2 7 12
3 8 13
4 9 14
5 10 15
Squad with rank
⌷⍤
1 3 4
⌷⍤
0 2
⊢
n
1 6 11
3 8 13
4 9 14
⎕
←n←
⍉
3 5
⍴⍳
15
1 6 11
2 7 12
3 8 13
4 9 14
5 10 15
Squad with rank
⌷⍤
1 3 4
⌷⍤
0 99
⊢
n
1 6 11
3 8 13
4 9 14
I ←
⌷⍤
0 99
"Sane" indexing
⎕
←n←
⍉
3 5
⍴⍳
15
1 6 11
2 7 12
3 8 13
4 9 14
5 10 15
(
⊂
1 3 4)
⌷
n
⍝
"Insane"
1 6 11
3 8 13
4 9 14
1 3 4 I n
1 6 11
3 8 13
4 9 14
I ←
⌷⍤
0 99
"Sane" indexing
⎕
←n←
⍉
3 5
⍴⍳
15
1 6 11
2 7 12
3 8 13
4 9 14
5 10 15
1 3 4 I n
1 6 11
3 8 13
4 9 14
1 0 1 1 0
⌿
n
1 6 11
3 8 13
4 9 14
'APPLE'[1 3 4]
⍝
Intuitive, beginner friendly
APL
1 0 1 1 0/'APPLE'
⍝
Booleans
APL
"Sane" indexing
1 3 4 I 'APPLE'
⍝
Sane
APL
1 0 1 1 0
⌿
'APPLE'
⍝
Rank polymorphic
APL
"Sane" indexing
I ← ((
⊃⊣
)
⌷⊢
)
⍤
0 99
The Indexer AKA Select
I ← ((
⊃⊣
)
⌷⊢
)
⍤
0 99
The Indexer AKA Select
1 I A 1
⌷
A A[1;;] 1
⌷⍤
0 99
⊢
A
ABCD
EFGH
IJKL
I ← ((
⊃⊣
)
⌷⊢
)
⍤
0 99
The Indexer AKA Select
(
1 2
)(
2 3
) I A
EFGH
UVWX
A[(1 2,¨2 3)
∘
.,
⍳
4]
EFGH
UVWX
⎕
←A←2 3 4
⍴⎕
A
ABCD
EFGH
IJKL
MNOP
QRST
UVWX
I ← ((
⊃⊣
)
⌷⊢
)
⍤
0 99
The Indexer AKA Select
⎕
←A←2 3 4
⍴⎕
A
ABCD
EFG
H
IJKL
MNOP
QRST
UVWX
(
1 2 4
)(
2 3
) I A
H
UVWX
I ← ((
⊃⊣
)
⌷⊢
)
⍤
0 99
The Indexer AKA Select
⎕
←A←2 3 4
⍴⎕
A
ABCD
EFG
H
IJKL
MNOP
QRST
UVWX
(
1 2 4
)(
2 3
) I A
H
UVWX
r←
≢⍴
A
3
k←0
r-k
3
I ← ((
⊃⊣
)
⌷⊢
)
⍤
0 99
The Indexer AKA Select
⎕
←A←2 3 4
⍴⎕
A
ABCD
EFG
H
IJKL
MNOP
QRST
UVWX
(
1 2 4
)(
2 3
) I A
H
UVWX
r←
≢⍴
A
3
k←1
r-k
2
I ← ((
⊃⊣
)
⌷⊢
)
⍤
0 99
The Indexer AKA Select
(1 2 4)(2 3) I A
H
UVWX
NB. The "from" verb in J
(0 1 3;1 2) { AH
UVWX
I ← ((
⊃⊣
)
⌷⊢
)
⍤
0 99
The Indexer AKA Select
1(1 3)
⌷
A
ABCD
IJKL
NB. The "from" verb in J
(<0;0 2) { AABCD
IJKL
⎕
←A←2 3 4
⍴⎕
A
ABCD
EFGH
IJKL
MNOP
QRST
UVWX
Squad with rank
⌷⍤
(↑(1 1 1)(2 1 4)(1 3 4))
⌷⍤
1 99
⊢
A
APL
Choose ←
⌷⍤
1 99
⎕
←A←2 3 4
⍴⎕
A
ABCD
EFGH
IJKL
MNOP
QRST
UVWX
Squad with rank
⌷⍤
3
⌷⍤
99 2
⊢
A
IJKL
UVWX
Cells ←
⌷⍤
99 k
⎕
←A←2 3 4
⍴⎕
A
ABCD
EFGH
IJ
K
L
MNOP
QRST
UV
W
X
Squad with rank
⌷⍤
3
3
⌷⍤
99 2
⊢
A
KW
Cells ←
⌷⍤
99 k
⎕
←A←2 3 4
⍴⎕
A
ABCD
EFGH
IJKL
MNOP
QRST
UVWX
Squad with rank
⌷⍤
(
⊂
2 3
)
⌷⍤
99 2
⊢
A
EFGH
IJKL
QRST
UVWX
Cells ←
⌷⍤
99 k
Selecting from arrays
[ ]
⌷
⊃
⌷
[]
⌷⍤
I ←
⌷⍤
0 99
⍝
Sane
I ← ((
⊃⊣
)
⌷⊢
)
⍤
0 99
Choose ←
⌷⍤
1 99
Cells ←
⌷⍤
k
Performance
Pre v18.0
⌷⍤
0 k
New in v18.0
⌷⍤
1 99
⌷⍤
99 k
1=
≢⍴⍺
:
⌷⍤
k
Indexed assignment
A
ABCD
EFGH
IJKL
MNOP
QRST
UVWX
Indexed assignment
A[1 2;1 3;1 4]←'
⍥
'
⍥
BC
⍥
EFGH
⍥
JK
⍥
⍥
NO
⍥
QRST
⍥
VW
⍥
Search: Indexed assignment
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Selective assignment
Functions for Selective Assignment
↑
Take
↓
Drop
,
Ravel
⍪
Table
⌽⊖
Reverse, Rotate
⍴
Reshape
⊃
Disclose, Pick
⍉
Transpose (Monadic and Dyadic)
/
⌿
Replicate
\
⍀
Expand
⌷
Index
∊
Enlist (
⎕
ML≥1)
Search: Selective assignment
help.dyalog.com
Merge arrays with
@
0@((,1 3 5
∘
.,1 3),(2 4
∘
.,2))
⊢
n
0 6 0
2 0 12
0 8 0
4 0 14
0 10 0
Merge arrays with
@
-@(2|
⊢
)
⊢
n
¯1 6 ¯11
2 ¯7 12
¯3 8 ¯13
4 ¯9 14
¯5 10 ¯15
Selecting from arrays
[ ]
⌷
⊃
⌷
[]
⌷⍤
I ←
⌷⍤
0 99
⍝
Sane
I ← ((
⊃⊣
)
⌷⊢
)
⍤
0 99
Choose ←
⌷⍤
1 99
Cells ←
⌷⍤
k
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A ← 2 3 4
⍴⎕
A
Unlock the power of array selection and indexing techniques through a series of educational slides. Explore different methods for selecting elements from arrays and dive into various indexing strategies, suitable for beginners and experienced professionals alike. Gain insights into cell structures, subarrays, and major elements within 3D arrays, along with practical examples showcasing efficient indexing practices in data manipulation.
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Presentation Transcript
1 Selecting from Arrays Richard Park (16/04/2020)
2 What? Indexing? Pfffft
3 Selecting from Arrays: Audience Mainly beginners Experienced APLers also
4 Simple Choose Reach The rank operator Sane Select Choose Cells
5 Simple Choose Reach Indexed assignment A 'YEAST' A[3 4] 'E' Modified assignment A 1 9 A[1]+ 5 Optimised
8 Cells, subarrays and elements 3D Array Major cell: Matrix Dimensions / Axes A 2 3 4 A A 2 3 4 A A 2 3 4 A A 2 3 4 A A 2 3 4 A M N O P A A B B C C D D Q R S T E E F F G G H H U V W X I I J J K K L L
9 Cells, subarrays and elements 3D Array Major cell: Matrix 1-cell:Vector A 2 3 4 A M N O P A B C D Q R S T E F G H U V W X I J K L
10 Cells, subarrays and elements 3D Array Major cell: Matrix 1-cell:Vector 0-cell: Scalar A 2 3 4 A M N O P A B C D Q R S T E F G H U V W X I J K L
11 Simple indexing A 2 3 4 A A[1;;] ABCD EFGH IJKL A B C D E F G H I J K L
12 Simple indexing A 2 3 4 A 1 A ABCD EFGH IJKL A B C D E F G H I J K L
13 Simple indexing A 2 3 4 A A[1;2;] EFGH E F G H
14 Simple indexing A 2 3 4 A 1 2 A EFGH E F G H
15 Simple indexing A 2 3 4 A A[1;2;3] G G
16 Simple indexing A 2 3 4 A 1 2 3 A G G
19 Simple indexing A 2 3 4 A A[1 2;2 3;3 4] (1 2)(2 3)(3 4) A GH KL ST WX M N O P A B C D Q R S T E F G H U V W X I J K L
20 Simple indexing A 2 3 4 A A[1 2;1 3;1 4] (1 2)(1 3)(1 4) A AD IL MP UX M N O P A B C D Q R S T E F G H U V W X I J K L
21 Simple indexing A 2 3 4 A ABCD EFGH IJKL MNOP QRST UVWX A[1 2;1 3;1 4] (1 2)(1 3)(1 4) A AD IL MP UX
25 Choose indexing A 2 3 4 A ABCD EFGH IJKL MNOP QRST UVWX A[(1 1 1)(2 1 4)(1 3 4)] APL
26 Choose indexing A 2 3 4 A ABCD EFGH IJKL MNOP QRST UVWX A[(1 1 1)(2 1 4)(1 3 4)] APL
27 Reach indexing nest 2 2 2 (2 2 'DYAL') 1 2 3 (2 2 'ABCD') ('AE' 'IO' 'U') 'NT' 4 DY 1 AL 2 3 AB CD AE IO U NT 4
28 Reach indexing nest[ 2 1 2] AE IO U 2 1 2 2 1 2 nest DY 1 AL 2 3 AB CD AE IO U NT 4
29 Reach indexing nest[ (2 1 2)2] IO (2 1 2)2 2 1 2 2 nest DY 1 AL 2 3 AB CD AE IO U NT 4
30 Reach indexing nest[ (2 1 2)2(2)] nest DY 1 AL 2 3 AB CD AE IO U NT 4 O (2 1 2)2(2) 2 1 2 2 2
31 Reach indexing nest DY 1 AL 2 3 AB CD AE IO U NT 4 DOMAIN ERROR ( (2 1 2)2(2)) nest (2 1 2)2(2) 2 1 2 2 2
32 Pick Reach indexing ((2 1 2))2(2) nest nest DY 1 AL 2 3 AB CD AE IO U NT 4 O (2 1 2)2(2) 2 1 2 2 2
33 Pick Reach indexing 'this' 'that' 'the other thing' this that theother thing 3 'this' 'that' 'the other thing' the other thing
34 Simple Subarrays Choose 0-cells AKA Scalars Reach Nested arrays
35 Squad Indexing as a function you can use operators A 2 3 4 A ABCD EFGH IJKL MNOP QRST UVWX 2 2 A 2 [2]A EFGH QRST
37 Squad with axis [] A 2 3 4 A 2 [1]A MNOP QRST UVWX M N O P A B C D Q R S T E F G H U V W X I J K L
38 Squad with rank A 2 3 4 A 2 3 A MNOP QRST UVWX M N O P A B C D Q R S T E F G H U V W X I J K L
39 Squad with axis [] A 2 3 4 A 2 [2]A EFGH QRST M N O P A B C D Q R S T E F G H U V W X I J K L
40 Squad with rank A 2 3 4 A 2 2 A EFGH QRST M N O P A B C D Q R S T E F G H U V W X I J K L
41 Squad with rank A 2 3 4 A 2 2 A EFGH QRST M N O P A B C D Q R S T E F G H U V W X I J K L
42 Squad with axis [] A 2 3 4 A 2 [3]A BFJ NRV M N O P A B C D Q R S T E F G H U V W X I J K L
43 Squad with rank A 2 3 4 A 2 1 A BFJ NRV M N O P A B C D Q R S T E F G H U V W X I J K L
44 Squad with rank A 2 3 4 A 2 1 A BFJ NRV M N O P A B C D Q R S T E F G H U V W X I J K L
45 Squad with rank A 2 3 4 A 2 1 A BFJ NRV M N O P A B C D Q R S T E F G H U V W X I J K L
46 Squad with rank A 2 3 4 A 2 1 A BFJ NRV M N O P A B C D Q R S T E F G H U V W X I J K L
47 Squad with rank A 2 3 4 A 2 1 A BFJ NRV M N O P A B C D Q R S T E F G H U V W X I J K L
48 Squad with rank A 2 3 4 A 2 1 A BFJ NRV M N O P A B C D Q R S T E F G H U V W X I J K L
51 Squad with rank n 3 5 15 1 3 4 0 2 n 1 6 11 2 7 12 3 8 13 4 9 14 5 10 15 1 6 11 3 8 13 4 9 14
52 Squad with rank n 3 5 15 1 3 4 0 99 n 1 6 11 2 7 12 3 8 13 4 9 14 5 10 15 1 6 11 3 8 13 4 9 14
53 "Sane" indexing I 0 99 n 3 5 15 ( 1 3 4) n "Insane" 1 6 11 3 8 13 4 9 14 1 6 11 2 7 12 3 8 13 4 9 14 5 10 15 1 3 4 I n 1 6 11 3 8 13 4 9 14
54 "Sane" indexing I 0 99 n 3 5 15 1 3 4 I n 1 6 11 3 8 13 4 9 14 1 0 1 1 0 n 1 6 11 3 8 13 4 9 14 1 6 11 2 7 12 3 8 13 4 9 14 5 10 15
55 "Sane" indexing 'APPLE'[1 3 4] Intuitive, beginner friendly APL 1 0 1 1 0/'APPLE' Booleans APL
56 "Sane" indexing 1 3 4 I 'APPLE' Sane APL 1 0 1 1 0 'APPLE' Rank polymorphic APL
57 The Indexer AKA Select I (( ) ) 0 99
58 The Indexer AKA Select I (( ) ) 0 99 1 I A 1 A A[1;;] 1 0 99 A ABCD EFGH IJKL
59 The Indexer AKA Select I (( ) ) 0 99 A 2 3 4 A ABCD EFGH IJKL MNOP QRST UVWX (1 2)(2 3) I A EFGH UVWX A[(1 2, 2 3) ., 4] EFGH UVWX
60 The Indexer AKA Select I (( ) ) 0 99 A 2 3 4 A ABCD EFGH IJKL MNOP QRST UVWX (1 2 4)(2 3) I A H UVWX
