Classic Edition: the symbol ⌸ is not available in Classic Edition, and the Key operator is instead represented by ⎕U2338.
f may be any dyadic function that returns a result.
If X is specified, it is an array whose major cells specify keys for corresponding major cells of Y. The Key operator ⌸ applies the function f to each unique key in X and the major cells of Y having that key.
If X is omitted, Y is an array whose major cells represent keys. In this case, the Key operator applies the function f to each unique key in Y and the elements of ⍳≢Y having that key. f⌸Y is the same as Y f⌸⍳≢Y.
The elements of R appear in the order in which they first appear in Y.
Key is similar to the GROUP BY clause in SQL.
⎕CT and ⎕DCT are implicit arguments of the Key operator.
Example
In this example, both arrays are vectors so their major cells are their elements. The function {⍺':'⍵} is applied between the unique elements in suits ('Spades' 'Hearts' 'Clubs') and the elements in cards grouped according to their corresponding elements in suits, that is, ('2' 'Ace'), ('Queen' 'Jack') and (,'4').
cards←'2' 'Queen' 'Ace' '4' 'Jack'
suits←'Spades' 'Hearts' 'Spades' 'Clubs' 'Hearts'
suits,[1.5]cards
Spades 2
Hearts Queen
Spades Ace
Clubs 4
Hearts Jack
suits {⍺':'⍵}⌸ cards
Spades : 2 Ace
Hearts : Queen Jack
Clubs : 4
Monadic Examples
{⍺ ⍵} ⌸ suits ⍝ indices of unique major cells
Spades 1 3
Hearts 2 5
Clubs 4
{⍺,≢⍵} ⌸ suits ⍝ count of unique major cells
Spades 2
Hearts 2
Clubs 1
letters←'zabayza'
{⍺(≢⍵)}⌸letters
z 2
a 3
b 1
y 1
Further Examples
x is a vector of stock codes, y is a corresponding matrix of values.
⍴x
10
⍴y
10 2
x,y
IBM 13 75
AAPL 45 53
GOOG 21 4
GOOG 67 67
AAPL 93 38
MSFT 51 83
IBM 3 5
AAPL 52 67
AAPL 0 38
IBM 6 41
If we apply the function {⍺ ⍵} to x and y using the ⌸ operator, we can see how the rows (its major cells) of y are grouped according to the corresponding elements (its major cells) of x.
x{⍺ ⍵}⌸y
IBM 13 75
3 5
6 41
AAPL 45 53
93 38
52 67
0 38
GOOG 21 4
67 67
MSFT 51 83
More usefully, we can apply the function {⍺(+⌿⍵)}, which delivers the stock codes and the corresponding totals in y:
x{⍺(+⌿⍵)}⌸y
IBM 22 121
AAPL 190 196
GOOG 88 71
MSFT 51 83
There is no need for the function to use its left argument. So to obtain just the totals in y grouped by the stock codes in x:
x{+⌿⍵}⌸y
22 121
190 196
88 71
51 83
Defined Function Example
This example appends the data for a stock into a component file named by the symbol.
∇ r←stock foo data;fid;file
[1] file←⊃stock
[2] :Trap 0
[3] fid←file ⎕FTIE 0
[4] file ⎕FERASE fid
[5] :EndTrap
[6] fid←file ⎕FCREATE 0
[7] r←data ⎕FAPPEND fid
[8] ⎕FUNTIE fid
∇x foo⌸y 1 1 1 1
Example
{⍺ ⍵} ⌸ suits ⍝ indices of unique major cells
Spades 1 3
Hearts 2 5
Clubs 4
{⍺,≢⍵} ⌸ suits ⍝ count of unique major cells
Spades 2
Hearts 2
Clubs 1
Another Example
Given a list of names and scores., the problem is to sum the scores for each unique name. A solution is presented first without using the Key operator, and then with the Key operator.
names ⍝ 12, some repeat
Pete Jay Bob Pete Pete Jay Jim Pete Pete Jim
Pete Pete
(∪names)∘.≡names
1 0 0 1 1 0 0 1 1 0 1 1
0 1 0 0 0 1 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 1 0 0 1 0 0
scores
66 75 71 100 22 10 67 77 55 42 1 78
b←↓(∪names)∘.≡names
]disp b/¨⊂⍳12
┌→──────────────┬───┬─┬────┐
│1 4 5 8 9 11 12│2 6│3│7 10│
└~─────────────→┴~─→┴→┴~──→┘
+/¨b/¨⊂scores
399 85 71 109
]disp {⊂⍵}⌸ names
┌→──────────────┬───┬─┬────┐
│1 4 5 8 9 11 12│2 6│3│7 10│
└~─────────────→┴~─→┴→┴~──→┘
names {+/⍵}⌸ scores
399 85 71 109