# Distributors¶

' \: /: ':

A distributor is an extender that derives a uniform extension that applies the map once to each item of a dictionary, a list, or conforming lists.

There are five distributors.

glyph operator map rank extension rank
' Each any same as map
\: Each Left binary binary
/: Each Right binary binary
': Each Parallel unary unary
': Each Prior binary ambivalent

## Each¶

Apply a map item-wise to a dictionary, list, or conforming lists and/or dictionaries.

Syntax: (m')x, x m'y, m'[x;y;z]

An Each extension evaluates its map on each item of a list, dictionary or on corresponding items of conforming lists. The extension has the same rank as the map.

q)(count')abc!(1 2 3;4 5;6 7 8 9)        / unary
a| 3
b| 2
c| 4


### each keyword¶

The mnemonic keyword each can be used to apply a unary map without parentheses.

q)count each string ClashFixxTheWho
5 4 3 3


Each Both

Each applied to a binary map is sometimes called Each Both and can be applied infix.

q)1 2 3 in'(1 0 1;til 100;5 6 7)            / binary, infix
110b


Extensions of ternary and higher-rank maps are applied with brackets.

q){x+y*z}'[1000000;1 0 1;5000 6000 7000]    / ternary
1005000 1000000 1007000


## Each Left and Each Right¶

Apply a binary map between one argument and each item of the other.

Each Left Each Right
syntax: x m\:y x m/:y
equivalent: (m[;y]')x (m[x;]')y

The extenders Each Left and Each Right take binary maps and derive binary functions that apply one argument to each item of the other. Effectively, the extender projects its map on one argument and applies Each.

q)"abcde",\:"XY"             / Each Left
"aXY"
"bXY"
"cXY"
"dXY"
"eXY"
q)"abcde",/:"XY"             / Each Right
"abcdeX"
"abcdeY"
q)m                          / binary map
"abcd"
"efgh"
"ijkl"
q)m[0 1;2 3] ~ 0 1 m\:2 3
1b
q)0 1 m/:2 3
"cg"
"dh"
q)(flip m[0 1;2 3]) ~ 0 1 m/:2 3
1b


### Left, right, cross¶

Each Left combined with Each Right resembles the result obtained by cross.

q)show a:{x,/:\:x}til 3
0 0 0 1 0 2
1 0 1 1 1 2
2 0 2 1 2 2
q)show b:{x cross x}til 3
0 0
0 1
0 2
1 0
1 1
1 2
2 0
2 1
2 2
q){}0N!a
((0 0;0 1;0 2);(1 0;1 1;1 2);(2 0;2 1;2 2))
q){}0N!b
(0 0;0 1;0 2;1 0;1 1;1 2;2 0;2 1;2 2)
q)raze[a] ~ b
1b


Atoms and lists in the domains of these extenders

The domains of \: and /: extend beyond binary maps to include certain atoms and lists.


q)(", "/:)("quick";"brown";"foxes")
"quick, brown, foxes"
q)(0x0\:)3.14156
0x400921ea35935fc4


This is exposed infrastructure: use the keywords vs and sv instead.

## Each Parallel¶

Assign sublists of the argument list to slave tasks, in which the unary map is applied to each item of the sublist.

Syntax: (m':)x

The Each Parallel extender takes a unary map as argument and derives a unary function. The extension m': divides its list or dictionary argument x between available slave tasks. Each slave task applies the map to each item of its sublist.

\$ q -s 2
KDB+ 3.4 2016.06.14 Copyright (C) 1993-2016 Kx Systems
m32/ 2()core 4096MB sjt mark.local 192.168.0.17 NONEXPIRE

q)\t ({sum exp x?1.0}' )2#1000000  / each
185
q)\t ({sum exp x?1.0}':)2#1000000  / peach
79
q)peach
k){x':y}


### peach keyword¶

The mnemonic keyword peach can be used as a mnemonic alternative: e.g. instead of (m:') write m peach list.

Higher-rank maps

To parallelize a map of rank >1, use Apply to evaluate it on a list of arguments.

Alternatively, define the map as a function that takes a parameter dictionary as argument, and pass the extension a table of parameters to evaluate.

## Each Prior¶

Apply a binary map between each item of a list and its preceding item.

Syntax: (m':)x, x m':y

The Each Prior extender takes a binary map and derives an ambivalent function. The extension applies the map between each item of a list or dictionary and the item prior to it.

q)(-':)1 1 2 3 5 8 13
1 0 1 1 2 3 5


The first item of a list has no prior item. If the extension is applied as a binary, its left argument is taken as the ‘seed’ – the value preceding the first item.

q)1950 -': SJC!1952 1954 1960
S| 2
J| 2
C| 6


If the extension is applied as a unary, and the map is an operator with an identity element $I$ known to q, $I$ will be used as the seed.

q)(*':)2 3 4                        / 1 is I for *
2 6 12
q)(,':)2 3 4                        / () is I for ,
2
3 2
4 3
q)(-':) SJC!1952 1954 1960       / 0 is I for -
S| 1952
J| 2
C| 6


If the extension is applied as a unary, and the map is not an operator with a known identity element, a null of the same type as the argument (first 0#x) is used as the seed.

q){x+2*y}':[2 3 4]
0N 7 10


### prior keyword¶

The keyword priorcan be used as a mnemonic alternative to ':.

q)(-':) 5 16 42 103
5 11 26 61
q)(-) prior 5 16 42 103
5 11 26 61
q)deltas 5 16 42 103
5 11 26 61


## Empty lists¶

A distributive extension is a uniform function. Applied to an empty right argument it returns an empty list without evaluating its map.

q)()~{x+y*z}'[foo;mt;mt]    / generic empty list ()
1b


Watch out for type changes when evaluating lists of unknown length.

q)type (2*')til 5
7h
q)type (2*')til 0
0h
q)type (2*)til 0
7h