Vocabulary/tilde
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~ Reflex Adverb
Rank Infinity -- operates on x and y as a whole -- WHY IS THIS IMPORTANT?
(u~ y) is the same as (y u y)
u is executed as a dyad with x=y
+~ 1 2 3
2 4 6
y=. 6 3 2
y +/ .* y NB. computing the dot product of y and itself
49
%: y +/ .* y NB. taking the square root to get the vector length
7
%: +/ .*~ y NB. omitting left argument by using Reflex on verb (+/ .*)
7
NB. Source of this gem: [Jchat] 'One day ...', Raul Miller, 2017-12-11
*/^~1+i.5x NB. using (^~) instead of (]^])
86400000
24*60*60*1000 NB. one day (in millisecs)
86400000
Common uses
1. Produce an operator table
avoids having to specify the same noun as both left and right arguments
*/~ i.10 NB. instead of: (i.10) */ (i.10) 0 0 0 0 0 0 0 0 0 0 0 1 2 3 4 5 6 7 8 9 0 2 4 6 8 10 12 14 16 18 0 3 6 9 12 15 18 21 24 27 0 4 8 12 16 20 24 28 32 36 0 5 10 15 20 25 30 35 40 45 0 6 12 18 24 30 36 42 48 54 0 7 14 21 28 35 42 49 56 63 0 8 16 24 32 40 48 56 64 72 0 9 18 27 36 45 54 63 72 81
2. Sort an array.
Sort x /: y is defined as sorting x into the order specified by y. To sort an array into ascending (or descending) order, x and y must be the same, so use /:~ or \:~
/:~ 3 1 4 1 5 9 2 6 5 3 5 1 1 2 3 3 4 5 5 5 6 9 \:~ 2 7 1 8 2 8 1 8 2 8 4 8 8 8 8 7 4 2 2 2 1 1
3. Self-classify.
To find the sets of identical items, use i.~ y which looks for each item of y within y itself. The result will split y into classes of identical values:
pi =: 3 1 4 1 5 9 2 6 5 3 5 NB. A list ]classes =: i.~ pi NB. a class for each item 0 1 2 1 4 5 6 7 4 0 4 pi ,: classes NB. classes shown beneath items 3 1 4 1 5 9 2 6 5 3 5 0 1 2 1 4 5 6 7 4 0 4
4. Apply u on sets of identical items of y. Use u/.~ y which applies u to each set of identical items. One thing you could do is count them:
pi =: 3 1 4 1 5 9 2 6 5 3 5 (~. pi) ,: #/.~ pi NB. Show counts beneath the unique values 3 1 4 5 9 2 6 2 2 1 3 1 1 1
~ Passive Adverb
Rank -- depends on the rank of u -- WHY IS THIS IMPORTANT?
Swaps the arguments of a dyad. Thus, x u~ y is the same as y u x .
3 - 4 _1 3 -~ 4 NB. arguments are swapped 1 3 -~~ 4 NB. reverting to previous state of affairs with (u~)~ _1 7 |~ 2 NB. 7 modulo 2 1
x u~ y is never necessary, since you can achieve the same effect with parentheses, but it can make code shorter or easier to read
] digits=. (48 + i. 10) { a. NB. calling From
0123456789
] digits=. a. {~ 48 + i. 10 NB. same, using Passive
0123456789
i. 11
0 1 2 3 4 5 6 7 8 9 10
(i. 11) % 10 NB. defining 10 equally spaced sections in interval [0;1],
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
10 %~ i. 11 NB. getting rid of parentheses using Passive,
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
10 %~ i. >: 10 NB. reducing to same argument,
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
(%~ [: i. >:) 10 NB. argument "factored out"
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Common uses
1. x u~ y will save parentheses if you would need parentheses around y in y u x.
boxedline =: <'A line of text' (> boxedline) , CRLF NB. Unbox text and append CRLF A line of text CRLF ,~ > boxedline NB. Same effect without parentheses A line of text
2. u~ can avoid the use of [ and ] in tacit forms:
5 (+:@[ + ]) 10 NB. Double x and add to y 20 5 (+~ +:)~ 10 NB. Same without [] 20
3. J style is for dyads to accept "data" as y, with "control information" as x. x u~ y can be used if a verb is mis-specified, or if you want the other order. Examples of J primitives that are backwards for historical reasons are %, e., -, and -.
'abcde' i. 'ef' NB. Find index of y in x 4 5 'abcde' e.~ 'ef' NB. is y in x? 1 0
Another exception from the rule is Sort (x /: y) which expects the "data" as x and the sort order ("control information") as y; where that seems inconvenient one may use (x /:~ y) to sort y into the order specified by x.
4. /:~~ is a cute trick:
- the monad /:~~y is equivalent to y /: y, i.e. it sorts y
- the dyad x /:~~ y is equivalent to x /: y, i.e. it sorts x into the order specified by y .