x=:1 1 0 0 0 1 0 0 1 1 y=:3 4 8 2 5 6 9 4 5 4 x +/ ;. 1 y 3 19 19 5 4 x < ;. 1 y +-------------------+ ¦3¦4 8 2 5¦6 9 4¦5¦4¦ +-------------------+ x < ;. 2 y +-------------------+ ¦3¦4¦8 2 5 6¦9 4 5¦4¦ +-------------------+ x +/ ;. 2 y 3 4 21 18 4
The foregoing expressions illustrate the use of the cut conjunction (;.) to apply the functions sum (+/) and box (<) over partitions or fields of the right argument y demarked by the boolean left argument x. The case of the box gives a clear picture of the partitioning performed; in case 1, the ones in the left argument mark the beginnings of fields, and in case 2 they mark the ends.
A function (such as the sum scan) that produces non-scalar results illustrates the fact that the box of such a function provides a more readable result:
x +/\ ;. 2 y 3 0 0 0 4 0 0 0 8 10 15 21 9 13 18 0 4 0 0 0 x <@(+/\) ;. 2 y +------------------------+ ¦3¦4¦8 10 15 21¦9 13 18¦4¦ +------------------------+ ; x <@(+/\) ;. 2 y 3 4 8 10 15 21 9 13 18 4
We therefore define a corresponding conjunction:
cut=: 2 : ';@(<@x.;.y.)' x +/\ cut 1 y 3 4 12 14 19 6 15 19 5 4 x +/\ cut 2 y 3 4 8 10 15 21 9 13 18 4
c0=: cut=: 2 : ';@(<@x.;.y.)' | |
a1=: c1=: cut 1 | Case 1 of cut |
a2=: c2=: cut 2 | Case 2 of cut |
d3=: pmax=: >./ c1 | Partitioned max over (case 1) |
d4=: pmax2=: >./c2 | Partitioned max over (case 2) |
d5=: pmaxs=: >./\ c1 | Partitioned max scan |
d6=: pnub=: ~. c1 | Partitioned nub |
d7=: psort=: /:~ c1 | Partitioned sort |
d8=: prev=: |. c1 | Partitioned reverse |
m9=: <;._2@(,&':');._2 | UNIX /etc/passwd relation |
x 1 1 0 0 0 1 0 0 1 1 y 3 4 8 2 5 6 9 4 5 4 (x pmax y) ,: (x pmax2 y) 3 8 9 5 4 3 4 8 9 4 x([ , ] ,psort ,: prev)y 1 1 0 0 0 1 0 0 1 1 3 4 8 2 5 6 9 4 5 4 3 2 4 5 8 4 6 9 5 4 3 5 2 8 4 4 9 6 5 4 p=: >;:'sparkle out among the fern to bicker down a valley' x (,.@[ ; ,.@] ; psort ; prev) p +-------------------------+ ¦1¦sparkle¦sparkle¦sparkle¦ ¦1¦out ¦among ¦fern ¦ ¦0¦among ¦fern ¦the ¦ ¦0¦the ¦out ¦among ¦ ¦0¦fern ¦the ¦out ¦ ¦1¦to ¦bicker ¦down ¦ ¦0¦bicker ¦down ¦bicker ¦ ¦0¦down ¦to ¦to ¦ ¦1¦a ¦a ¦a ¦ ¦1¦valley ¦valley ¦valley ¦ +-------------------------+ x p psort prev
The monadic case of the 1-cut partitions at each occurrence of the leading item of the argument. Moreover a negative case suppresses the partitioning item. For example:
q=: 0 4 2 3 0 4 7 6 0 2 < c1 q +-------------------+ ¦0 4 2 3¦0 4 7 6¦0 2¦ +-------------------+ psort q 0 2 3 4 0 4 6 7 0 2 r=: >;:'/do you love me / or do you not / you told me once / but I forgot' < cut 1 r +---------------------------+ ¦/ ¦/ ¦/ ¦/ ¦ ¦do ¦or ¦you ¦but ¦ ¦you ¦do ¦told ¦I ¦ ¦love ¦you ¦me ¦forgot¦ ¦me ¦not ¦once ¦ ¦ +---------------------------+ < cut _1 r +---------------------------+ ¦do ¦or ¦you ¦but ¦ ¦you ¦do ¦told ¦I ¦ ¦love ¦you ¦me ¦forgot¦ ¦me ¦not ¦once ¦ ¦ +---------------------------+