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 |
|
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 ¦ ¦
+---------------------------+
|