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5B. Partition
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 | | +---------------------------+