parts: partition functions

Partitions are typically given by a boolean with 1's marking the beginning or end of each partition. Partitions are also sometimes given in terms of the lengths of each partition.

Verbs defined here assume that boolean 1's mark the beginning of each partition - see comments at the end for examples of end-partition verbs.

The verbs psum and psumscan illustrate definitions appropriate for verbs that return scalar or non-scalar results, respectively. utility used to build non-scalar partition functions:

Examples:

  1 0 0 1 0 0 0 = firstones 1 1 0 1 1 1 0
  0 0 1 0 1 = lastones 1 1 1 0 1
  2 3 1 = lfp 1 0 1 0 0 1
  1 1 0 1 0 0 1 = partition 1 9 9 4 4 4 9
  0 0 0 1 2 2 3 = runindices 3 1 2 1
  1 2 3 1 = runlengths 1 9 9 4 4 4 9

  x=. 1 0 1 0 0 [ y=. 5 3 2 2 7

  3 5 7 2 2 = x preverse y
  3 5 2 2 7 = x psort y
  8 11 = x psum y
  5 8 2 4 11 = x psumscan y

Name	Type	Description
firstones	verb	first 1's in partition
lastones	verb	last 1's in partition
lfp	verb	lengths from partition
partition	verb	partition items (1 marks new item)
pfl	verb	partition from lengths
preverse	verb	partioned reverse
psort	verb	partioned sort
psum	verb	partioned sum
psumscan	verb	partioned sumscan
runindices	verb	indices from run lengths
runlengths	verb	lengths of each run

firstones

first 1's in partition
form: firstones part

lastones

last 1's in partition
form: lastones part

lfp

lengths from partition
form: lfp part

partition

partition items (1 marks new item)
form: partition dat
partition=: 1: , }. ~: }:

pfl

partition from lengths
form: pfl len

preverse

partioned reverse
form: part preverse dat

psort

partioned sort
form: part psort dat

psum

partioned sum
form: part psum dat

psumscan

partioned sumscan
form: part psumscan dat

runindices

indices from run lengths
form: runindices

runlengths

lengths of each run
form: runlengths dat