blog

J's #: (base) can be used to compute the offset of an array element as it would appear in memory. Why so? x #: y is +/w*y, where w is formed as */\.}.x,1—w is precisely the strides of an array with dimensions x.

See that this works:

   dims=.2 3
   ix=.1 2
   (<ix) { (dims$i.6)
5
   ((|.ix) #. dims) { i.6
5

Recall the examples:

   2 2 2 #. 1 0 1
5

   24 60 60 #. 23 59 59
86399

The latter tallies seconds from hours-minutes-seconds.

Computing element offsets resembles forming a number from its multibase "digits," with indices corresponding to "digits," and dimensions corresponding to base.