In J, to find the number of elements you can use # right?
e.g.
# 2 3 4 5 6
5
OK. So what about a multidimensional array
b=: 2 3 4 $ i.2
b
0 1 0 1
0 1 0 1
0 1 0 1
0 1 0 1
0 1 0 1
0 1 0 1
Here #b is 2. I guess because the first dimension has length 2. i.e. the frame of the array.
So if I change it slightly:
b=:3 2 4 $ i.2
b
0 1 0 1
0 1 0 1
0 1 0 1
0 1 0 1
0 1 0 1
0 1 0 1
This has tally 3, because the leading dimension has length 3, right?
But I can't explain this:
#\b
1 2 3
I run tally through the elements of b. So I would think each 2x4 sub array would be used and I would expect #\b to give
2 2 2
because:
c=:2 4 $i.2
c
0 1 0 1
0 1 0 1
#c
2
So my question is, why is #\b = 1 2 3? I think it has something to do with verb ranks, right? I'm struggling to understand this topic...
The easiest way to see what's going on is to box < your \b:
<\b
┌───────┬───────┬───────┐
│0 1 0 1│0 1 0 1│0 1 0 1│
│0 1 0 1│0 1 0 1│0 1 0 1│
│ │ │ │
│ │0 1 0 1│0 1 0 1│
│ │0 1 0 1│0 1 0 1│
│ │ │ │
│ │ │0 1 0 1│
│ │ │0 1 0 1│
└───────┴───────┴───────┘
u\y applies u to y's prefixes:
<\1 2 3
┌─┬───┬─────┐
│1│1 2│1 2 3│
└─┴───┴─────┘
#\1 2 3
1 2 3
*/\1 2 3
1 2 6
So, #\b gives you the number of items of each of b's prefixes.
What you probably thought you would get, is the 2-rank number of items of b:
#"2 b
2 2 2
<"2 b
┌───────┬───────┬───────┐
│0 1 0 1│0 1 0 1│0 1 0 1│
│0 1 0 1│0 1 0 1│0 1 0 1│
└───────┴───────┴───────┘