Misunderstanding of J Tally(#)

Question

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...

Answer 1

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│
└───────┴───────┴───────┘

Answer 2

To get the count of rank-0 items in a multidimensional array, do this:

   rank_0s =: */&$
   wild1 =: 2 3 4 $ 'abcdefghijklmnopqrstuvwxyz'

   rank_0s wild1
24