Shape, Rank, and Depth

Shape (⍴)

The shape of an array is a vector of non-negative integers giving the length along each axis. You get it with monadic ⍴.

      ⍴ 42
⍝ (empty — scalar has no axes)
      ⍴ 1 2 3
3
      ⍴ 3 4⍴⍳12
3 4

Rank

The rank is the number of axes -- the length of the shape vector. You get it with ≢⍴ or ⍴⍴.

      ⍴⍴ 42
0
      ⍴⍴ 1 2 3
1
      ⍴⍴ 3 4⍴⍳12
2

Array type	Rank	Example shape
Scalar	0	(empty)
Vector	1	5
Matrix	2	3 4
3D array	3	2 3 4

Depth

MARPLE arrays are flat -- all elements are simple scalars (numbers or characters). There is no nesting. Depth is always 0 for a scalar or 1 for an array of scalars.

Tally (≢)

Monadic ≢ returns the length of the first axis. For a scalar it returns 1.

      ≢ 1 2 3
3
      ≢ 3 4⍴⍳12
3
      ≢ 42
1

See also

• Empty Arrays
• Fill Elements