The Shape Function ⍴
Monadic Use On Scalars
When used monadically ⍴ returns the shape of an object. If the object is a scalar the result is a blank line
⍴ 3
Monadic Use On Arrays
If the object has shape, if it is an array, r returns the shape:
⍴ 3 4 5
3
It works on all scalars
⍴ 1J2 3J4
2
Dyadic Use On Scalars
Dyadically ⍴ is used to reshape an object. If necessary it will create an array of the appropriate shape and populate it with the scalar:
2 3 ⍴ 4
4 4 4
4 4 4
This extends to higher dimensions:
2 3 4 ⍴ 4
4 4 4 4
4 4 4 4
4 4 4 4
4 4 4 4
4 4 4 4
4 4 4 4
Dyadic Use On Arrays
Dyadically ⍴ is used to reshape an object. It will stripe an existing vector over its space:
2 3 4 ⍴ 9 8 7
9 8 7 9
8 7 9 8
7 9 8 7
9 8 7 9
8 7 9 8
7 9 8 7
It also works on arrays of arrays:
A ← 2 ⍴ 9
B ← 2 ⍴ 99
2 3 ⍴ A B
┌─────┐ ┌─────┐ ┌─────┐
│ 9 9│ │99 99│ │ 9 9│
└─────┘ └─────┘ └─────┘
┌─────┐ ┌─────┐ ┌─────┐
│99 99│ │ 9 9│ │99 99│
└─────┘ └─────┘ └─────┘
The left hand side must be an array of integers:
2.2 3 4 ⍴ 9 8 7
Error
2.2 3 4 ⍴ 9 8 7
^
DOMAIN ERROR [dyadic ⍴ only accepts integer arguments to the left and was called with: Left: [2.2,3,4] - Right: [9,8,7] ] on line 1 at character 1
The formatter likes to keep things neat, which is nice:
3 4⍴ 9999 8 7
with some cheeky alignments going on:
9999 8 7 9999
8 7 9999 8
7 9999 8 7
⍴ is a procrustean operator - if there aren’t enough elements on the right hand side it will generate them:
2 3 ⍴ 9 8 7 6
giving:
9 8 7
6 9 8
If there are too many it will chop some off:
1 2 ⍴ 4 4 4
giving:
4 4
Dyadic Use On Scalars
It can take a scalar as an argument on the left side:
1 ⍴ 2 3
2
It can take a scalar as an argument on the right side:
1 2 ⍴ 3
3 3
It can take a scalar as an argument on the both sides:
1 ⍴ 2
2
It always returns a vector.
If the left hand side is not an integer scalar an error will be thrown:
1.1 ⍴ 2 3
Error
1.1 ⍴ 2 3
^
DOMAIN ERROR [dyadic ⍴ only accepts integer arguments to the left and was called with: Left: [1.1] - Right: [2,3] ] on line 1 at character 1