Flattening and unflattening arrays
To flatten a two-dimensional array into a one-dimensional array,
use the prelude function flatten, which has the following type:
> :t flatten
(xs: [n₀][m₁]t₂) -> [n₀ * m₁]t₂> :t flatten [[1,2,3],[4,5,6]]
[2 * 3]i32
> flatten [[1,2,3],[4,5,6]]
[1, 2, 3, 4, 5, 6]To unflatten, use the function unflatten.
> :t unflatten
(xs: [n₁ * m₂]t₀) -> [n₁][m₂]t₀One curious aspect of unflatten is that it requires the size of
the array to syntactically be of the form n*m, for some known
n and m. This means we cannot simply unflatten an array of some
known integral size:
> unflatten (iota 9)
Cannot apply "unflatten" to "(iota 9)" (invalid type).
Expected: [n₁ * m₂]t₀
Actual: [9]i64
Sizes "n₁ * m₂" and "9" do not match.Instead we can use a size coercion to instruct the language on the desired structure of the dimension:
> unflatten (iota 9 :> [3*3]i64)
[[0, 1, 2],
[3, 4, 5],
[6, 7, 8]]In many cases, a Futhark program can be written to propagate the intended structure, and then such coercions are not necessary:
> unflatten (iota (3*3))
[[0, 1, 2],
[3, 4, 5],
[6, 7, 8]]Since size coercions can be a bit verbose when used frequently, it
can be valuable to define an unflatten_to function:
def unflatten_to 't [k] (n: i64) (m: i64) (A: [k]t) : [n][m]t =
unflatten (A :> [n * m]t)> unflatten_to 2 3 [1,2,3,4,5,6]
[[1, 2, 3],
[4, 5, 6]]