Pairwise L₁ distances

First we define a function for computing the L₁ distance between two vectors:

def L1 [n] (xs: [n]f64) (ys: [n]f64) : f64 =
  map2 (-) xs ys |> map f64.abs |> f64.sum

We use the forward pipe operator in the definition above.

To compute the pairwise L₁ distances between all rows in a matrix, we map over the rows twice, then compute the distances between two rows:

def pairwise_L1 [n][m] (xss: [n][m]f64) : [n][n]f64 =
  map (\a -> map (\b -> L1 a b) xss) xss

This pattern is very similar to matrix multiplication.

See also