(+/"1)@:*:@:(-"1)
Henry Rich
On 2/20/2021 2:40 PM, Emir U wrote:
Regarding the efficient computation of a squared Euclidean distance matrix.
There wasn't very much on the topic so far as I could find. In previous
discussion this formulation was suggested:
+/ @: *:@:-"1
You might use it like this to find the distance between the row vector x and
the row vectors in y:
(1 2) ed/ (3 4,. 5 6)
It is very elegant, but it is in effect a Cartesian join and even for
moderately sized distance matrices ends up being inefficient since all
computation is performed at a cell level.
In my code, I replaced it with this:
ed=: 4 : 0
row=. 4 : '+/ *: (x - (|: y))'
(row & y) each < "1 x
)
Used like this:
(1 2) ed (3 4,. 5 6)
It lacks the elegance, but it is general (although size of x should be <= y)
and several orders of magnitude faster than the tabled solution because it
operates on a row at a time so presumably benefits from SIMD and the like.
Emir
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