# Extension to outer()

Jonathan Rougier J.C.Rougier@durham.ac.uk
Mon, 22 Mar 1999 12:40:03 +0000 (GMT)

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A couple of weeks ago I asked if anyone had generalised outer to include
bound extents -- effectively taking the diagonal of an outer product.
Attached is my take on the solution.  There is an extra argument to outer,
BIND, which if null results in a simple outer product.  I've used a
slightly different algorithm which I think is more transparent than the
original code, and also generalises better.

If BIND is not null, then outer(A, B, BIND = c(i, j)) computes an array
with extent j of B bound along extent i of A.  For example, if A and B are
both matrices and V is the result with BIND=c(1,1), then V[i, j, k] =
FUN(A[i, j], B[i, k], ...).  One use for the BIND argument is in computing
Euclidean distances:

"gdist" <- function(X, Y)
{
X <- as.matrix(X)
Y <- as.matrix(Y)
sqrt(apply(outer(X, Y, "-", BIND = c(2,2))^2, c(1,3), sum))
}

which, unlike dist() from `mva' can provide submatrices of the full
distance matrix -- very useful for covariances.

This BIND argument to outer turns out to be very useful in lots of
different areas of our work.  If anyone has any feedback on the code I
would be very grateful for it.  Many thanks, Jonathan.

Jonathan Rougier                       Science Laboratories
Department of Mathematical Sciences    South Road
University of Durham                   Durham DH1 3LE

"[B]egin upon the precept ... that the things we see are to be
weighed in the scale with what we know"  (Meredith, 1879, The Egoist)

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```