crossprod {base} | R Documentation |
Given matrices x
and y
as arguments, return a matrix
cross-product. This is formally equivalent to (but usually slightly
faster than) the call t(x) %*% y
(crossprod
) or
x %*% t(y)
(tcrossprod
).
crossprod(x, y = NULL) tcrossprod(x, y = NULL)
x, y |
numeric or complex matrices (or vectors): |
A double or complex matrix, with appropriate dimnames
taken
from x
and y
.
When x
or y
are not matrices, they are treated as column or
row matrices, but their names
are usually not
promoted to dimnames
. Hence, currently, the last
example has empty dimnames.
In the same situation, these matrix products (also %*%
)
are more flexible in promotion of vectors to row or column matrices, such
that more cases are allowed, since R 3.2.0.
Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988) The New S Language. Wadsworth & Brooks/Cole.
(z <- crossprod(1:4)) # = sum(1 + 2^2 + 3^2 + 4^2) drop(z) # scalar x <- 1:4; names(x) <- letters[1:4]; x tcrossprod(as.matrix(x)) # is identical(tcrossprod(as.matrix(x)), crossprod(t(x))) tcrossprod(x) # no dimnames m <- matrix(1:6, 2,3) ; v <- 1:3; v2 <- 2:1 stopifnot(identical(tcrossprod(v, m), v %*% t(m)), identical(tcrossprod(v, m), crossprod(v, t(m))), identical(crossprod(m, v2), t(m) %*% v2))