Matrix Crossproduct

Description

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).

Usage

crossprod(x, y = NULL)

tcrossprod(x, y = NULL)

Arguments

Value

A double or complex matrix, with appropriate dimnames taken from x and y.

Note

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.

References

Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988) The New S Language. Wadsworth & Brooks/Cole.

See Also

%*% and outer product %o%.

Examples

(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))