Matrix Cross-Product

Description

Given matrices x and y as arguments, return a matrix cross-product. This is formally equivalent to (but faster than) the call t(x) %*% y (crossprod) or x %*% t(y) (tcrossprod).

These are generic functions since R 4.4.0: methods can be written individually or via the matOps group generic function; it dispatches to S3 and S4 methods.

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.

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.

The propagation of NaN/Inf values, precision, and performance of matrix products can be controlled by options("matprod").

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))