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crossprod {base}

Matrix Crossproduct
Package: 
base
Version: 
R 3.0.1

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

x, y
numeric or complex matrices: y = NULL is taken to be the same matrix as x. Vectors are promoted to single-column or single-row matrices, depending on the context.

Values

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

References

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

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.

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))

Documentation reproduced from R 3.0.1. License: GPL-2.