base (version 3.3.2)

kronecker: Kronecker Products on Arrays

Description

Computes the generalised kronecker product of two arrays, X and Y.

Usage

kronecker(X, Y, FUN = "*", make.dimnames = FALSE, …)
X %x% Y

Arguments

X

A vector or array.

Y

A vector or array.

FUN

a function; it may be a quoted string.

make.dimnames

Provide dimnames that are the product of the dimnames of X and Y.

…

optional arguments to be passed to FUN.

Value

An array A with dimensions dim(X) * dim(Y).

Details

If X and Y do not have the same number of dimensions, the smaller array is padded with dimensions of size one. The returned array comprises submatrices constructed by taking X one term at a time and expanding that term as FUN(x, Y, ...). %x% is an alias for kronecker (where FUN is hardwired to "*").

References

Shayle R. Searle (1982) Matrix Algebra Useful for Statistics. John Wiley and Sons.

See Also

outer, on which kronecker is built and %*% for usual matrix multiplication.

Examples

# simple scalar multiplication
( M <- matrix(1:6, ncol = 2) )
kronecker(4, M)
# Block diagonal matrix:
kronecker(diag(1, 3), M)

# ask for dimnames

fred <- matrix(1:12, 3, 4, dimnames = list(LETTERS[1:3], LETTERS[4:7]))
bill <- c("happy" = 100, "sad" = 1000)
kronecker(fred, bill, make.dimnames = TRUE)

bill <- outer(bill, c("cat" = 3, "dog" = 4))
kronecker(fred, bill, make.dimnames = TRUE)