kronecker {base}R Documentation

Kronecker Product of Arrays

Description

Computes the generalised kronecker product of two arrays, X and Y. kronecker(X, Y) returns an array A with dimensions dim(X) * dim(Y).

Usage

kronecker(X, Y, FUN = "*", ...)
X %x% Y

Arguments

X vector or array.
Y vector or array.
FUN a function, possibly specified as character (string).
... optional arguments to be passed to FUN.

Details

If X and Y do not have the same number of dimensions, the smaller array is padded with dimensions of size one. A consists of 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 "*").

Author(s)

Jonathan Rougier

References

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

See Also

outer on which kronecker is built and matmult for usual matrix multiplication.

Examples

# simple scalar multiplication
( M <- matrix(1:6, ncol=2) )
all(kronecker(4, M) == 4 * M)

( A <- matrix(0:3, ncol=2) )
A %x% cbind(2:3)
# Block diagonal array:
kronecker(diag(3), M)
all(kronecker(diag(3), M) == diag(3) %x% M)
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