| 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 |
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) )
stopifnot(kronecker(4, M) == 4 * M)
( A <- matrix(0:3, ncol=2) )
A %x% cbind(2:3)
# Block diagonal array:
kronecker(diag(3), M)
stopifnot(kronecker(diag(3), M) == diag(3) %x% M)