| kronecker {base} | R Documentation |
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 |
logical: provide dimnames that are the product of the
dimnames of |
... |
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. 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 "*").
Value
An array A with dimensions dim(X) * dim(Y).
Author(s)
Jonathan Rougier
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)