For an application, I have formulas defined in terms of a left Kronecker
product of matrices,
A,B, meaning
A \otimes_L B = {A * B[i,j]} -- matrix on the left multiplies each element on
the right.
The standard kronecker() function is the right Kronecker product,
A \otimes_R B = {A[i,j] * B} -- matrix on the right multiplies each element on
the left.
The example below shows the result of kronecker() and what I want, but
kronecker() is now defined in generic S4 methods, and I can't see
how to use more basic functions to get the result I want. Or, alternatively
how to transform the result of kronecker() to give my wanted.
---- test code ---
A <- matrix(1:4, 2,2, dimnames=list(c("a1", "a2"), c("a1","a2")))
B <- diag(2)
dimnames(B) <- list(c("b1", "b2"), c("b1","b2"))
# standard, right kronecker product: each A[i,j] * B
kronecker(A, B, make.dimnames=TRUE)
# left kronecker product: A * each B[i,j]
wanted <- rbind(
cbind(A * B[1,1], A*B[1,2]),
cbind(A * B[2,1], A*B[2,2]))
rownames(wanted) <- colnames(wanted) <- paste(rep(c("b1", "b2"), each=2),
rownames(wanted), sep=":")
wanted
---- R output ----
A <- matrix(1:4, 2,2, dimnames=list(c("a1", "a2"), c("a1","a2")))
B <- diag(2)
dimnames(B) <- list(c("b1", "b2"), c("b1","b2"))
# standard, right kronecker product: each A[i,j] * B
kronecker(A, B, make.dimnames=TRUE)
a1:b1 a1:b2 a2:b1 a2:b2
a1:b1 1 0 3 0
a1:b2 0 1 0 3
a2:b1 2 0 4 0
a2:b2 0 2 0 4
# left kronecker product: A * each B[i,j]
wanted <- rbind(
+ cbind(A * B[1,1], A*B[1,2]),
+ cbind(A * B[2,1], A*B[2,2]))
rownames(wanted) <- colnames(wanted) <- paste(rep(c("b1", "b2"), each=2),
rownames(wanted), sep=":")
wanted
b1:a1 b1:a2 b2:a1 b2:a2
b1:a1 1 3 0 0
b1:a2 2 4 0 0
b2:a1 0 0 1 3
b2:a2 0 0 2 4
