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
>
--
Michael Friendly Email: friendly AT yorku DOT ca
Professor, Psychology Dept. & Chair, Quantitative Methods
York University Voice: 416 736-2100 x66249 Fax: 416 736-5814
4700 Keele Street Web: http://www.datavis.ca
Toronto, ONT M3J 1P3 CANADA
On 23-02-2013, at 20:46, Michael Friendly <friendly at yorku.ca> wrote:> 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 > >How about kronecker(B, A, make.dimnames=TRUE) Berend