# [R] how to calculate left kronecker product?

Michael Friendly friendly at yorku.ca
Sun Feb 24 01:00:35 CET 2013

Ugh. So simple!  Thanks, Berend.

On 2/23/2013 2:58 PM, Berend Hasselman wrote:
> 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
>
> kronecker(B, A, make.dimnames=TRUE)
>
> Berend
>
>

--
Michael Friendly     Email: friendly AT yorku DOT ca
Professor, Psychology Dept. & Chair, Quantitative Methods
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