R help - Jul 2005 - Kronecker matrix product

Hi

I want to write a little function that takes a matrix X of size
m-by-n, and a list L of length  "m",  whose elements are matrices all
of which have
the same number of columns but possibly a different number of rows.

I then want to get a sort of dumbed-down kronecker product in which
X[i,j] is replaced by X[i,j]*L[[j]]

where L[[j]] is the j-th of the "m" matrices.  For example, if

X = matrix(c(1,5,0,2),2,2)

and

L[[1]] = matrix(1:4,2,2)
L[[2]] = matrix(c(1,1,1,1,1,10),ncol=2)

I want


      [,1] [,2] [,3] [,4]
[1,]    1    3    0    0
[2,]    2    4    0    0
[3,]    5    5    2    2
[4,]    5    5    2    2
[5,]    5   50    2   20
 >


see how, for example, out[3:5,1:2]  == 5*L[[2]], the "5" coming from X
[2,1].

[
I can bind L together into a single matrix with

do.call("rbind",L)

and calculate the number of rows with

sapply(L,nrow)

but I don't see how this can help.
]






--
Robin Hankin
Uncertainty Analyst
National Oceanography Centre, Southampton
European Way, Southampton SO14 3ZH, UK
  tel  023-8059-7743

>>>>> "RH" == Robin Hankin <r.hankin at
noc.soton.ac.uk> writes:
    RH> I want to write a little function that takes a matrix X of
    RH> size m-by-n, and a list L of length "m", whose elements are
    RH> matrices all of which have the same number of columns but
    RH> possibly a different number of rows.

    RH> I then want to get a sort of dumbed-down kronecker product in which
    RH> X[i,j] is replaced by X[i,j]*L[[j]]

    RH> where L[[j]] is the j-th of the "m" matrices.  For example,
if

    RH> X = matrix(c(1,5,0,2),2,2)

    RH> and

    RH> L[[1]] = matrix(1:4,2,2)
    RH> L[[2]] = matrix(c(1,1,1,1,1,10),ncol=2)

    RH> I want


    RH> [,1] [,2] [,3] [,4]
    RH> [1,]    1    3    0    0
    RH> [2,]    2    4    0    0
    RH> [3,]    5    5    2    2
    RH> [4,]    5    5    2    2
    RH> [5,]    5   50    2   20
> tmp <- sapply(1:length(L), function(j, mat, list)
kronecker(X[j,,drop=FALSE], L[[j]]), mat=X, list=L)
> do.call("rbind", tmp)
     [,1] [,2] [,3] [,4]
[1,]    1    3    0    0
[2,]    2    4    0    0
[3,]    5    5    2    2
[4,]    5    5    2    2
[5,]    5   50    2   20
> 
HTH.

Cheers,

        Berwin

========================== Full address ===========================Berwin A
Turlach                      Tel.: +61 (8) 6488 3338 (secr)
School of Mathematics and Statistics        +61 (8) 6488 3383 (self)      
The University of Western Australia   FAX : +61 (8) 6488 1028
35 Stirling Highway                   
Crawley WA 6009                e-mail: berwin at maths.uwa.edu.au
Australia                        http://www.maths.uwa.edu.au/~berwin

>>>>> "BT" == Berwin A Turlach <berwin at
maths.uwa.edu.au> writes:
    >> tmp <- sapply(1:length(L), function(j, mat, list)
kronecker(X[j,,drop=FALSE], L[[j]]), mat=X, list=L)

Uups, should proof read more carefully before hitting the send
button.  This should be, of course:

tmp <- sapply(1:length(L),
              function(j, mat, list) kronecker(mat[j,,drop=FALSE], list[[j]]),
              mat=X, list=L)

Cheers,

        Berwin

========================== Full address ===========================Berwin A
Turlach                      Tel.: +61 (8) 6488 3338 (secr)
School of Mathematics and Statistics        +61 (8) 6488 3383 (self)      
The University of Western Australia   FAX : +61 (8) 6488 1028
35 Stirling Highway                   
Crawley WA 6009                e-mail: berwin at maths.uwa.edu.au
Australia                        http://www.maths.uwa.edu.au/~berwin