[R] Sparse matrix multiplication

[Martin Maechler]

>>>>> "FL" == Feng Li <m at feng.li>
>>>>>     on Sat, 29 Jan 2011 19:46:48 +0100 writes:

    FL> I meant "sparse matrix", sorry for the typo.
aha.. :-)


    FL> On Sat, Jan 29, 2011 at 7:02 PM, Feng Li <m at feng.li> wrote:

    >> Dear R,
    >> 
    >> I have a simple question concerning with a special case of
    >> sparse matrix multiplications. Say A is a 200-by-10000 dense
    >> matrix. B is a 10000-by-10000 block- diagonal matrix, and each
    >> diagonal block B_i is 100-by-100. The usual way I did A%*%B
    >> will take about 30 seconds which is to time consuming because I
    >> have to do this thousands of times. I also tried to partition A
    >> into 100 small blocks and use mapply function to multiply by
    >> each B_i, but that is even slower.
    >> 
    >> I am wondering if there is an efficient way to perform this
    >> type of multiplication with R?

yes: e.g., via the (recommended, i.e. already installed) Matrix
package's  bdiag() :

require(Matrix)
set.seed(1)
A <- matrix(rnorm(2e6), 200, 10000)
Blis <- lapply(1:100, function(i)matrix(rnorm(1e4), 100,100))

system.time(B. <- .bdiag(Blis)) # 1.28 sec
system.time(cc <- A %*% B.)     # 1.7  sec
class(cc)# "dgeMatrix" .. i.e. dense
## and depending on the context you may revert to traditional unclassed matrices
## via
c2 <- as(cc, "matrix")


    >> Thanks in advance!

you are welcome.
Martin Maechler, ETH Zurich


    >> Feng
    >> 
    >> --
    >> Feng Li Department of Statistics Stockholm University 106 91
    >> Stockholm, Sweden http://feng.li/