# [R] Sparse matrix multiplication

Martin Maechler maechler at stat.math.ethz.ch
Sat Jan 29 23:59:03 CET 2011

```>>>>> "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")

you are welcome.
Martin Maechler, ETH Zurich

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

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