You might want to compare the performance of your version to the kronecker
method of Matrix (Matrix package) that has appropriate versions for sparse
matrices etc.
-Christos
> -Original Message-
> From: r-help-boun...@r-project.org
> [mailto:r-help-boun...@r-project.org] On Behalf Of Camarda,
> Carlo Giovanni
> Sent: Monday, February 23, 2009 1:18 PM
> To: r-h...@stat.math.ethz.ch
> Subject: [R] trade-off between speed and storage in matrix
> multiplications
>
> Dear R-users,
>
> I coded two equivalent ways to perform (in a simplified
> version) some matrix multiplications I would like to use in a
> more general framework.
> In the first case I used Kronecker product and vectorization
> of a certain matrix. This approach takes less time, but, as
> you may guess, I run out of memory when dimensions are large.
> In the second approach, I profited of sparseness and
> structure of the matrices and use outer-functions for
> performing operations. Here it takes more time, but I have
> not problem of memory.
>
> Is there any way to enhance the second approach for
> speeding-up the whole process? Or, in computing, this is a
> well-known trade-off between speed and storage-spaces which
> I'm not aware (sorry for that).
>
> Please have a look to the example below.
>
> Needless to say that I'd appreciate any suggestion.
>
> Best,
> Carlo Giovanni
>
>
> # dimensions
> m <- 10
> n <- 15
> # A-matrix
> rnA <- runif(m*m)
> A <- matrix(rnA, m, m)
> # vector
> v <- runif(n)
> # B-matrix
> rnB <- runif(m*n)
> B <- matrix(rnB, m, n)
>
> # first solution: vectorize B + kronecker product => faster
> but storage issues system.time( for(i in 1:100){
> b <- c(B)
> vKron.A <- kronecker(diag(v), A)
> SOL1 <- vKron.A %*% b
> })
>
> # second solution: orig. dims + apply + mapply => slower, but
> w/o storage issues system.time( for(i in 1:100){
> Av <- outer(A, v, FUN="*")
> Av.df1 <- apply(Av, 3, as.data.frame)
> Av.df2 <- lapply(X=Av.df1, FUN=as.matrix, nrow=m, ncol=m)
> SOL2 <- mapply(FUN="%*%", Av.df2, as.data.frame(B)) # as a matrix
> })
>
>
>
>
>
> --
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