[R] Sparse matrix calculation

[Tamas K Papp]

On Wed, Nov 15, 2006 at 01:22:19PM -0500, YONGWAN CHUN wrote:

> I work on large matrices and found something interesting. For multiplication of matrices, the order has a huge influence on computing time when one of them is a sparse matrix. In the below example, M is a full matrix and A is a sparse matrix in a regular matrix class. A %*% M takes much more time than M %*% A; moreover, t(t(M) %*% t(A)) is much faster than A %*% M with same result. I would like to know how it is possible. Even though I do not have an exact reason, this fact may be helpful to others. 
> 
> > n <- 1000
> > M <- diag(n) - matrix(1/n,n,n)
> > A <- matrix(rnorm(n*n)>2,n,n)
> > system.time(M %*% A)
> [1] 0.10 0.03 0.12   NA   NA
> > system.time(A %*% M)
> [1] 3.47 0.03 3.50   NA   NA
> > system.time(t(t(M) %*% t(A)))
> [1] 0.23 0.00 0.23   NA   NA

Hi Yongwan,

Sorry but I could not reproduce this:

> n <- 1000
> M <- diag(n) - matrix(1/n,n,n)
> A <- matrix(rnorm(n*n)>2,n,n)
> system.time(M %*% A)
[1] 3.466 0.060 3.744 0.000 0.000
> system.time(A %*% M)
[1] 3.327 0.088 4.046 0.000 0.000
> system.time(t(t(M) %*% t(A)))
[1] 3.681 0.089 3.814 0.000 0.000

What OS, R version, linalg package are you using?

Tamas