R: optimal way of computing the "product" of two vectors

Question

Hi,

Let's assume that I have a vector

r <- rnorm(4)

and a matrix W of dimension 20000*200 for example:

W <- matrix(rnorm(20000*200),20000,200)

I want to compute a new matrix M of dimension 5000*200 such that m11 <- r%*%W[1:4,1], m21 <- r%*%W[5:8,1], m12 <- r%*%W[1:4,2] etc. (i.e. grouping rows 4-by-4 and computing the product).

What's the optimal (speed,memory) way of doing this?

Thanks in advance.

Answer 1

I don't know if this is optimal in speed or memory, but probably one of the simple way:

m<-apply(array(W,c(4,5000,200)),c(2,3),"%*%",r)


> m[1,1:10]==r%*%W[1:4,1:10]
     [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
[1,] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE  TRUE
> m[2,1:10]==r%*%W[5:8,1:10]
     [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
[1,] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE  TRUE

Answer 2

First on my mind is apply over shorter dim:

M <- apply(W, 2, function(x) r%*%matrix(x,4,5000))

m11 <- r%*%W[1:4,1]
m21 <- r%*%W[5:8,1]
m12 <- r%*%W[1:4,2]

m11 - M[1,1]
#      [,1]
# [1,]    0
m21 - M[2,1]
#      [,1]
# [1,]    0
m12 - M[1,2]

#      [,1]
# [1,]    0

Profiled kohske answer:

M <- apply(array(W,c(4,5000,200)), 3, function(x) r%*%x)

to iterated over shorter dim (again).

Answer 3

This seems to run fastest for me:

array(r %*% array(W, c(4, 20000 * 200 / 4)), c(5000, 200))