Help with improving efficiency

Dear All,

I have a problem that I think could be solved much
more efficiently, but
I don't have a clue how to accomplish this. I have a
matrix W with
dimensions k*(p+1):

Let's say W is 5*4 and looks like this:

W

      [,1] [,2] [,3] [,4]
 [1,]    1   -1   -1    1
 [2,]    1    1    1    1
 [3,]    1    2   -2   -1
 [4,]    1    0   -1   -1
 [5,]    1   -2   -1    0

I want to take each row (a p*1 vector), transpose it
(1*p column
vector), and then multiply that by the same row
vector, which will give
me a p*p matrix. So, for each row, I calculate:

as.matrix(W[i,]) %*% W[i,]	for i = 1, ..., k.

Next, I want to find the sum of the k (p*p)
matrices. The following code
seems to work fine:


k <- 5
p <- 3
W <- matrix(c( rep(1, k), round(rnorm(n=(p*k),
mean=0, sd=1), 0)),
     ncol=(p+1), nrow=k) 		# create a random W
matrix
m1 <- matrix(0, nrow=p+1, ncol=p+1)
for (i in 1:k) {
   m1 <- m1 + as.matrix(W[i,]) %*% W[i,]
}


but this just seems terribly inefficient. Any
suggestions for improving
this? Thanks in advance.

Wolfgang

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The "real" answer will tell us something about R
syntax, arrays, vectorization, etc. I would also love
to know it.

But as it happens, the function you are describing is
equal to t(W)%*%W.

The "real" answer will tell us something about R
syntax, arrays, vectorization, etc. I would also love
to know it.

But as it happens, the function you are describing is
equal to t(W)%*%W.

I must admit that I completely didn't notice that my code is just a
cumbersome way of calculating the crossproduct of the W matrix (which
could be accomplished even faster with the crossprod() function, as one
person pointed out to me off-line).

However, I guess I should have mentioned that the code within the loop
is just a subset of the operations that are being performed on the row
vectors.

So, for example, let's say that each of the k (p*p) matrices is also
being multiplied by a value v[i]:


k <- 5
p <- 3
W <- matrix(c( rep(1, k), round(rnorm(n=(p*k), mean=0, sd=1), 0)),
     ncol=(p+1), nrow=k)                # create a random W matrix
v  <- rnorm(n=k, mean=0, sd=1)		# create random v values
m1 <- matrix(0, nrow=p+1, ncol=p+1)
for (i in 1:k) {
   m1 <- m1 + v[i] * as.matrix(W[i,]) %*% W[i,]
}


Obviously, this is different from simlpy taking the crossproduct of W.
The best way to optimize the code probably depends on the types of
operations being performed within the loop, but I am hoping to gain a
general idea of how to optimize this particular code and then maybe I
can apply that knowledge to the actual problem I am dealing with (and
the "real" answer, as pointed out, might serve a nice illustration of
how to write efficient code in general).

Wolfgang


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