applying a function over a matrix 2N x M to produce a matrix N x M

Hello,

mat1 only consists of 0s and 1s:
0 0 1 0 0 0
1 1 0 1 1 0
1 1 1 0 1 0
0 1 1 0 0 1
1 0 0 1 0 0
0 1 0 1 0 1

N = 3
M = 6

I would like to "compress" mat1 every two rows, applying summation  
over the two rows (per column), at each step, to yield:

mat2
1 1 1 1 1 0
1 2 2 0 1 1
1 1 0 2 0 1

Then, in mat2, I shall have to count the number of 0s, 1s and 2s,  
per column, which is my final aim.

I am aware of possibilities such as

counts <- sapply(mat2,2,fun1)

but I do not know how to write fun1.


Besides, it was perhaps not necessary to waste memory producing the  
temporary matrix mat2.

Can somebody help ?

I thank you in advance for your answer.

Best regards,

Christine Sinoquet

I like David's answer and it can be made much faster.
I show three refinements, each faster than the preceding one.

Rich

system.time(for (i in 1:1000)

+   mat[seq(1, nrow(mat), by=2), ]+mat[seq(2, nrow(mat), by=2), ]
+ )
   user  system elapsed
   0.18    0.00    0.19

system.time(for (i in 1:1000)

+   mat[seqn <- seq(1, nrow(mat), by=2), ]+mat[seqn+1, ]
+ )
   user  system elapsed
   0.08    0.00    0.08

system.time(for (i in 1:1000)

+   mat[seqn <- seq(1, length=nrow(mat)/2, by=2), ]+mat[seqn+1, ]
+ )
   user  system elapsed
   0.05    0.00    0.05

system.time(for (i in 1:1000)

+   {mat2 <- mat; dim(mat2) <- c(2,3,6); mat2[1,,]+mat2[2,,]}
+ )