Blockwise sum of matrix elements

Question

I want to go from something like this:

1> a = matrix(c(1,4,2,5,2,5,2,1,4,4,3,2,1,6,7,4),4)
1> a
     [,1] [,2] [,3] [,4]
[1,]    1    2    4    1
[2,]          


        

Answer 1

tapply(a, list((row(a) + 1L) %/% 2L, (col(a) + 1L) %/% 2L), sum)
#    1  2
# 1 12 15
# 2 10 16

I used 1L and 2L instead of 1 and 2 so indices remain integers (as opposed to numerics) and it should run faster that way.