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

You can use matrix multiplication for this.

# Computation matrix:

mat <- function(n, r) {
  suppressWarnings(matrix(c(rep(1, r), rep(0, n)), n, n/r))
}

Square-matrix example, uses a matrix and its transpose on each side of a:

# Reduce a 4x4 matrix by a factor of 2:

x <- mat(4, 2)
x
##      [,1] [,2]
## [1,]    1    0
## [2,]    1    0
## [3,]    0    1
## [4,]    0    1

t(x) %*% a %*% x
##      [,1] [,2]
## [1,]   12   15
## [2,]   10   16

Non-square example:

b <- matrix(1:24, 4 ,6)
t(mat(4, 2)) %*% b %*% mat(6, 2)
##      [,1] [,2] [,3]
## [1,]   14   46   78
## [2,]   22   54   86