Possibly homework. (I never trust simple problems like this, where the goal is simply to move thigns around in a matrix. They are almost always homework assignments.) But you already have two answers, and you have accepted one. So I might as well show the pretty way to solve the problem. You can do it via matrix multiplies. I've built it to perform the swaps using sparse matrices, to make it efficient for large matrices.
The trick is to pre-multiply and post-multiply by a sparsely constructed permutation matrix.
A = reshape(1:16,4,4)'
A =
1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 16
A = swapblocks(A)
A =
11 12 9 10
15 16 13 14
3 4 1 2
7 8 5 6
timeit(@() swapblocks(A))
And that seems reasonably fast for a 5kx5k matrix permutation.
Do you see how it works? For the 4x4 mtrix, here is how it works. Constriuct a 4x4 transformation matrix, that looks like this:
T = [zeros(2),eye(2);eye(2),zeros(2)]
T =
0 0 1 0
0 0 0 1
1 0 0 0
0 1 0 0
See what happens when we multiply T*A.
A = reshape(1:16,4,4)'
A =
1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 16
T*A
ans =
9 10 11 12
13 14 15 16
1 2 3 4
5 6 7 8
As you can see, that swaps the blocks from top to bottom. Essentially, it swaps the rows to go from [1 2 3 4] to [3 4 1 2]. Next, when we post multiply by T, it swaps the columns, in the same blockwise fashion.
T*A*T
ans =
11 12 9 10
15 16 13 14
3 4 1 2
7 8 5 6
But of course, swapblocks was written to use a sparse matrix T. That maks the matrix multiplies far more efficient when A is large.
function Aswap = swapblocks(A)
if (N~=M) || (mod(N,2)==1)
error('A must be a square matrix with an even number of rows and columns')
Anyway, if this was homework, your teacher will never believe you solved it yourself like this.
