Construct columns from submatrices in Matlab

Question

In Matlab, I'm trying to transform a matrix A to another matrix B such that B 's columns are made up of square submatrices of A . For example, if A is:

A = [1 1 2 2
     1 1 2 2
     3 3 4 4
     3 3 4 4];

I'd like B to be:

B = [1 2 3 4
     1 2 3 4
     1 2 3 4
     1 2 3 4]

A could be, say 16-by-16, and constructing B from 4-by-4 squares would result in B being 4-by-64.

Is there an efficient way to do this using reshape in combination with some other commands? Or some other approach? I am currently iterating in a loop, which is very slow with a large number of large source matrices.

Answer 1

Assume your matrix is a bit more general, and made of 3x2 blocks:

A = [1 1 2 2 
     1 1 2 2
     1 1 2 2
     3 3 4 4
     3 3 4 4
     3 3 4 4
     5 5 6 6
     5 5 6 6
     5 5 6 6];

b   = [3 2];
szA = size(A);

Transpose, reshape, permute, reshape.

nb   = prod(szA./b); % Number of blocks
nelb = prod(b);      % Number of elements per block
out1 = reshape(permute(reshape(A',szA(2),b(1),szA(1)/b(1)),[2,1,3]),nelb,nb)

Alternatively, slower and memory intensive but more readable:

d1  = repmat(b(1),1,szA(1)/b(1));
d2  = repmat(b(2),1,szA(2)/b(2));
out = reshape(mat2cell(A,d1,d2)',1,nelb);
out = reshape([out{:}],nelb,nb)

Now, if the blocks are square, simply set b = [2,2] or b = [3,3] , etc..., or simplify the general formulation removing indexing of b and prod .