Algorithmically construct block matrices (matlab)

Question

Let Matrices = [A B C D] be a set of square matrices. I want to construct

H = [A B C D;
     B A B C;
     C B A B;
     D C B A]

If all I was interested in was the 4 by 4 case, then this would be enough. However, I want to construct the analogous matrix when Matrices = [A B C D E F] etc. What code could I write to do this?

Answer 1

This can be done as follows:

• Concatenate the matrices into a 3D array;
• Build the basic with numbers instead of matrices using toeplitz;
• Extend this structure so that using linear indexing into the 3D array produces the desired result.

N = 2; % matrix size
M = 3; % number of matrices
matrices = arrayfun(@(x) {randi(9,N)}, 1:M); % input matrices
matrices_3D = cat(3, matrices{:}); % concatenate the matrices along the third dim
ind1 = repmat(reshape(1:N^2, N, N), M, M); % linear indices within each matrix
ind2 = (repelem(toeplitz(1:M), N, N)-1)*N^2; % linear indices to select the matrices
result = matrices_3D(ind1 + ind2); % build result

Example run:

>> celldisp(matrices)
matrices{1} =
     1     4
     2     6
matrices{2} =
     6     4
     5     9
matrices{3} =
     5     4
     6     5
>> result
result =
     1     4     6     4     5     4
     2     6     5     9     6     5
     6     4     1     4     6     4
     5     9     2     6     5     9
     5     4     6     4     1     4
     6     5     5     9     2     6