Extended block diagonal matrix in Matlab

Question

I know that to generate a block-diagonal matrix in Matlab the command blkdiag generates such a matrix:

Answer 1

This could be one approach based on kron, tril & triu -

%// Take all A1, A2, A3, etc in a cell array for easy access and same for B
A = {A1,A2,A3,A4}
B = {B1,B2,B3}

%// Setup output array with the A blocks at main diagonal
out = blkdiag(A{:})

%// logical array with 1s at places where kth diagonal elements are to be put
idx = kron(triu(true(numel(A)),k) & tril(true(numel(A)),k),ones(size(A{1})))>0

%// Put kth diagonal blocks using the logical mask
out(idx) = [B{1:numel(A)-k}]

Sample run with k = 1 for 2 x 2 sizes matrices -

>> A{:}
ans =
    0.3467    0.7966
    0.6228    0.7459
ans =
    0.1255    0.0252
    0.8224    0.4144
ans =
    0.7314    0.3673
    0.7814    0.7449
ans =
    0.8923    0.1296
    0.2426    0.2251
>> B{:}
ans =
    0.3500    0.9275
    0.2871    0.0513
ans =
    0.5927    0.8384
    0.1629    0.1676
ans =
    0.5022    0.3554
    0.9993    0.0471
>> out
out =
    0.3467    0.7966    0.3500    0.9275         0         0         0         0
    0.6228    0.7459    0.2871    0.0513         0         0         0         0
         0         0    0.1255    0.0252    0.5927    0.8384         0         0
         0         0    0.8224    0.4144    0.1629    0.1676         0         0
         0         0         0         0    0.7314    0.3673    0.5022    0.3554
         0         0         0         0    0.7814    0.7449    0.9993    0.0471
         0         0         0         0         0         0    0.8923    0.1296
         0         0         0         0         0         0    0.2426    0.2251