Block diagonal matrix on lower diagonals

Hello I want to create a matrix which has block matrices on every diagonal. So on the first diagonal there is the matrix B(1) on the second diagonal the matrix B(2) and so on:

A =

   1.0e-04 *

    0.4059    0.0125         0         0         0         0         0         0
    0.0125    0.4059         0         0         0         0         0         0
    0.0845    0.0208    0.4059    0.0125         0         0         0         0
    0.0208    0.0845    0.0125    0.4059         0         0         0         0
    0.0425    0.0170    0.0845    0.0208    0.4059    0.0125         0         0
    0.0170    0.0425    0.0208    0.0845    0.0125    0.4059         0         0
    0.0267    0.0135    0.0425    0.0170    0.0845    0.0208    0.4059    0.0125
    0.0135    0.0267    0.0170    0.0425    0.0208    0.0845    0.0125    0.4059

As this matrix can be quite large I want to avoid any loops. The main diagonal is no problem as I can use blkdiag but how can I solve the problem with the other diagonals?

Thank you a lot in advance!!

Answer 1

[Stephen23]

New Answer! Simply define a cell vector of matrices, which must all be the same size. The rest happens automagically. Some fake data:

B{1} = [0,1;2,3];
B{2} = [4,5;6,7];
B{3} = [8,9;10,11];
B{4} = [12,13;14,15];

Create numeric matrix A with the elements of B on the diagonals:

N = numel(B);
X = tril(true(N));
Y = hankel(ones(1,N));
[R,C] = find(Y);
U = accumarray(R,find(X),[],@(n){n});
Z = cell(N);
for k = 1:N
    Z(U{k}) = B(k);
end
Z(~X) = {zeros(size(B{1}))};
A = cell2mat(Z);

And the example output array:

>> A
A =

      0    1    0    0    0    0    0    0
      2    3    0    0    0    0    0    0
      4    5    0    1    0    0    0    0
      6    7    2    3    0    0    0    0
      8    9    4    5    0    1    0    0
     10   11    6    7    2    3    0    0
     12   13    8    9    4    5    0    1
     14   15   10   11    6    7    2    3

Yes it has a loop, but only a small one that loops once over the elements of B.

[M.K.123]

Thanks a lot! It works great!! Do you maybe also know an efficient method to save this matrix and to use it later in a backslash operator?

[Stephen23]

If you want to save a variable to a file then the fastest and most efficient way is to use save:

save(filename,'A')

And the load the data later from the file:

X = load(filename);
X.A