What's the best way to build a block sparse matrix whose entries are diagonal matrices?

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I want to construct a square block matrix out of square matrices, whose entries all lie on their respective diagonals. For example,
clear
N = 3;
M = 5;
MFull = zeros(N * M, N * M);
for n = 1 : M
for m = 1 : M
Mblock = rand(N,1) * m * n;
MFull((n - 1) * N + 1:n * N, (m - 1) * N + 1:m * N) = diag(Mblock);
end
end
When this matrix becomes big, this is clearly inefficient. I would like to define MFull as a sparse matrix to avoid memory issues and speed things up. Any suggestions are appreciated! To clarify: I would like to avoid creating MFull as a full matrix, and then converting it to a sparse matrix.

Accepted Answer

David Cyncynates
David Cyncynates on 20 Dec 2020
Here's a solution that seems to work for me:
clear
N = 3;
M = 5;
BlockContainer = zeros(N * M, 2 * M - 1);
for n = 1 : M
for m = 1: M
row = m;
column = M + m - n;
Mblock = rand(N,1) * m * n;
BlockContainer((row - 1) * N + 1:(row) * N,column) = Mblock;
end
end
MFull = spdiags(BlockContainer,-(M - 1) * N:N:(M - 1) * N, N * M, N * M)

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