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

Question

David Cyncynates 2020-12-19

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https://ww2.mathworks.cn/matlabcentral/answers/698345-what-s-the-best-way-to-build-a-block-sparse-matrix-whose-entries-are-diagonal-matrices

编辑： David Cyncynates 2020-12-20

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.

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Answer 1

David Cyncynates 2020-12-20

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https://ww2.mathworks.cn/matlabcentral/answers/698345-what-s-the-best-way-to-build-a-block-sparse-matrix-whose-entries-are-diagonal-matrices#answer_580155

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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)