How can I create a sparse matrix containing (3,3) block matrices on the main diagonal and on diagonals below and above the main diagonal without using loops?

The idea is to create a (3m,3m) sparse matrix with small (3,3) matrices on the main diagonal and on diagonals below and above the main diagonal. By saying this, I want that each time the main diagonal of the small (3,3) matrix is on the main diagonal or on another diagonal respectively. There is no gap between the small (3,3) matrices on the diagonals. How can I use the functions sparse, spdiags, blkdiag to create this matrix? If there are other functions guaranteeing sparsity that's fine.

[Cedric]

Did you generate these m 3x3 sparse matrices already or do you want to avoid building them and build directly the block diagonal large sparse matrix? If you have these small matrices already defined, what have you tried so far using BLKDIAG?

[Manuel]

I've got all the 3x3 matrices (they are not sparse) already. Basically they are the local Hessian operator on a manifold. Now I want to store them in this huge sparse matrix to do a Newton step (Newton Method). I've thought of using the Tensor Toolbox since blkdiag doesn't give me a sparse matrix.

Answer 1

[Cedric]

BLKDIAG will give you a sparse matrix if one of its inputs is sparse. Try building the 3x3 matrices as sparse, or converting them (or just one) to sparse, before using BLKDIAG; it should work fine.

[Manuel]

Hey Cedric, Thanks a lot for your answer. That's been a great help. Manuel

Answer 2

[Iain]

You can initialise a sparse matrix as:

matrix = sparse(zeros(3*m,3*m));

If you then use it as:

matrix(1:3,1:3) = [a b c; d e f; g h i];

matrix(3+1:3,3+1:3) = [j k l; m n o; p q r];

... etc you will get what I think you're asking for.

[Manuel]

Thanks lain for your answer. You got my idea. But my matrix will be huge and with your idea I'll have to use a loop. But loops are way to slow for what I'm doing.