Testing for block diagonal form
in [Matlab]
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From: Frank on 1 Jun 2010 19:54 Hello, is there a computationally cheap procedure to determine whether a (large) matrix can be written (by row and column permutations) in a block diagonal form? I know that 'symrcm' can reorder rows and columns, and with a subsequent 'spy' the block diagonal form can be assessed by visual inspection. What I need, however, is a computational (cheap) assessment whether the matrix is in (or rewritable as) block diagonal. Thanks a lot!
From: John D'Errico on 1 Jun 2010 20:06 "Frank " <FPOELW(a)utsouthwestern.edu> wrote in message <hu46ir$m79$1(a)fred.mathworks.com>... > Hello, is there a computationally cheap procedure to determine whether a (large) matrix can be written (by row and column permutations) in a block diagonal form? > I know that 'symrcm' can reorder rows and columns, and with a subsequent 'spy' the block diagonal form can be assessed by visual inspection. What I need, however, is a computational (cheap) assessment whether the matrix is in (or rewritable as) block diagonal. > Thanks a lot! Yes. In fact, it is trivial, if you do not specify the size of the blocks. ANY matrix can be viewed as a block diagonal matrix. The block may be NxN of course. John
From: Frank on 1 Jun 2010 20:34
"John D'Errico" <woodchips(a)rochester.rr.com> wrote in message <hu479b$8os$1(a)fred.mathworks.com>... > > Yes. In fact, it is trivial, if you do not specify the > size of the blocks. ANY matrix can be viewed as a > block diagonal matrix. The block may be NxN of > course. > > John Ah, that's not what I mean. For what I need, within the blocks no zeros are allowed. So on the diagonal should be submatrices that contain no zeros and the off-diagonal matrices should be all zeros (that is, the full matrix being the direct sum of the submatrices). To be more specific: I have a symmetric matrix of which I can re-order the non-zero elements towards the diagonal (with 'symrcm') and then the question is whether this new matrix is block diagonal. It could be the full NxN matrix indeed, but only if that does not contain any zeros. Thanks! Frank |