How to create a block diagonal matrix from the slices of a 3D matrix

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Mohammed
Mohammed 2014-10-2
评论： Yunsong Liu 2019-7-18
I have a large 3D matrix (K) composed of 200 slices , and I want to create a block diagonal matrix from the slices of it without looping. For example
K(:,:,1) =[1 2;3 4]
K(:,:,2) =[5 6;7 8]
K(:,:,3) =[9 10;11 12]
.
.
.
K(:,:,200) =[1 10;13 15]
if we assume the number of slice is 3, the output should be
1 2 0 0 0 0
3 4 0 0 0 0
0 0 5 6 0 0
0 0 7 8 0 0
0 0 0 0 9 10
0 0 0 0 11 12
But how the block diagonal matrix created from all the 200 slices without looping?

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采纳的回答

Azzi Abdelmalek
Azzi Abdelmalek 2014-10-2
k(:,:,1) =[1 2;3 4]
k(:,:,2) =[5 6;7 8]
k(:,:,3) =[9 10;11 12]
q=num2cell(k,[1,2])
blkdiag(q{:})
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Matt J
Matt J 2014-10-2
Note that this still uses a for-loop inside num2cell.m, though how much that hurts you, I don't know.
Note also that my 2nd answer here was the same as this, except that it returns the result in sparse form, which is normally more desirable for block diagonal matrices with small blocks.

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更多回答（3 个）

Matt J
Matt J 2014-10-2
编辑：Matt J 2014-10-2
I doubt that avoiding loops leads to the fastest code, but the following does avoid them,
[m,n,p]=size(K);
BlockMatrix=kron(speye(p), ones(m,n));
BlockMatrix(logical(BlockMatrix))=K(:);
Matt J
Matt J 2014-10-2
编辑：Matt J 2014-10-2
This doesn't avoid a loop, even if it looks like it does, but it might be the fastest way.
Kcell = cellfun(@sparse, num2cell(K,[1,2]), 'uni',0 );
BlockMatrix=blkdiag(Kcell{:});
Azzi Abdelmalek
Azzi Abdelmalek 2014-10-2
k(:,:,1) =[1 2;3 4]
k(:,:,2) =[5 6;7 8]
k(:,:,3) =[9 10;11 12]
out=[];
for ii=1:size(k,3)
out=blkdiag(out,k(:,:,ii))
end

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