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

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?

Answer 1

[Azzi Abdelmalek]

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{:})

[Mohammed]

Thank you so much for the nice solution. It works perfect

[Mohammed]

شكرا جزيلا

[Azzi Abdelmalek]

هذه إحدى التقنيات تعلمتها في هذا المنتدى

[Matt J]

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.

Answer 2

[Matt J]

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(:);

[Mohammed]

thank for posting, but where is the output matrix

[Azzi Abdelmalek]

The output is

full(BlockMatrix)

Answer 3

[Matt J]

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{:});

[Yunsong Liu]

Thanks Matt. It works very well.

Answer 4

[Azzi Abdelmalek]

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

[Mohammed]

Thank for posting your answer, but I need an answer without loops