# Sparse Block diagonal matrix

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David on 19 Aug 2012
Answered: Daniel Fortunato on 21 Apr 2022
I have an N by M matrix and I want to store its columns in block diagonal form. This matrix is enormous, so if I can directly store it as a sparse matrix that would be helpful.
To give more detail:
X = ones(30, 1000);
And I want this without having to type it out (because the matrix actually has 1 million columns).
sparse(blkdiag(X(:,1), X(:,2), X(:,3), .... , X(:,1000)).
By the way, my best attempt is this:
a = cell(M,1);
for i = 1:M
[a{i}]= deal(sparse(X(:,i)));
end
X=blkdiag(a{:});
But I'm using a loop and am worried this is inefficient.

Oleg Komarov on 19 Aug 2012
Edited: Oleg Komarov on 19 Aug 2012
The easy way:
X = num2cell(X,1);
sparse(blkdiag(X{:}))
Or, creating the sparse matrix directly:
[r,c] = size(X);
i = 1:numel(X);
j = repmat(1:c,r,1);
B = sparse(i',j(:),X(:));
The second method is not only ~30-40 times faster but avoids creating the intermediate blkdiag() double matrix, which can easily cause out of memory.
Honestly, I don't know if you have that kind of memory:
(30 * 1e6) rows * 1e6 cols * 8 bytes ~ 218.2 TB
Therefore, go for the second method.

### More Answers (2)

Alec on 18 Jul 2014
Or, if you can, call `sparse` before `blkdiag`:
X = ones(30, 1000);
X = num2cell(sparse(X),1);
B = blkdiag(X{:});

Daniel Fortunato on 21 Apr 2022
You can also use MATLAB's internal sparse block-diagonal routine, which will create a sparse block-diagonal matrix even from dense blocks:
B = matlab.internal.math.blkdiag(X{:});

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