Asked by Yuzixuan Zhu
on 13 Sep 2018 at 16:44

I wish to create m = 10^5 sparse matrices of size n by n, say n = 10^4. I have been using

A = cell(m, 1); for i = 1:m row = ...; col = ...; val = ...; % here ... means some certain assignment in column vectors A{i} = sparse(row, col, val, n, n); end

But it is too slow. So I tried to use the types ndSparse (https://www.mathworks.com/matlabcentral/fileexchange/29832-n-dimensional-sparse-arrays) and sptensor (https://www.sandia.gov/~tgkolda/TensorToolbox/index-2.6.html). They do the job fast by creating m matrices all at once in 3d (n*n*m). It requires concatenating index and value vectors, where the speed is acceptable. However, I then need individual matrices for some operations that do NOT work on types ndSparse and sptensor. For example,

[R, p] = chol(A(:, :, i));

does not work. If I convert the object to Matlab sparse type as

[R, p] = chol(sparse(A(:, :, i)));

then it is even slower than creating A one by one in the for loop. Considering that Matlab does not support multidimensional sparse arrays (so I cannot reshape the abovementioned types into Matlab sparse tensor), how can I speed up creating m sparse matrices? Thank you!

Answer by Matt J
on 13 Sep 2018 at 18:20

Edited by Matt J
on 13 Sep 2018 at 18:44

Accepted Answer

Once you have A in ndSparse form, you can then split it into the cell array form you were originally trying to get using mat2cell:

Ar=sparse( reshape(A,n,m*n) );

Acell=mat2cell(Ar,n,ones(1,m)*n);

and then

[R, p] = chol(Acell{i});

Matt J
on 14 Sep 2018 at 16:23

Yuzixuan Zhu
on 15 Sep 2018 at 5:06

I've been trying to think of a way to not use them simultaneously but haven't found a solution. However I found a way to work around building big sparse matrix (thanks for reminding me that even empty big sparse matrix can take up a lot of memory):

[C, ~, ic] = unique([row{i}; col{i}]); len_C = length(C); len_ic2 = length(ic)/2; Ai = sparse(ic, [ic((len_ic2 + 1):end); ic(1:len_ic2)], val{i}, len_C, len_C);

This works for all my operations. However, the "unique" function in the first line above takes even more time than before... Is there any way to make it faster?

Yuzixuan Zhu
on 16 Sep 2018 at 15:29

I came up with a way to not keep all matrices at the same time, and codes as in the 3rd comment in this answer seem to save 50% time for the large data. Thank you!

May I know what the proper way to include "ndSparse.m" in my software is? Is it enough to include "license.txt" and cite the webpage "https://www.mathworks.com/matlabcentral/fileexchange/29832-n-dimensional-sparse-arrays" in my document?

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Answer by Matt J
on 13 Sep 2018 at 19:11

Edited by Matt J
on 13 Sep 2018 at 19:13

It might also be a good idea, instead of constructing a 3D sparse array or a cell array of separate matrices, to instead create a big block diagonal matrix, where each n x n matrix is one of the diagonal blocks. That way you can do the entire Cholesky decomposition in a single call to CHOL.

Matt J
on 13 Sep 2018 at 19:41

How does it "not apply" to your application?

Making CHOL a method of ndSparse will not address the problem because the bottleneck would still be in accessing the sub-matrices A(:,:,i). Even with normal 2D sparse matrices, you are seeing that that is problem.

Matt J
on 13 Sep 2018 at 19:47

What are the densities of these matrices nnz(A)/numel(A) ?

Yuzixuan Zhu
on 13 Sep 2018 at 19:53

Very sparse -- less then 10 nonzero elements for each matrix.

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Answer by Christine Tobler
on 13 Sep 2018 at 20:10

The `sparse` function will often be faster if the second input, `col`, is sorted in ascending order. If you can cheaply construct `col` in a way that this is the case, that should help a bit with performance.

Yuzixuan Zhu
on 14 Sep 2018 at 0:42

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## 1 Comment

## Steven Lord (view profile)

Direct link to this comment:https://www.mathworks.com/matlabcentral/answers/418890-how-to-build-many-sparse-matrices#comment_610077

How are you planning to use those 1e5

sparsematrices later in your code? I want to see if it is possible to reduce the number ofsparsematrices you need to create while still achieving your ultimate goal by using a different approach or algorithm.Sign in to comment.