how to build many sparse matrices
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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!
1 Comment
Steven Lord
on 13 Sep 2018
How are you planning to use those 1e5 sparse matrices later in your code? I want to see if it is possible to reduce the number of sparse matrices you need to create while still achieving your ultimate goal by using a different approach or algorithm.
Accepted Answer
More Answers (2)
Matt J
on 13 Sep 2018
Edited: Matt J
on 13 Sep 2018
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.
4 Comments
Christine Tobler
on 13 Sep 2018
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.
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