how to build many sparse matrices

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Melody
Melody 2018-9-13
编辑： Melody 2018-9-16
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!
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Steven Lord
Steven Lord 2018-9-13
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.

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采纳的回答

Matt J
Matt J 2018-9-13
编辑：Matt J 2018-9-13
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});
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Melody
Melody 2018-9-15
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?
Melody
Melody 2018-9-16
编辑：Melody 2018-9-16
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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更多回答（2 个）

Matt J
Matt J 2018-9-13
编辑：Matt J 2018-9-13
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.
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Matt J
Matt J 2018-9-13
What are the densities of these matrices nnz(A)/numel(A) ?
Melody
Melody 2018-9-13
Very sparse -- less then 10 nonzero elements for each matrix.

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Christine Tobler
Christine Tobler 2018-9-13
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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Melody
Melody 2018-9-14
Thank you for your advice! It may probably work well with denser matrices, but my matrices only have less than 10 nonzero entries each, so sorting them then creating the sparse matrix actually takes more time. :(

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