Sum over cell array of sparse matrices error: Dimension for sparse matrix concatenation must be <= 2.

Hi all,

I have a cell contains sparse matrices,

K>> a
a =
  2×1 cell array
    [12×12 double]
    [12×12 double]

Now I'd like to sum these 2 sparse matrices into 1. I tried:

K>> sum(cat(3, a{:}), 3)

which gave me error:

Error using cat
  Dimension for sparse matrix concatenation must be <= 2.

This line works for non-sparse matrices, but not for sparse matrices. Manually extract cell elements and sum them is not acceptable. Any idea how to do it? I CANNOT go back to full matrices and sum them.

Thanks!

Answer 1

[James Tursa]

For your particular example, of course

result = a{1} + a{2};

What are the sizes of your real problem? I.e., what are the dimensions of "a" and all of the cell elements?

[Xiaohan Du]

Maybe I did not explain my problem clearly, I do not want to add them manually like you did, I'd like to sum these matrices in one go.

[James Tursa]

The simple way:

result = a{1};
for k=2:numel(a)
    result = result + a{k};
end

[Xiaohan Du]

Well yeah, I'm solving my problem using same way as your post, I just don't get why Matlab gave me error

Error using cat
  Dimension for sparse matrix concatenation must be <= 2.

Cause

sum(cat(3, a{:}), 3)

works for full matrices but not for sparse matrices. Why would Matlab do such a thing?

[James Tursa]

MATLAB gives you that error because MATLAB does not support multi-dimensional sparse matrices. MATLAB only supports 2D matrices. So the cat across the 3rd dimension with sparse matrices fails, because you are trying to build a 3D sparse matrix which is not supported. There is an FEX submission by Matt J that you can use if you really want to:

https://www.mathworks.com/matlabcentral/fileexchange/29832-n-dimensional-sparse-arrays

[Koen Ruymbeek]

Probably it is already far too late, but for someone who has the same question:

In fact you do not need the work around with 3-dimensional sparse arrays. You can first convert the matrices in the cell to a vector, and then sum them using cat. In matlab-language, this is

n = 1000;
Ahelp = {randn(n,n), randn(n,n), randn(n,n), randn(n,n)}
Ahelp = cellfun( @(x) x(:), Ahelp, 'Uniform', false);
A = reshape( sum( cat(2, Ahelp{:}),2),n,n);