Concatenating large matrices - out of memory

I have four 4096x4096 sparse matrices namely A, B, C, and D and they only have elements on the diagonal.

I tried to make a matrix X = [ A B; C D] which is 8192x8192 but I get an out of memory error.

Essentially, I need to multiply X with a 8192x1 vector Y.

Is there a more sophisticated way to do this?

Answer 1

[Matt J]

X=[sparse(A),sparse(B);sparse(C), sparse(D)];

result = X*Y;

Or,

a=diag(A);
b=diag(B);
c=diag(C);
d=diag(D);

   y1=Y(1:4096);
   y2=Y(4097:end);

   result = [a.*y1+b.*y2; c.*y1 + d.*y2];

[John]

Thanks but for your first solution, A, B , C, and D are already sparse. Does it change anything if you apply the sparse function again when it's being concatenated.

[Matt J]

Are you sure they are already sparse? Or, are you sure the out-of-memory is coming from the statement X=[A B;C D]?

It doesn't make sense that diagonal sparse matrices of that size would give you any problems with memory. If you are on a 32 bit machine and you accidentally made those matrices non-sparse, I could see you getting such an error

Answer 2

[Konrad Malkowski]

Have you tried explicitly storing the matrix as sparse?

See http://www.mathworks.com/help/matlab/ref/sparse.html

[John]

Yes, the matrices are sparse