Kronecker Tensor Product for very large matrices

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William Kett
William Kett on 15 Jul 2021
Edited: Matt J on 18 Jul 2021
I need to build a 2D kronecker tensor product of with a size of approximately 10^6 x 10^6. The problem is that I get the following message:
%Out of memory. Type HELP MEMORY for your options.
Is there any way to get around this memory limitation? My code is posted below:
nx = 1000;ny = 1000; %Number of points along x and y
dx = 1/(nx-1);dy = 1/(ny-1); %Spacing between each point
diag_block = eye(ny-1) * (-2/dx^2-2/dy^2); %Identity Matrix of ny-1 points
diag_block = diag_block + diag(ones(ny-2,1)/dy^2,1); %
diag_block = sparse(diag_block) + sparse(diag(ones(ny-2,1)/dy^2,-1)); %
Matrix = kron(sparse(eye(nx-1)),sparse(diag_block)); %Using sparse() made this line work
Matrix = Matrix + diag(ones((nx-2) * (ny-1),1)/dx^2, ny-1); %FAILS HERE!!!
Matrix = Matrix + diag(ones((nx-2) * (ny-1),1)/dx^2, -(ny-1)); %AND HERE!!!

Accepted Answer

Matt J
Matt J on 16 Jul 2021
Edited: Matt J on 16 Jul 2021
You need the matrices generated by diag() in sparse form, too. Use spdiags() instead, e.g.,
nx = 3;ny =3; dx=1; %Number of points along x and y
Qfull=diag(ones((nx-2) * (ny-1),1)/dx^2, ny-1)
Qfull = 4×4
0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0
Bin=[0;0;ones((nx-2) * (ny-1),1)/dx^2];
Q=spdiags(Bin,ny-1,4,4)
Q =
(1,3) 1 (2,4) 1
full(Q)
ans = 4×4
0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0
  4 Comments
Matt J
Matt J on 18 Jul 2021
Could this be why?
Yes, you should review the documentation for spdiags() and/or re-examine the example I gave. you It's syntax is very different from that of diag().

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