Kronecker Tensor Product for very large matrices
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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!!!
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Matt J
2021 年 7 月 16 日
編集済み: Matt J
2021 年 7 月 16 日
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)
Bin=[0;0;ones((nx-2) * (ny-1),1)/dx^2];
Q=spdiags(Bin,ny-1,4,4)
full(Q)
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