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Extreme memory usage when using gather

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Hi! I have a code that solves a tridiagonal system and, because of the large sizes of the matrices, I'm trying to solve the A\V on GPU.
At each iteration I modify the diagonal elements and need to solve on the GPU like the below code:
After the GPU have solved the system, I need to get the present result and store in a matrix. For this I'm using abs(gather(head(ffield,savez-TERRAIN+1))); and when this commands are called, the memory usage goes beyond 130 GB.
What is happening here to the memory goes crazy like that? Also, there are any tips to improve my code? In summary, I have to solve a large tridiagonal system at each iteration of a large loop (like hundreds of thousands iterations). It'd be better if I could create the matrices on the GPU once and simply modify its diagonals values directly on the GPU, but I couldn't do this yet, so I'm modifying a normal matrix and sending it to the GPU again at each iteration.
A = spdiags([[subdiagA;0] zeros(N-1,1) [0;superdiagA]],-1:1,N-1,N-1);
B = spdiags([[subdiagB;0] zeros(N-1,1) [0;superdiagB]],-1:1,N-1,N-1);
ffield = gpuArray(complex(field));
indicesDiag = (1:N:(N-1)^2)';
for m = 2:M
a_mj = k0^2*delz^2*(m_ref_curr(2:end).^2 - 1);
% modify matrix A diagonal
diagA = c*(-2 + b + a_mj);
% modify matrix B diagonal
diagB = conj(c)*(-2 + conj(b) + a_mj);
% some boundary conditions
km = delz*(alpha_BC(m) + 1i*k0*0.5*slopes(m)^3);
if PEC && POL == 'V'
km = delz*1i*k0*0.5*slopes(m)^3;
% modify first and last elements of matrices A and B diagonals
diagA(1) = diagA(1) + c/(1 - km + 0.5*km^2);
diagB(1) = diagB(1) + conj(c)/(1 - km + 0.5*km^2);
diagA(end) = 1;
diagB(end) = 1;
elseif POL == 'V' % NEUMANN
diagA(end) = diagA(end)/2;
diagB(end) = diagB(end)/2;
% update the diagonal terms of matrix A and send to GPU
A(indicesDiag) = diagA;
AA = gpuArray(complex(A)); % AA is the version of A on the GPU
% update the diagonal terms of matrix A and send to GPU
B(indicesDiag) = diagB;
BB = gpuArray(complex(B)); % BB is the version of matrix B on the GPU
% update another GPU array
ffield = ffield.*exp(-1i*k0*slopes(m)*z);
VV = BB*ffield(2:end); % operation on GPU
% solve the tridiagonal system on GPU
ffield(2:end) = AA\VV;
ffield(1) = ffield(2)/(1 - km + 0.5*km^2);
% some operations to prepare for the next operation
ffield = ffield.*exp(1i*k0*(slopes(m)*z + 0.5*slopes(m)^2*delx + delx));
ffield(zwin:end) = ffield(zwin:end).*win;
% here i need to get the result that is in the GPU array ffield and
% store part of it in a normal matrix u()
TERRAIN = floor(terreno(m)/delz)+1;
u(TERRAIN:end,m) = abs(gather(head(ffield,savez-TERRAIN+1))); %% when this line is executed, memory usage goes above 130 GB and the thing crashes
Joss Knight
Joss Knight on 1 Apr 2024
Edited: Joss Knight on 1 Apr 2024
I would have to do a deeper dive to give really good advice, but I can surmise this much. If your system is tridiagonal then store it as an n-by-3 matrix on the GPU and update it as such; only create a sparse matrix out of it to solve the system. The slowness of spdiags on the GPU is I think only because diagA is not a gpuArray. Make it one and it should speed things up.
So I would probably make diagA and diagB gpuArray objects and store A and B (and AA and BB) as 3-column dense matrices, for which you are updating the middle column. When you do the system solve, convert to sparse only temporarily:
ffield(2:end) = spdiags(AA,-1:1)\VV;
I'm assuming here that you are using R2021a or later, which was when sparse tridiagonal solves were optimized.
Lorenco Santos Vasconcelos
Maybe replacing
ffield(2:end) = A\V; % A and V are g
[ffield(2:end),~] = pcg(A,V);
could do a better work but I think that the bottleneck is not the system solver (mldivide or iterative with preconditioner), but the modification of the matrices at each iteration and passing this arrays to the GPU.

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Accepted Answer

Joss Knight
Joss Knight on 1 Apr 2024
Edited: Joss Knight on 14 Apr 2024
As others have worked out, it looks like the issue is the indexed assignment into u:
u(TERRAIN:end,m) = abs(gather(head(ffield,savez-TERRAIN+1)));
Because u is in the base workspace, this needs to make a second copy of u during the assignment, to protect your workspace.
The normal way to fix this is to make your code into a function which returns u, so that it doesn't exist in the base workspace while the function is running. If this is impossible for you, there are ways to 'move' the variable u into a function for update, but they are a little bit advanced and I'm not even sure how safe it is to give this advice...
u = updateU(u, head, ffield, savez, TERRAIN, m);
function u = updateU(u, head, ffield, savez, TERRAIN, m)
% Delete u in parent workspace
assignin('base', 'u', []);
% Now the only copy of u is local and the assignment can be inplace
u(TERRAIN:end,m) = abs(gather(head(ffield,savez-TERRAIN+1)));
Of course, you could also try to rework your code so that you're not storing hundreds of gigs of data in a single variable. Even breaking it up into a cell array (e.g. each column is a different cell element) would help because only the element being overwritten would need to be copied.

More Answers (1)

Taylor on 28 Mar 2024
gather is just doing what it's supposed to do. Namely, "On a gpuArray: transfers the elements of A from the GPU to the local workspace and assigns them to X." Here's more info on running MATLAB functions on a GPU.
Taylor on 28 Mar 2024
I'm wondering if it is related to calling gather multiple times with the for loop. Have you tried minimizing your number fo gather calls using the [X1,X2,...,Xn] = gather(A1,A2,...,An) syntax outside of the loop instead?
Lorenco Santos Vasconcelos
It could be, but I think no because I put a breakpoint inside the loop jat the gather line and run only the first iteration. Once I press F10 to execute gather, the MATLAB proccess that is taking about 2GB of RAM jumps to 20, 50, almost 100 GB.
The idea of avoid the gather could work, but unfortunately this is not possible for me. I could create the entire matrix u as a gpuArray, fill it with the loop and than gather it at the end, but this would mean to store a big matrix in the gpu shared memory. For this reason I've preferred to store in the gpu only one column at a time and gather this column at each iteration to fill the complete local workspace matrix.
Do you think it'd be better to create the entire matrix as a gpuArray and avoid the gather at each iteration?
Just to make the context available, the problem is straightforward:
big matrix u(N,M) represents a physical quantity over a domain. I have initial values at the first column of u, i.e u(:,1); With the initial column, I compute the next colum u(:,m) by solving a large tridiagonal system on the GPU. So, at each iteration, the GPU computes an array of size (m,1) and I gather this and put on u(:,m).

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