GPU memory usage for Hadamard product

I have a GPU with 48 Gb of RAM.

I have a large matrix A (complex single 45927x45927, gpuArray) taking 16 Gb of my GPU.

I get to the following Hadamard product with a vector B (complex single 45927x1, gpuArray) with approximately 28 Gb of free RAM on the GPU:

C = A .* (B.')

But this throws an "out of memory on the device" error, despite there being enough memory for C (also 16 Gb). Why is this happening? Does MATLAB implicitly convert B to a full matrix? Is there a way to get this multiplication to work on the GPU within the available memory? (maybe this has been fixed in later releases of MATLAB?)

[Matt J]

What happens if you do,

A = A.*B.'

[Walter Roberson]

I seem to recall that additional memory is needed for complex arrays, due to differences in the layout of complex vectors.

[Walter Roberson]

The rule of thumb is that you should avoid having arrays that are more than 1/3 of the GPU memory: otherwise the creation of temporary variables for calculation runs the risk of overflowing memory.

[Walter Roberson]

You could try

N = size(A,1);
C = zeros(N, N, 'gpuArray');
for K = 1 : N
    C(:,K) = A(:,K) .* B(1,K);
end

[Massimiliano Zanoli]

Thanks for the suggestion. I guess you meant B(K, 1) ?

I tried:

C = zeros(size(A), "like", B);
for n = 1 : length(B)
    C(:, n) = A(:, n) .* B(n);
end

This works, technically, but it becomes extremely slow and kind of defeats the purpose of using the GPU...

(The first line is the fastest way I found to directly initialize a complex single array on the GPU)

[Matt J]

But the fact that it works without giving you out-of-memory error messages is important. It indicates that the problems you are having are because of temporary memory allocation, and not because MATLAB is failing to allocate space for the final result C.

[Massimiliano Zanoli]

@Matt J: I get the same error if I do:

A = A.*B.'

[Matt J]

What happens if you do other operations, like,

C=A+A
C=A+B
C=gpuArray.zeros(size(A))+1j*gpuArray.ones(size(A));

Answer 1

[Sivsankar]

Hi,

I believe that you are probably limited by the size of RAM of your GPU. I can suggest some ideas that you can implement which may work.

• Upgrade to the latest version of MATLAB.
• Pre-allocate the memory for the resultant gpuArray matrix C.
• Clear any existing gpuArray that may take up the RAM.
• Reset GPU device to release memory.

You can leverage this MATLAB answer that highlights a similar issue.

https://www.mathworks.com/matlabcentral/answers/504069-gpu-out-of-memory

You can also make use of this MathWorks documentation that explains on how to resolve such “out of memory” errors.

https://www.mathworks.com/help/matlab/matlab_prog/resolving-out-of-memory-errors.html

Hope this works for you. Thanks.

[Massimiliano Zanoli]

Thanks for the suggestions. I tried clearing and pre-allocating, but MATLAB still seemingly attempts to allocate 3 * 16 Gb for the operation, even though it should take only 2 * 16 Gb. Is it meant to be that way? Otherwise, I will try with a newer version of MATLAB to see if this has been fixed.

Answer 2

[Matt J]

This is just a guess, but possibly the GPU memory is fragmented. I.e., maybe your available 28GB is broken into blocks that are smaller than 16GB and therefore Matlab cannot find enough space to allocate C.

Answer 3

[Catalytic]

Does MATLAB implicitly convert B to a full matrix?

When you say this, are you implying that issparse(B)=true? If so, then it is possible that C could consume up to 32 GB.

[Matt J]

I don't think that would be possible. If B were sparse, you would get a different error if you tried to multiply it with a single matrix.

[Massimiliano Zanoli]

No, I improperly meant "full" as in matrix instead of vector, sorry for the confusion. I was wondering whether B is repeated from 45927x1 to 45927x45927, that could explain the memory requirement.

Answer 4

[Joss Knight]

I can't reproduce this.

You say you have 48Gb of GPU memory available...have you checked this? Try running gpuDevice and looking at the output. Maybe you have other variables taking up space. Maybe you have another MATLAB running and using the GPU?

Also, did it work the first time you ran it but not the second? If C already exists then you would need space for A, C and the new C all at once, and you would run out of memory.

[Massimiliano Zanoli]

I get there with more or less 28 Gb free...

I now tried with another GPU with 24 Gb of total RAM and smaller matrix size (~8 Gb), but I still get the same error.

This is a copy of the command window when I type some commands when hitting a breakpoint right before the operation:

473         C = A .* (B.');
>> gpuDevice

ans = 

CUDADevice with properties:

Name: 'NVIDIA A10'
Index: 1
ComputeCapability: '8.6'
SupportsDouble: 1
DriverVersion: 12.2000
ToolkitVersion: 11
MaxThreadsPerBlock: 1024
MaxShmemPerBlock: 49152
MaxThreadBlockSize: [1024 1024 64]
MaxGridSize: [2.1475e+09 65535 65535]
SIMDWidth: 32
TotalMemory: 2.3942e+10
AvailableMemory: 1.4382e+10
MultiprocessorCount: 72
ClockRateKHz: 1695000
ComputeMode: 'Default'
GPUOverlapsTransfers: 1
KernelExecutionTimeout: 0
CanMapHostMemory: 1
DeviceSupported: 1
DeviceAvailable: 1
DeviceSelected: 1

>> (numel(A) * 32 * 2 / 8) / 1024 / 1024 / 1024 % [Gb]
ans =

8.0181

>> (numel(B) * 32 * 2 / 8) / 1024 / 1024 % [Mb]
ans =

0.2503

>> (gpuDevice().AvailableMemory) / 1024 / 1024 / 1024 % [Gb]
ans =

13.3945

And when I hit continue, the error happens:

Error using  .* 
Out of memory on device. To view more detail about available memory on the GPU, use 'gpuDevice()'. If the problem persists, reset the GPU by
calling 'gpuDevice(1)'.

[Joss Knight]

Your gpuDevice output seems to indicate you have quite an old version of MATLAB. What version are you on?

[Joss Knight]

Never mind. I can't reproduce this in any old version, on Linux or Windows.

Just to be sure, make sure your script is standalone and is the only thing you run after you've started MATLAB. It should contain no other computation than creating A and B and then computing C, so for instance:

n = 45927;
proto = gpuArray(single(1i));
A = randn(n,'like',proto);
B = randn(n,1,'like',proto);
C = A.*(B.');
gpuDevice
whos