removing FOR loop to solve Ax=B on multidimensional arrays on GPU

Hi,

my code looks this way now(Its an example code i wrote):

A=gpuArray(rand([1000 1000 1000]));
B=gpuArray(rand([1000 1 1000]));

for kk=1:1000
C(:,kk)=A(:,:,kk)\B(:,kk);
end

Assume that A,B,C matrices are GPU matrices. Is it possible to remove FOR loop and perform same operation as above lines on GPU using GPU matrices?.(Assume that i do not want to use 'while' or 'if' or any other loops )

The closest i could find was on fileexchange . However she/he does not talk about 'A\B' kind of operations. Also she/he does not talk about GPU computing.

Thank you.

Answer 1

[Matt J]

C=pagefun(@mldivide,A,B)

[pb]

Thank you Matt. I will try it.

[pb]

I ran the following code :

A=gpuArray(rand([1000 1000 1000]));
B=gpuArray(rand([1000 1000]));

C=pagefun(@mldivide,A,B);

I got the following error:

Error using gpuArray/pagefun
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)'.

Error in gputests (line 11)
C=pagefun(@mldivide,A,B);

my gpu details are:

>> gpu = gpuDevice();
>> gpu

gpu = 

  CUDADevice with properties:

                      Name: 'Tesla K40m'
                     Index: 1
         ComputeCapability: '3.5'
            SupportsDouble: 1
             DriverVersion: 9.2000
            ToolkitVersion: 9
        MaxThreadsPerBlock: 1024
          MaxShmemPerBlock: 49152
        MaxThreadBlockSize: [1024 1024 64]
               MaxGridSize: [1×3 double]
                 SIMDWidth: 32
               TotalMemory: 1.1997e+10
           AvailableMemory: 3.4881e+09
       MultiprocessorCount: 15
              ClockRateKHz: 745000
               ComputeMode: 'Default'
      GPUOverlapsTransfers: 1
    KernelExecutionTimeout: 1
          CanMapHostMemory: 1
           DeviceSupported: 1
            DeviceSelected: 1

Can you tell me how to solve this error?

thank you

[Matt J]

You have a typo in your definition of B.

B=gpuArray(rand([1000, 1, 1000]));

[pb]

Thank you Matt.

for the following code the results was fine:

close all;
clear all;
clc;
gpuDevice(1)

A=gpuArray(rand([1000, 1000, 100]));
B=gpuArray(rand([1000, 1, 100]));
C=pagefun(@mldivide,A,B);

however when i move to higher matrix sizes,it seems i do not have sufficent GPU size, for example:

close all;
clear all;
clc;
gpuDevice(1)

A=gpuArray(rand([1000, 1000, 1000]));
B=gpuArray(rand([1000, 1, 1000]));
C=pagefun(@mldivide,A,B);

-------
output:
Error using gpuArray/pagefun
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)'.

Error in gputests (line 13)
C=pagefun(@mldivide,A,B);

[Matt J]

1000^3 is very large. Maybe change to single floats and see how bad the loss of precision is.

[pb]

Thanks Matt.

Changing the precision might help. I will try it.

[Joss Knight]

There's also no harm in dividing things up into a few separate batches. Ultimately that's all the GPU is doing, once it is fully utilized.

[pb]

Hi Joss,

Thank you for the answer.

I plan to call the below command 10^5 times. In each case B would be changing.My A is 1000x1000x1000 and B is 1000x1x1000. :

C=pagefun(@mldivide,A,B)

Would not breaking A,B into 2 or more parts for calculation on GPU, slow down my code (I am expecting slow down beacuse of transfer times between GPU and memory/RAM ) ?

[Matt J]

Could you batch B's together as well? I.e., instead of applying pagefun to a 1000x1x1000 chunk of B data, apply to a chunk that is 1000 x BatchSizeB x 1000 or 1000 x BatchSizeB x BatchSizeA.

[Joss Knight]

Yes, that. MLDIVIDE already works with multiple right-hand-sides, stacked along the columns of b. You only need PAGEFUN if A is changing.