Three-dimensional DCT implementation for GPU computation in Matlab

Question

This is a follow-up question for Three-dimensional DCT spatial frequency components illustration and Parallel 3D Discrete Cosine Transformation Implementation in Matlab. I am trying to perform three-dimensional DCT calculation by leveraging GPU computing power. Based on Cris Luengo's answer and the vectorization techniques, a function DCT3D_gpuArray has been implemented.

The experimental implementation

DCT3D_gpuArray function implementation:

function out = DCT3D_gpuArray(x)
    if ~isgpuarray(x)
        x = gpuArray(x);
    end
    out = DCT1D_gpuArray(x, 1);
    out = DCT1D_gpuArray(out, 2);
    out = DCT1D_gpuArray(out, 3);
    [N1,N2,N3] = size(x);
    out = gather(8 .* out ./ (N1 * N2 * N3));
end

function out = DCT1D_gpuArray(x, dim) 
    N = size(x, dim); 

    if (dim == 1 || dim == 2)
        alpha = cos(pi/(2*N)*(2*(0:N-1)'+1)*(0:N-1));
        alpha(:,1) = alpha(:,1) / sqrt(2);
        if dim == 1
            out = pagemtimes(alpha, 'transpose', x, 'none');
        elseif dim == 2
            out = pagetranspose(pagemtimes(alpha, 'transpose', pagetranspose(x), 'none'));
        end
        return;
    end

    sz = ones(1,3); 
    sz(dim) = N; 
    index = {':',':',':'}; 
    out = gpuArray(zeros(size(x))); 

    for n = 0:N-1
       alpha = cos(pi/(2*N)*(2*(0:N-1)+1)*n);
       alpha = reshape(alpha, sz);
       index{dim} = n + 1;
       sum_result = sum(x .* alpha, dim);
       if n == 0
           sum_result = sum_result / sqrt(2);
       end
       out(index{:}) = sum_result;
    end
end

Test Case for DCT3D_gpuArray function

tic;

%% Create test cells
testCellsSize = 10;

test = zeros(testCellsSize, testCellsSize, testCellsSize);
for x = 1:size(test, 1)
    for y = 1:size(test, 2)
        for z = 1:size(test, 3)
            test(x, y, z) = x * 100 + y * 10 + z;
        end
    end
end

%% Perform test
result = DCT3D_gpuArray(test);

%% Print output
for z = 1:size(result, 3)
    fprintf('3D DCT result: %d plane\n' , z);
    for x = 1:size(result, 1)
        for y = 1:size(result, 2)
            fprintf('%f\t' , result(x, y, z));
        end
        fprintf('\n');
    end
    fprintf('\n');
end

%% Visualize results

for z = 1:size(result, 3)
    figure;
    mesh(result(:, :, z));
end

elapsedTime = toc;

The output of the test code above:

3D DCT result: 1 plane
1726.754760 -80.720722  -0.000000   -8.646042   -0.000000   -2.828427   0.000000    -1.143708   -0.000000   -0.320717   
-807.207224 -0.000000   0.000000    -0.000000   0.000000    -0.000000   -0.000000   -0.000000   0.000000    -0.000000   
-0.000000   0.000000    0.000000    0.000000    -0.000000   -0.000000   -0.000000   -0.000000   0.000000    0.000000    
-86.460422  -0.000000   0.000000    -0.000000   0.000000    -0.000000   -0.000000   -0.000000   0.000000    -0.000000   
-0.000000   0.000000    0.000000    0.000000    0.000000    -0.000000   0.000000    -0.000000   0.000000    0.000000    
-28.284271  -0.000000   0.000000    -0.000000   0.000000    -0.000000   -0.000000   -0.000000   0.000000    0.000000    
0.000000    -0.000000   0.000000    0.000000    0.000000    0.000000    0.000000    0.000000    0.000000    0.000000    
-11.437076  -0.000000   0.000000    -0.000000   0.000000    -0.000000   0.000000    -0.000000   -0.000000   -0.000000   
-0.000000   0.000000    0.000000    0.000000    0.000000    0.000000    0.000000    0.000000    0.000000    -0.000000   
-3.207174   -0.000000   0.000000    -0.000000   0.000000    -0.000000   -0.000000   -0.000000   0.000000    0.000000    

3D DCT result: 2 plane
-8.072072   -0.000000   -0.000000   0.000000    -0.000000   0.000000    0.000000    0.000000    -0.000000   0.000000    
-0.000000   0.000000    0.000000    -0.000000   0.000000    -0.000000   -0.000000   -0.000000   -0.000000   -0.000000   
0.000000    -0.000000   0.000000    0.000000    -0.000000   0.000000    -0.000000   -0.000000   0.000000    -0.000000   
-0.000000   -0.000000   -0.000000   0.000000    -0.000000   -0.000000   -0.000000   0.000000    -0.000000   -0.000000   
-0.000000   0.000000    -0.000000   -0.000000   0.000000    0.000000    -0.000000   -0.000000   0.000000    -0.000000   
-0.000000   -0.000000   0.000000    0.000000    -0.000000   0.000000    -0.000000   -0.000000   -0.000000   -0.000000   
-0.000000   0.000000    -0.000000   -0.000000   -0.000000   -0.000000   -0.000000   0.000000    -0.000000   -0.000000   
-0.000000   0.000000    -0.000000   0.000000    0.000000    -0.000000   -0.000000   0.000000    0.000000    -0.000000   
0.000000    -0.000000   0.000000    -0.000000   -0.000000   0.000000    -0.000000   0.000000    -0.000000   -0.000000   
-0.000000   -0.000000   -0.000000   0.000000    0.000000    0.000000    0.000000    -0.000000   -0.000000   0.000000    

3D DCT result: 3 plane
-0.000000   0.000000    0.000000    0.000000    0.000000    0.000000    -0.000000   0.000000    -0.000000   -0.000000   
0.000000    0.000000    0.000000    -0.000000   0.000000    0.000000    0.000000    0.000000    0.000000    0.000000    
-0.000000   -0.000000   -0.000000   -0.000000   -0.000000   0.000000    0.000000    -0.000000   0.000000    0.000000    
0.000000    -0.000000   -0.000000   0.000000    -0.000000   -0.000000   0.000000    0.000000    -0.000000   0.000000    
0.000000    -0.000000   0.000000    -0.000000   -0.000000   0.000000    -0.000000   -0.000000   0.000000    0.000000    
-0.000000   -0.000000   0.000000    -0.000000   0.000000    -0.000000   0.000000    0.000000    0.000000    -0.000000   
-0.000000   0.000000    -0.000000   0.000000    0.000000    0.000000    0.000000    0.000000    0.000000    -0.000000   
0.000000    0.000000    -0.000000   -0.000000   -0.000000   -0.000000   -0.000000   -0.000000   -0.000000   0.000000    
0.000000    -0.000000   0.000000    -0.000000   0.000000    -0.000000   0.000000    0.000000    0.000000    -0.000000   
0.000000    0.000000    -0.000000   -0.000000   0.000000    0.000000    0.000000    0.000000    -0.000000   -0.000000   

3D DCT result: 4 plane
-0.864604   0.000000    0.000000    -0.000000   0.000000    -0.000000   -0.000000   0.000000    0.000000    -0.000000   
-0.000000   -0.000000   -0.000000   -0.000000   0.000000    0.000000    -0.000000   -0.000000   -0.000000   0.000000    
-0.000000   -0.000000   -0.000000   0.000000    -0.000000   -0.000000   0.000000    -0.000000   -0.000000   -0.000000   
-0.000000   0.000000    0.000000    -0.000000   0.000000    -0.000000   0.000000    0.000000    -0.000000   0.000000    
0.000000    0.000000    -0.000000   0.000000    -0.000000   0.000000    0.000000    -0.000000   -0.000000   -0.000000   
-0.000000   0.000000    -0.000000   -0.000000   0.000000    -0.000000   -0.000000   -0.000000   0.000000    -0.000000   
-0.000000   -0.000000   -0.000000   -0.000000   -0.000000   0.000000    0.000000    0.000000    0.000000    0.000000    
0.000000    -0.000000   -0.000000   0.000000    0.000000    0.000000    -0.000000   0.000000    -0.000000   -0.000000   
0.000000    -0.000000   -0.000000   -0.000000   -0.000000   -0.000000   -0.000000   -0.000000   0.000000    0.000000    
0.000000    -0.000000   -0.000000   -0.000000   -0.000000   0.000000    0.000000    0.000000    0.000000    -0.000000   

3D DCT result: 5 plane
-0.000000   0.000000    -0.000000   -0.000000   0.000000    0.000000    0.000000    0.000000    0.000000    -0.000000   
0.000000    -0.000000   0.000000    0.000000    -0.000000   0.000000    0.000000    0.000000    -0.000000   0.000000    
-0.000000   0.000000    -0.000000   0.000000    -0.000000   0.000000    -0.000000   -0.000000   0.000000    0.000000    
0.000000    0.000000    -0.000000   -0.000000   0.000000    -0.000000   0.000000    -0.000000   0.000000    0.000000    
0.000000    0.000000    0.000000    -0.000000   -0.000000   -0.000000   -0.000000   0.000000    -0.000000   0.000000    
0.000000    -0.000000   -0.000000   0.000000    0.000000    -0.000000   -0.000000   0.000000    -0.000000   0.000000    
0.000000    0.000000    -0.000000   0.000000    0.000000    0.000000    0.000000    0.000000    0.000000    -0.000000   
0.000000    -0.000000   0.000000    0.000000    -0.000000   0.000000    0.000000    0.000000    -0.000000   0.000000    
0.000000    0.000000    0.000000    0.000000    -0.000000   -0.000000   -0.000000   -0.000000   -0.000000   0.000000    
-0.000000   -0.000000   0.000000    0.000000    -0.000000   -0.000000   0.000000    -0.000000   0.000000    -0.000000   

3D DCT result: 6 plane
-0.282843   -0.000000   -0.000000   0.000000    -0.000000   -0.000000   -0.000000   0.000000    -0.000000   0.000000    
-0.000000   0.000000    -0.000000   0.000000    -0.000000   0.000000    0.000000    0.000000    -0.000000   0.000000    
-0.000000   -0.000000   0.000000    0.000000    0.000000    -0.000000   -0.000000   -0.000000   0.000000    -0.000000   
-0.000000   -0.000000   -0.000000   -0.000000   0.000000    -0.000000   0.000000    0.000000    -0.000000   -0.000000   
-0.000000   0.000000    0.000000    -0.000000   -0.000000   -0.000000   -0.000000   -0.000000   -0.000000   -0.000000   
-0.000000   -0.000000   -0.000000   0.000000    0.000000    -0.000000   0.000000    0.000000    0.000000    -0.000000   
0.000000    -0.000000   -0.000000   0.000000    -0.000000   -0.000000   0.000000    -0.000000   -0.000000   0.000000    
-0.000000   -0.000000   -0.000000   0.000000    -0.000000   0.000000    0.000000    -0.000000   0.000000    0.000000    
0.000000    0.000000    -0.000000   -0.000000   -0.000000   0.000000    0.000000    0.000000    -0.000000   0.000000    
0.000000    0.000000    0.000000    -0.000000   0.000000    0.000000    -0.000000   -0.000000   0.000000    -0.000000   

3D DCT result: 7 plane
0.000000    -0.000000   -0.000000   0.000000    -0.000000   -0.000000   0.000000    0.000000    0.000000    -0.000000   
-0.000000   -0.000000   0.000000    0.000000    -0.000000   -0.000000   -0.000000   -0.000000   -0.000000   -0.000000   
0.000000    -0.000000   0.000000    -0.000000   -0.000000   -0.000000   -0.000000   -0.000000   0.000000    -0.000000   
-0.000000   0.000000    -0.000000   -0.000000   -0.000000   -0.000000   -0.000000   0.000000    0.000000    -0.000000   
0.000000    0.000000    -0.000000   0.000000    -0.000000   -0.000000   -0.000000   0.000000    0.000000    -0.000000   
-0.000000   -0.000000   -0.000000   0.000000    -0.000000   -0.000000   0.000000    0.000000    0.000000    -0.000000   
-0.000000   -0.000000   0.000000    0.000000    -0.000000   0.000000    -0.000000   0.000000    -0.000000   -0.000000   
0.000000    0.000000    0.000000    0.000000    0.000000    0.000000    -0.000000   -0.000000   -0.000000   -0.000000   
0.000000    -0.000000   0.000000    0.000000    0.000000    0.000000    -0.000000   -0.000000   0.000000    -0.000000   
-0.000000   -0.000000   -0.000000   -0.000000   0.000000    0.000000    -0.000000   -0.000000   0.000000    0.000000    

3D DCT result: 8 plane
-0.114371   -0.000000   0.000000    0.000000    -0.000000   -0.000000   0.000000    0.000000    -0.000000   -0.000000   
-0.000000   0.000000    0.000000    -0.000000   -0.000000   -0.000000   0.000000    0.000000    -0.000000   0.000000    
-0.000000   0.000000    -0.000000   -0.000000   0.000000    -0.000000   0.000000    -0.000000   0.000000    -0.000000   
-0.000000   0.000000    -0.000000   0.000000    -0.000000   0.000000    0.000000    -0.000000   -0.000000   0.000000    
0.000000    0.000000    0.000000    -0.000000   0.000000    -0.000000   0.000000    -0.000000   -0.000000   -0.000000   
-0.000000   0.000000    -0.000000   -0.000000   -0.000000   -0.000000   -0.000000   0.000000    0.000000    -0.000000   
-0.000000   -0.000000   0.000000    0.000000    0.000000    -0.000000   -0.000000   0.000000    0.000000    -0.000000   
-0.000000   -0.000000   0.000000    0.000000    0.000000    -0.000000   -0.000000   -0.000000   -0.000000   -0.000000   
0.000000    0.000000    0.000000    0.000000    -0.000000   -0.000000   -0.000000   0.000000    0.000000    -0.000000   
-0.000000   -0.000000   0.000000    0.000000    0.000000    -0.000000   -0.000000   0.000000    -0.000000   0.000000    

3D DCT result: 9 plane
-0.000000   -0.000000   -0.000000   -0.000000   -0.000000   0.000000    0.000000    0.000000    -0.000000   0.000000    
0.000000    0.000000    0.000000    0.000000    0.000000    -0.000000   0.000000    0.000000    -0.000000   0.000000    
-0.000000   -0.000000   0.000000    -0.000000   0.000000    0.000000    -0.000000   0.000000    0.000000    -0.000000   
0.000000    0.000000    -0.000000   -0.000000   -0.000000   0.000000    -0.000000   -0.000000   0.000000    0.000000    
-0.000000   -0.000000   -0.000000   0.000000    0.000000    -0.000000   -0.000000   -0.000000   -0.000000   -0.000000   
0.000000    -0.000000   0.000000    0.000000    -0.000000   -0.000000   0.000000    0.000000    0.000000    0.000000    
-0.000000   -0.000000   0.000000    -0.000000   -0.000000   0.000000    0.000000    -0.000000   -0.000000   0.000000    
-0.000000   0.000000    0.000000    -0.000000   -0.000000   -0.000000   0.000000    -0.000000   0.000000    -0.000000   
0.000000    -0.000000   -0.000000   -0.000000   0.000000    0.000000    -0.000000   -0.000000   -0.000000   0.000000    
0.000000    -0.000000   -0.000000   0.000000    0.000000    -0.000000   0.000000    0.000000    0.000000    0.000000    

3D DCT result: 10 plane
-0.032072   -0.000000   0.000000    -0.000000   -0.000000   0.000000    -0.000000   -0.000000   0.000000    0.000000    
-0.000000   -0.000000   -0.000000   0.000000    -0.000000   -0.000000   0.000000    0.000000    -0.000000   0.000000    
0.000000    0.000000    -0.000000   0.000000    -0.000000   0.000000    -0.000000   0.000000    -0.000000   0.000000    
-0.000000   -0.000000   -0.000000   -0.000000   -0.000000   0.000000    0.000000    -0.000000   -0.000000   -0.000000   
-0.000000   0.000000    0.000000    0.000000    0.000000    -0.000000   -0.000000   -0.000000   0.000000    -0.000000   
-0.000000   0.000000    0.000000    0.000000    -0.000000   -0.000000   -0.000000   -0.000000   -0.000000   0.000000    
-0.000000   -0.000000   -0.000000   0.000000    0.000000    -0.000000   -0.000000   -0.000000   -0.000000   0.000000    
-0.000000   0.000000    -0.000000   0.000000    0.000000    -0.000000   0.000000    -0.000000   -0.000000   0.000000    
0.000000    0.000000    0.000000    -0.000000   -0.000000   0.000000    -0.000000   0.000000    -0.000000   -0.000000   
-0.000000   0.000000    0.000000    0.000000    -0.000000   -0.000000   0.000000    0.000000    0.000000    0.000000

All suggestions are welcome.

The summary information:

Which question it is a follow-up to?

Three-dimensional DCT spatial frequency components illustration and

Parallel 3D Discrete Cosine Transformation Implementation in Matlab
What changes has been made in the code since last question?

Performing three-dimensional DCT calculation by leveraging GPU computing power.
Why a new review is being asked for?

If there is any possible improvement, please let me know.

Are the dimensions of the transform fixed? E.g code for 8x8x8 dct can run much faster than code for arbitrary dimensions. — Stand with Gaza, Sep 8, 2022 at 7:48
@Björn Lindqvist Thank you for your comment. > Are the dimensions of the transform fixed? If the word "dimensions" means "size" (not rank), nope, you can perform the 3D-DCT calculation using some kind of cube like 5x6x7 with the proposed function, actually. — JimmyHu, Sep 8, 2022 at 12:07

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