Could you repeat IW_matrix K times as blocks along the diagonal of IW_matrix_big?

Do the same for the reshaped y vector to make y_big. 

Then do X_big = IW_matrix_big*y_big*IW_matrix_big'.

Then extract and reshape the diagonal blocks of X_big to make X.

The only problem is, I don't know of any Matlab commands that does the block manipulations I mentioned. And even if they existed, I don't know if the big (sparse)matrix MUL operation would be faster than your for loop.   

you can try running the profiler in matlab to see what is taking the most time. then focus on optimizing those sections. its tough to say what is taking the most time.

I had a look at your code and tried to understand the dimensions of the input variables: x, Dct_matrix, IW_matrix

This is the result, which runs without errors. Are the dimensions correct ?

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close all; clear all; clc

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x = rand(10,64);

Dct_matrix = rand(10,64);

IW_matrix = rand(8,8);

%

[K,MN]=size(x);

block_size = 8;

X = zeros(block_size,block_size,K);

temp = zeros(block_size,block_size);

y = (Dct_matrix'*x);

for k = 1:K

temp = reshape(y(k,:),block_size,block_size);

X(:,:,k) = IW_matrix*temp*IW_matrix';

end

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If this is correct, then you need to find a way of vectorizing the reshape command, which uses only the k-th row of y. I am not very familiar with the reshape command, but I think it is possible to give the reshape command the whole matrix y.

Dear Mr. Lindner,

i am afraid you are wrong about the dimensions, in my humble opinion it is likely to be

x = rand(10,64);

Dct_matrix = rand(10,10);

IW_matrix = rand(8,8);

since otherwise the loop over K will only consider the first few rows of y. Pulling out the reshape will not significantly increase performance.

Regarding the initial question, you can perform a slice-by-slice matrix multiplication of 3D matrices using pagefun on the GPU or you can use the mtimesx library (http://www.mathworks.com/matlabcentral/fileexchange/25977-mtimesx-fast-matrix-multiply-with-multi-dimensional-support)

Since your question is poorly formulated i will not further elaborate on examples how to proceed with these options.

Best,

Markus Durst