Matrix multiplication of 3d arrays

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Riaz Patel
Riaz Patel 2018-5-16
回答： michio 2020-10-12
Hi
I have a 3d array of dimension 2*5000*150 and another array of dimension 5000*1*150. I would like to take each 2*5000 matrix in the first 3d array and multiply it with the corresponding 5000*1 matrix in the second 3d array.
I need to do this in as efficient a way as possible and without any additional functions that are not preinstalled on a standard matlab installation.

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回答（3 个）

michio
michio 2020-10-12
Ameer Hamza
Ameer Hamza 2018-5-16
Just use for loop
result = zeros(2,1,150);
for i=1:150
result(:,:,i) = matrix1(:,:,i)*matrix2(:,:,i);
end
  2 个评论
Riaz Patel
Riaz Patel 2018-5-16
I need it to be extremely fast, the assignment I'm working on has a component for speed of the code.
Also these 3d arrays are already generated in a for loop. So I'm trying to avoid a nested loop.
Ameer Hamza
Ameer Hamza 2018-5-16
The MATLAB syntax does not allow such mixing of element-wise and matrix multiplication between two matrices in a single command. Any other manipulation you will try to do will just add extra time or memory overhead. For example, you can make you code compact to just one line
result = cell2mat(cellfun(@(x,y) x*y, num2cell(x,[1 2]), num2cell(y,[1 2]), 'UniformOutput', false));
but this is very slower than for loop. MATLAB matrix operations are already very optimized so even creating a mex file is unlikely to help. for loop will be the fastest you can get in this case.

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James Tursa
James Tursa 2018-5-16
编辑：James Tursa 2018-5-16
Some options from the FEX:
MULTIPROD:
https://www.mathworks.com/matlabcentral/fileexchange/8773-multiple-matrix-multiplications--with-array-expansion-enabled
MTIMESX: (C-mex code requiring C compiler) needs updated build routine for later MATLAB versions
https://www.mathworks.com/matlabcentral/fileexchange/25977-mtimesx-fast-matrix-multiply-with-multi-dimensional-support
MMX: (C-mex code requiring C compiler)
https://www.mathworks.com/matlabcentral/fileexchange/37515-mmx-multithreaded-matrix-operations-on-n-d-matrices
And raw times code:
result = sum(bsxfun(@times,matrix1,reshape(matrix2,1,5000,150)),2);
or
result = sum(matrix1.*reshape(matrix2,1,5000,150),2); % later versions of MATLAB

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