# Matrix multiplication of 3d arrays

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Riaz Patel on 16 May 2018
Answered: michio on 12 Oct 2020
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.

michio on 12 Oct 2020

Ameer Hamza on 16 May 2018
Just use for loop
result = zeros(2,1,150);
for i=1:150
result(:,:,i) = matrix1(:,:,i)*matrix2(:,:,i);
end
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Ameer Hamza on 16 May 2018
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.

James Tursa on 16 May 2018
Edited: James Tursa on 16 May 2018
Some options from the FEX:
MULTIPROD:
MTIMESX: (C-mex code requiring C compiler) needs updated build routine for later MATLAB versions
MMX: (C-mex code requiring C compiler)
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