Matrix multiplication of 3d arrays

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.

Answer 1

[michio]

Use pagemtimes available in R2020b.

https://jp.mathworks.com/help/matlab/ref/pagemtimes.html

Answer 2

[Ameer Hamza]

Just use for loop

result = zeros(2,1,150);
for i=1:150
  result(:,:,i) = matrix1(:,:,i)*matrix2(:,:,i);
end

[Riaz Patel]

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]

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.

Answer 3

[James Tursa]

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