3D matrix multiplication

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Kamuran on 24 Jun 2011
Commented: James Tursa on 10 Feb 2020
Hi,
I have two 3D matrices that I need to multiply in a specific way. I need to do for k=1:Z M(:,:,k)=A(:,:,k)*B(:,:,k) end
but I do not want to use for loop because it makes my code run slower and I need to this multiplication for a unsteady flow profile calculation (close to million time steps). Is there a more efficient way to do it?

Steven Lord on 6 Apr 2018
"but I do not want to use for loop because it makes my code run slower "
I know this question was originally asked several years ago, but I know others have this same belief. Before avoiding the for loop, consider if you think that the loop makes your code run slower or whether you have measured and confirmed that it makes your code run slower. If you haven't checked, check before seeking out an alternate solution.
We have improved the performance of MATLAB in many ways over the past several years and we continue to do so now, so that "slow for loop" may not be so slow any more.
James Tursa on 6 Apr 2018
In this particular case it really isn't the for-loop per-se that is slowing things down. It is the data copying of extracting the individual 2D slices that is the culprit (which can be avoided in a mex routine).
I'm still hoping that someday TMW will choose to do "implicit 2D slice expansion" for the * matrix multiply operator and \ and / slash operators in the same sense that they now do implicit scalar expansion for the .* and ./ etc operators.

James Tursa on 24 Jun 2011

1 Comment

James Tursa on 24 Jun 2011
P.S. If your 2D slices are small (4x4 or less), be sure to use 'SPEED' or 'SPEEDOMP' mode. This will cause inline code to be used that will run faster than the default BLAS library routine calls.

Walter Roberson on 24 Jun 2011
There is no built-in MATLAB support for 3D multiplications. The program James refers to is probably a good choice.
By the way, especially in the releases of the last few years, "for" loops are sometimes faster than vectorization, especially for large matricies.

Kamuran on 24 Jun 2011
to use this file I need to install a C compiler ? If so can you suggest me one, Because I never used C :) .
Thank you

Walter Roberson on 24 Jun 2011
Appropriate C compilers depend upon your OS and MATLAB release. You can start at the following, but be sure to look for information about your particular release, as the list of supported compilers is different between releases. Also note that 64 bit Windows has different compilers than 32 bit Windows.
http://www.mathworks.com/support/compilers/R2011a/win32.html
James Tursa on 24 Jun 2011
Type the following at the MATLAB prompt:
mex -setup
Then press Enter and see what shows up. If you have a 32-bit system then hopefully a compiler will already be there. If you have a 64-bit system then you will have to install one yourself unfortunately.
Walter Roberson on 24 Jun 2011
I checked back... we do not have any information about the OS or MATLAB version the poster is using.

Mr M. on 6 Apr 2018
I got the following error message:
Error using mtimesx_build (line 120) Unable to compile mtimesx.c
Error in mtimesx (line 271) mtimesx_build;

Mr M. on 6 Apr 2018
However XCode is installed and licence is accepted (mex -setup)
James Tursa on 6 Apr 2018
MTIMESX is way overdue for an update (TMW changed mex procedures some time ago). In the meantime, try this or some variation of this modified for your system:
lib_blas = fullfile(matlabroot,'extern','lib',computer('arch'),'microsoft','libmwblas.lib');
mex('mtimesx.c',lib_blas,'-largeArrayDims')

Daniel Frisch on 3 Feb 2020
Matrix multiplication can also be expressed using native Matlab code (times and sum):
% A : (a x c x Z)
% B : (c x b x Z)
Ap = permute(A,[2,1,4,3]); % (c x a x 1 x Z)
Bp = permute(B,[1,4,2,3]); % (c x 1 x b x Z)
M = Ap .* Bp; % (c x a x b x Z)
M = sum(M,1); % (1 x a x b x Z)
M = permute(M,[2,3,4,1]); % (a x b x Z)

1 Comment

James Tursa on 10 Feb 2020
Note that the permute( ) operations will involve a deep data copy, so this method will run slower than the mex routines.