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Multidimensional matrix multiplication

version 1.2.0.0 (1.75 KB) by Sandor Toth
The simple function performs fast matrix multiplication within multidimensional arrays.

1.3K Downloads

Updated 19 Aug 2013

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mmat(A,B) performs matrix multiplication, where the 2D matrices are part of multidimensional arrays. It is equivalent to the Matlab built in mtimes function for 2D arrays. However it naturally extends the mtimes function, where the two input arrays can have arbitrary number of extra dimensions. For example:

A = [1 2;2 1];
B = [3 4; 1 2];

mmat(A,B) == mtimes(A,B)

However A and B can be expanded along the 3rd dimension:

A = repmat([1 2; 2 1],[1 1 5]);

C = mmat(A,B) can be also performed, C will contains:
C(:,:,1) = A(:,:,1)*B;
C(:,:,2) = A(:,:,2)*B; ...

In the above example B was expanded along the singleton dimensions to match the size of A for the multiplication.

In the above examples the matrix multiplication was performed along the first two dimensions of A and B. However when called:
mmat(A,B,dim)
then dim selects two dimensions from A and B along which the matrix multiplication should be performed.

For example:
dim = [1 2] - default value
dim = [2 3] - C(ii,:,:) = A(ii,:,:) * B(ii,:,:);

This function contains only simple Matlab script without for loops!
Thus it is clean, fast and no compiling needed!

Please leave a comment if you like/dislike it, or you found a bug!
Enjoy!

Cite As

Sandor Toth (2021). Multidimensional matrix multiplication (https://www.mathworks.com/matlabcentral/fileexchange/41663-multidimensional-matrix-multiplication), MATLAB Central File Exchange. Retrieved .

MATLAB Release Compatibility
Created with R2012b
Compatible with any release
Platform Compatibility
Windows macOS Linux

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