Vectorized Multi-Dimensional Matrix Multiplication

Take Any N-D Matrix and Multiply it by another N-D Matrix Without a For-Loop
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Updated Fri, 07 Jul 2017 19:53:30 +0000

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If you want to multiply multi-dimensional matrices together without having to write a for-loop to cycle through each additional dimension beyond two, this routine is for you. Not a single for-loop was used in the development of this routine. Consequently, you should see a significant runtime improvement when using the multi-dimensional matrix multiply operations contained in this code.
mntimes will support 2-D matrix multiplication much like the built-in mtimes.m routine (so you can overload it if desired), it will support 3-D matrix multiplication, 4-D multiplication, and so on (until you run out of system memory). Matrices don't have to be the same size (i.e. 3x3 * 3x3) they can be 1x3 * 3x1, 1x3 * 3x3, 3x3 * 3x1, the choices are unlimited as long as it is a valid 2-D operation. If you are sure to identify which dimension corresponds to a row, and which to a column there shouldn't be a N-D matrix case this code can't handle.
Example Function call:
z = mntimes(x,y,xrowdim,xcoldim,yrowdim,ycoldim);
Input List:
x - N-D input matrix
y - N-D input matrix
xrowdim - row dimension specifier for x
xcoldim - column dimension specifier for x
yrowdim - row dimension specifier for y
ycoldim - column dimension specifier for y
Output List:
z - N-D output matrix (resulting product of the z = x*y operation)

Cite As

Darin Koblick (2024). Vectorized Multi-Dimensional Matrix Multiplication (https://www.mathworks.com/matlabcentral/fileexchange/47092-vectorized-multi-dimensional-matrix-multiplication), MATLAB Central File Exchange. Retrieved .

MATLAB Release Compatibility
Created with R2012a
Compatible with any release
Platform Compatibility
Windows macOS Linux
Categories
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Acknowledgements

Inspired: mmDerivative(t,y)

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Version Published Release Notes
1.2.0.0

*
Corrected bug which would not allow for transposing matricies when rowDim and colDim were swapped. This version was also regression tested.
Corrected routine to increase stability when dealing with higher dimensionality.

1.1.0.0

Updated last step on re-assembling the N-D matrix to ensure singleton dimension was preserved when set to one.

1.0.0.0