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### Highlights from Multidimensional matrix multiplication

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# Multidimensional matrix multiplication

### Sandor Toth (view profile)

06 May 2013 (Updated )

The simple function performs fast matrix multiplication within multidimensional arrays.

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Description

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!

Enjoy!

Required Products MATLAB
MATLAB release MATLAB 8.0 (R2012b)
09 Nov 2015 Hildo Bijl

### Hildo Bijl (view profile)

I would recommend defining nD as
nD = max([nDA nDB dim]);
The reason is that if you want to multiply along some high dimension dim, sometimes it may happen to be a singleton dimension. As a result, Matlab lowers the values of ndim(A) and ndim(B), which may cause the script to give an error.

16 Aug 2013 Sandor Toth

### Sandor Toth (view profile)

Thank you Jorge, indeed when dim not equal to [1 2] line 54/55 can throw an error. I corrected the code!

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16 Aug 2013 Jorge Campos

### Jorge Campos (view profile)

A little improvement:

Replace lines 54 and 55 by

nA = [size(A),ones(1,nD-nDA)]; nA = nA(dim);
nB = [size(B),ones(1,nD-nDB)]; nB = nB(dim);

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22 Jul 2013 Sandor Toth

### Sandor Toth (view profile)

You are right, the whole intermediate matrix is stored in memory during the calculation to increase speed.

Thx

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22 Jul 2013 Jorge Campos

### Jorge Campos (view profile)

Excellent and efficient, however it's not applicable to huge arrays

25 Jun 2013 Sandor Toth

### Sandor Toth (view profile)

You have to add the path of the file to the Matlab search path:

where pathName is the name of the folder where the mmat function is. After that, you can simply call mmat().

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25 Jun 2013 Shauryam

### Shauryam (view profile)

what path has to be given to the function?

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