Multiply a "stack" of matrices with a "stack" of vectors

I have a matrix 2 x 2 x n and a vector 2 x n. So basically, I have n layers of 2 x 2 matrices and n layers of vectors with 2 entries. I d like to do a matrix-vector multiplication on each layer.

I could easily do this using a for loop, but is there a way which directly supports such an operation?

Answer 1

[Jos (10584)]

One option:

n = 6
% M is your 2x2xn array of "matrices
M = rand(2,2,n)
% V is your 2xn array of "vectors"
V = rand(2,n)

fh = @(k) M(:,:,k) * V(:,k)
C = arrayfun(fh,1:n,'un',0)
C2 = cat(3,C{:})

Corrected.

[Michael]

There's one little error in your code on the last line I think. C2 = cat(3, C{;}) would be correct.

It works, but it's not much faster than in the for loop.

[Jos (10584)]

You did ask for " a way which directly supports such an operation ", not for a faster way! ;-)

To be honest, I think a straight forward for-loop is as good as the accumarray approach in this case.

[James Tursa]

If you want speed, I would suggest looking at one of the solutions I have posted.

Answer 2

[James Tursa]

Some options in the FEX:

C-mex code:

http://www.mathworks.com/matlabcentral/fileexchange/25977-mtimesx-fast-matrix-multiply-with-multi-dimensional-support

C-mex code:

http://www.mathworks.com/matlabcentral/fileexchange/37515-mmx-multithreaded-matrix-operations-on-n-d-matrices

m-code:

http://www.mathworks.com/matlabcentral/fileexchange/8773-multiple-matrix-multiplications-with-array-expansion-enabled

You may need to reshape the 2 x n to a 2 x 1 x n for some of these methods to work.

Also this explicit m-code:

result = sum(bsxfun(@times,M,reshape(v,1,2,n)),2);