Dot products of corresponding matrix slices

I have time series of rotation matrices (shape Nx3x3) and frequently need to take dot products of the corresponding matrices in two of such arrays. Can someone come up with a vectorized version of this? I actually have this problem in other situations as well, it's always about trying an "element-wise" operation, where the element is not a single value in an array, like with A .* B, but the element is one slice of a large array. I don't know any efficient way Matlab offers to handle this, here's a for loop version to illustrate what I'm doing. Expanding into matrices of shapes (N*3)x3 doesn't help because it computes all dot product combinations instead of only pairwise.

N = size(a, 1);
result = nan(N, 3, 3);
for i = 1 : N
  result(i, :, :) = reshape(a(i, :, :), 3, 3) * reshape(b(i, :, :), 3, 3);
end

Thanks for your help!

[Walter Roberson]

That is not a dot product, that is an inner product. If you were doing a dot product then it would just be

sum(A.*B,3)

[Julius Krumbiegel]

That's true, sorry, I'm talking about matrix multiplication. Sometimes I forget the correct terminology. So I want to do N matrix multiplications with pairs of 3x3 matrices that are stored in two Nx3x3 arrays. The result should be another Nx3x3 array of rotation matrices.

Answer 1

[Walter Roberson]

If you change the array order so that n is the third dimension then there is a file exchange contribution to do the matrix multiplication.

If you have the parallel computing toolbox and you make n the third dimension then imay be able to pagefun() if you have a supported Nvidia gpu.

[Julius Krumbiegel]

Thank you, I've found mtimesx on the file exchange after clearing up the dot product / matrix multiplication confusion (I know where it stemmed from now, numpy's dot function does matrix multiplication if the inputs have that shape). This does exactly what I needed.