multiprod implementation question for matrix multiplication optimization

Hi all. I'm trying to optimize matrix multiplication. What I am trying to do is take a stack of 3 x 3 matrices and multiply each matrix by one vector from an array of vectors .

I did find an implementation not using multiprod that solves this issue without for loops, but makes extensive use of repmat and performs worse than if I were to just use a for loop.

So for the case below: multiprod(A,B) would return [1 4 7] and [12 15 18].

    A = [1 2 3; 4 5 6; 7 8 9; 10 11 12; 13 14 15; 16 17 18;]
    B = [1 0; 0 0; 0 1]

Currently, multiprod assumes that you want to multiply each 3x3 by the 3x2 and as a result I get extraneous data. Adding the extra parameters about the inner dimensions to the function call did not work either.

So I guess my question is...can multiprod solve this issue and I'm just not implementing it correctly or am I better off using for loops?

Answer 1

[Matt J]

If we reshape your data slightly, we can use MTIMESX ( Download )

    >> A = cat(3,[1 2 3; 4 5 6; 7 8 9],[ 10 11 12; 13 14 15; 16 17 18])

    A(:,:,1) =

         1     2     3
         4     5     6
         7     8     9

    A(:,:,2) =

        10    11    12
        13    14    15
        16    17    18

    >> B=reshape(B,3,1,[])

    B(:,:,1) =

         1
         0
         0

    B(:,:,2) =

         0
         0
         1

    >> mtimesx(A,B)

    ans(:,:,1) =

         1
         4
         7

    ans(:,:,2) =

        12
        15
        18

[Daniel]

Interesting. Thanks for your answer!