How can I get rid of the 2 nested for loops for my calculations which include a 3D matrix and a 2D matrix.

So, To give a tiny bit of context: I am working on an interacting multi-model Kalmanfilter for event-detection.

The system has 8 state-variables, and I use 3 models. Therefore, My EEC matrix P is an (8x8x3) matrix. The other variable is a weighting matrix W (2D) of size (3x3).

What do I want to do? --> I want to update P(:,:,i) for all 3 models, so that the 8x8 values of that particular model are scaled by the same weight. I currently implemented this as 2 nested for-loops:

for i=1:Nmodel
    for j=1:Nmodel
        Pmix(:,:,i) = Pmix(:,:,i) + Wmix(j,i)*(Ppost(:,:,j)); ...  % Mixed EECs as weighted average    
    end
end

So to be clear: If

W = [W11, W12, W13; W21, W22, W23; W31,W32,W33], the following multiplications need to happen:

P(:,:,1) = W11*P(:,:,1) + W21*P(:,:,2) + W31*P(:,:3);
P(:,:,2) = W12*P(:,:,1) + W22*P(:,:,2) + W32*P(:,:3);
P(:,:,3) = W13*P(:,:,1) + W23*P(:,:,2) + W33*P(:,:3);

Please let me know whether it is possible to get rid of the for-loops and only use matrix multiplications?

This would hopefully speed up the Real-Time implementation. Thanks in Advance!

NOTE: The solution has to work in MATLAB r2015a due to contraints with regards to implementation on RT control system. Regards, Ricardo

Answer 1

[Matt J]

Yes, it's pretty easy to formulate it as as a matrix multiplication (plus some reshaping)

P=reshape(P,[],3)*W.';
P=reshape(P,8,8,3);

[Ricardo Shousha]

Thanks a lot for your help. I think you meant just W and not its transpose, as the non-transposed W yields the "correct" multiplications. The only thing still missing is that the Previous P has to be added, but I think I can work that out myself.

Thanks again for showing me this reshape method.

Ricardo

[Matt J]

You're right. It should be

 P=reshape(P,[],3)*W;
 P=reshape(P,8,8,3);