Getting rid of a for-loop (in order to optimise execution time) for 2 operations that involve the inverse of a 3D matrix

I am working on a RT Simulink implementation of an interacting multi-model Kalmanfilter used for event-detection in Fusion devices.

I am trying to get rid of all for-loops in the code to optimise for execution time. I already had help with my first problem, which could be solved by making use of the reshape-function.

However, I tried various ways to use this function for another set of for-loops that I have, but It does not work due to the fact that it is hard to calculate the inverse of a 3D matrix without for-loops to my knowledge.

The problem:

   Nmodel = 3
    exparg = zeros(Nmodel,1);
    L = zeros(Nmodel,1);
    for ii=1:Nmodel
        exparg(ii) = -.5*z(:,ii)'/S(:,:,ii)*z(:,ii); % Calculate arguments for the exp used in the Likelihood calculation
    end
    exparg = exparg - max(exparg);               % Only the Likelihood ratio's matter, so normalise expargs to prevent exp(-1000) = 0
    for ii=1:Nmodel
        L(ii) = 1./sqrt(det(S(:,:,ii))) * exp(exparg(ii));      % Model likelihoods based on measurement correspondence
    end
    L = L/sum(L);                        % Normalise likelihoods for plotting purposes

If somebody has any suggestions on which methods I could use to get rid of the for-loops (without introducing even slower operations) in order to optimise execution, I would be very thankful.

I know that this is the second question within a day, but changing for-loops to matrix multiplications is not my expertise, given that I do not know the "inner workings" of most matlab-functions.

Thanks a lot in advance!

PS: I know of the danger of taking 1/sqrt(det) if the determinant would be zero, but I have to implement the version of my predecessor before changing the code to much.

Ricardo

EDIT: so z has size (3,3) ; S has size (3,3,3); L has size(3,1); exparg has size (3,1)

[Matt J]

Optimizing such short loops in isolation from the rest of the code isn't going to make a significant improvement in execution time. You would need Nmodel in the hundreds or thousands until before it would even start to make a difference.

You need to address the outer loop which is calling the code segment you have shown and consider whether there is a way to vectorize that.