MATLAB: Best way to calculate the determinants of a series of matrices

determinantsMATLABmatrices

I've got a series of time-dependent matrices which I'd like to calculate the determinants of. These matrices are stored as a three-dimensional array, where the first dimension indicates the period; in other words, the matrix at time t is given by
Gt = squeeze(G(t, :, :))
I'd now like a snippet of code which, being run, will ensure that
Delta(t) = det(squeeze(G(t, :, :)))
holds for all t. Of course I could do this with a loop, but I feel that there must be a more succinct, vectorized way of doing it. Sadly, MATLAB's det function itself is of no help. Is there something else I could use, or will I have to bite the proverbial bullet and use a loop after all?

Best Answer

I reverse the order and put the page in third dimension (avoid to use squeeze).
For small size, you can save CPU time by 4 fold using MultipleQR available on FEX
A=rand(3,3,1e5);
tic
    n = size(A,1);
    % FEX https://fr.mathworks.com/matlabcentral/fileexchange/68976-multipleqr
    [Q,R] = MultipleQR(A);
    R = reshape(R,n*n,[]);
    d1 = (-1)^n * prod(R(1:n+1:end,:),1);
toc % Elapsed time is 0.087167 seconds.
tic
    d2 = arrayfun(@(k) det(A(:,:,k)), 1:size(A,3));
toc % Elapsed time is 0.376470 seconds.
% Check correctness
norm(d1-d2)/norm(d2) % 4.2026e-16
MultipleQR will be less efficient for large n.
Related Question