Evaluating svd() on slice of matrix array.

I have an array of matrices such that

size(A) == [3, 3, 1e3]

for example. These 1000 [3x3] matrices must be orthonormal so I am attempting to project each one to the nearest orthonormal basis, using svd() and the approximation

This function is made to work on a single [3x3] matrix at a time however. A workaround could be using for loops like

[~,~,np] = size(A);
for i=1:np
    [U,~,V] = svd(A(:,:,i));
    A(:,:,i) = U*V';
end

but this function will be called very often with high numbers of matrices so I am attempting to make efficient. Is there a better way to do this?

Answer 1

[David Goodmanson]

Hi Morten

I take it that your matrices are close to being orthonomal already. Try

[Q, ~] = qr(A(:,:,i));
A(:,:,i) = Q;

which is about three times faster, not counting overhead to read and write to A(:,:,i). The result is slightly different, but of course still orthogonal.