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Evaluating svd() on slice of matrix array.

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Morten Nissov
Morten Nissov on 20 Jan 2020
Edited: David Goodmanson on 23 Jan 2020
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?

Answers (1)

David Goodmanson
David Goodmanson on 23 Jan 2020
Edited: David Goodmanson on 23 Jan 2020
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.

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