Using pagemtimes multiplying from left and right side

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Morten Nissov 2021-5-3

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回答： Felipe Padua 2022-8-29

I have a 3D array I need to multiply on left and right sides by a constant 3x3 matrix, take a cholesky decomposition and multiply it by a random vector, I am trying to avoid for loops. The arrays are P 6x6xN and F 3x6. The equivalent for loop multiplication is

for i=1:length(Pf)
    w = chol(Fn*Pf(:,:,i)*Fn')*randn(3,1);
    out(:,i) = out(:,i) + w;
end

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Answer 1

Felipe Padua 2022-8-29

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You can use pagemtimes to perform both multiplications but, since chol accept only matrices (2D arrays) as arguments, you'll still need a loop. Try the code below:

n = size(Pf, 3);
aux = pagemtimes(Fn, Pf);
aux = pagemtimes(aux, Fn');
for i = 1:n
    aux (:,:,i) = chol(aux(:,:,i));
end
aux = pagemtimes(aux, rand(3,1,n));

If you desire retrieve the steps taken, you may avoid overwriting the aux variable renaming the sucessive results as aux1, aux2 etc, or other names of your preference.