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fastest way to apply A\B on each matrix page

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hosein Javan
hosein Javan on 17 Aug 2020
Commented: hosein Javan on 17 Aug 2020
I would like to find an efficient fast way for calculating:
for i = 1:n
X(:,:,i) = A(:,:,i)\B(:,:,i)
end
where A and B are 10*10*n, and 10*1*n size matrices respectively. the matrices are large and must be called meny times. therefore I was thinking of replacing "for loops" with a faster way that does it very fast and not iteratively.

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Accepted Answer

Bruno Luong
Bruno Luong on 17 Aug 2020
Edited: Bruno Luong on 17 Aug 2020
Why insist on ARRAYFUN, your for-loop is perfectly fine. ARRAYFUN is a "vectoriztion" scam.
n = 100;
A = rand(10,10,n);
B = rand(10,1,n);
X = arrayfun(@(p) A(:,:,p)\B(:,:,p), 1:n, 'unif', 0);
X = cat(3,X{:});

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hosein Javan
hosein Javan on 17 Aug 2020
there is also another way to concatenate all matrices of each page diagonally and make one A\B, this way is really fast with sparse matrices, but this way creates a huge matrix and after completion I need to extract unknowns manually which I don't like this method.
hosein Javan
hosein Javan on 17 Aug 2020
Bruno Luong. sorry for misunderstanding. I did not mean to decieve. I only thought that arrayfun is a best replace for "loop". I'll edit the question.
hosein Javan
hosein Javan on 17 Aug 2020
I studied your MultiSolver. it was using concatenation diagonally and make a sparse matrix as I said. I see there's no better way. however ur using of repmat and rehsape was something speedy to extract unknowns without loops. I accept your answer. thanks, but I'd like to mention once more that it was misunderstanding. please don't use words like "big scam". thanks again.

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