fastest way to apply A\B on each matrix page

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.

Answer 1

[Bruno Luong]

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{:}); 

[hosein Javan]

speed is required for too many matrices like that. I don't know, I'm just looking for the fastest way. from what I know, in a loop, a procedure is done on each iteration, meaning that an iteration must be completed so that the next one is done. I'm not sure there is a way to do them all in once. Thank you for reply.

[Bruno Luong]

For that very reason that you just state why I call ARRAYFUN is a big scam.

User have impression thing is done once, no it does iteratively just like a FOR-LOOP and usually it slowser.

If you want do it "once" this FEX file do it really at once, not sure if it's fatre though due to overhead.

[hosein Javan]

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]

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]

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.