A lot of eigenvalues

Hello everybody!

I have many 3x3 matrixes (e.g. 3 000 000 matrixes) and I need to compute their eigenvalues. Nowadays, I'm doing it in loop having 3 000 000 counts, but this way is very time consuming. I'd like to know if there is any possibility how to replace the loop by some matrix operation. For example, I can make a 3x3x3000000 matrix from which I would get the eigenvalues, somehow?

Can anybody help with this?

Thank you in advance,

Tom

[Oleg Komarov]

c(1:3e6) = {rand(3)};

tic

egv = cellfun(@eig,c,'un',0);

toc

23 seconds to me it seems fair.

Answer 1

[Doug Hull]

This from Oleg seems like an answer, not a comment. I prefer to see questions in the 'answered' state.

c(1:3e6) = {rand(3)}; 
tic 
egv = cellfun(@eig,c,'un',0); 
toc

23 seconds to me it seems fair.

[Walter Roberson]

That creates one random 3x3 matrix and finds its eigenvalues 3000000 times.

c = arrayfun(@(IDX) {rand(3)}, 1:3E6);

tic

egv = cellfun(@eig,c,'un',0);

toc

takes significantly longer on my system (35 seconds).

[tomas]

Olegs answer works. Although I don't understand last two input parameters of cellfun function - 'un',0. Can you tell me what they mean, please?

Thank you guys.

[Daniel Shub]

They are shorthand for 'uniform' and false

Answer 2

[Daniel Shub]

While the loop is ~20% slower on my machine then using cellfun, the answer is in a double array and not a cell array. There may be hidden costs of getting the information from the cell array into a usable form.

N = 3e6;
x = rand(3, 3, N);
tic
egv = zeros(3, N);
for ii = 1:N
  egv(:, ii) = eig(x(:, :, ii));
end
toc