Is there faster way to apply `det` function along the third dimension?

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I am trying to calculate the det of many 4*4 matrix. I store the data in a matrix with shape 4*4*n. (n =4000000). I am using the for loop to get the result as below. Is there any way to accelerate the progress? Like bsxfun or arrayfun, or some simillar ideas?
v = zeros(length(m),1);
for i=1:size(m,3)
v(i)=det(m(:,:,i));
end
  6 Comments
Walter Roberson
Walter Roberson on 18 Jul 2020
Bruno's criticism of the precision problems and the high length of the formula for increasing n, are valid criticisms. Generally speaking, it is often the case that making code faster comes at the price of making it less accurate towards the margins. Theoretical definitions that suppose infinite precision get substituted for more nuanced checks that deal with floating-point realities, and time gets saved by not making the checks to figure out what compensation is needed for each case.
If you have some time you should look at how hypot() (finding the length of a hypotenuse) has to be implemented in practice in order to maintain accuracy. Consider sqrt(A^2 + B^2) under the circumstance that A or B is smaller than sqrt(realmin) and so squaring it might underflow to 0...
wei zhang
wei zhang on 19 Jul 2020
@Bruno Luong Thank you for introducing the formula in wiki.
@Walter Roberson.
1. I am glad to know the matlabfunction command. It is much faster than combination of subs and syms.
2. Thank you for introducing the cause of error. It seems the error is increasing fast with the size of matrix increasing. May cause terrible results.Wow.

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Accepted Answer

Bruno Luong
Bruno Luong on 17 Jul 2020
Edited: Bruno Luong on 17 Jul 2020
I would note that Walter's solution that use recursive formal determinant formula might be fast but might be sensitive to umerical errors, that is how I was tough (for medium/large size matrix).

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