Possible bug in det (was: Possible loss of accuracy)

[Marco Caliari]

> Secondly, this makes use of ATLAS' multi core capabilities:
> % getting to 1 the hard way
> N = 2100; A = rand(N);
> tic, det(A*inv(A)), toc
> ans = Inf
> Elapsed time is 1.6111 seconds.
>
> N = 2000; A = rand(N);
> tic, det(A*inv(A)), toc
> ans =  1.0000
> Elapsed time is 1.436 seconds.

Here I suspect a bug: I get

N = 2100;
A = rand(N);
det(A*inv(A))
ans = Inf
prod(diag(chol(A*inv(A))))
ans =  1.00000 % <- correct
prod(diag([~,U]=lu(A*inv(A))))
ans =  1.00000 % <- correct

Shouldn't Octave use Cholesky factorization of A*inv(A) (or, if not 
recognized as hermitian, LU factorization) in order to compute its 
determinant?

Marco