Re: [eigen] Re: LU precision tuning

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> ... but I rather think that what is invalidated is the QR precision testing!
> Indeed your patch introduced m_precision in QR but it was never used
> in the computation of the QR decomposition, only in the rank() and
> solve() methods. So what's really needed is to make eps2 honor the
> m_precision.
> I can't tell whether the creation of random rank r matrices was
> affected by that or not.

It seems as if it was not really affected. After fixing the precision
usage, the results did not improve.

I took a short look at the code an briefly touched the literature
about RRQR (rank revealing QR) decompositions. Since the current QR
does (please correct me if I am wrong) no pivoting I assume it is
pretty safe to assume that it is not rank revealing. There are a bunch
of RRQR algorithms reviewed/described in Bischof & Quintana-Qrti,
"Computing Rank-Revealing QR Factorizations of Dense Matrices" and all
of them rely on pivoting.


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