Re: [eigen] Re: LU precision tuning

[Benoit Jacob <jacob.benoit.1@xxxxxxxxx>]

2009/5/11, Hauke Heibel <hauke.heibel@xxxxxxxxxxxxxx>:
> I could not help but thought about it again. The way we are currently
> creating orthogonal matrices involves the QR decomposition and the
> eps2 in QR was always computed as
>
> RealScalar eps2 = precision<RealScalar>()*precision<RealScalar>();

Ah, that needed to be updated as well!

> Maybe this caused problems with the orthogonal matrices computed via
> QR. I am wondering whether this code
>
> http://rafb.net/p/K58Ni284.html

This code seems OK, ...

>
> maybe more appropriate for the creation of random orthogonal matrices.
> The code uses Gram-Schmidt orthogonalization to do so.
>
> I will give it a try when I come back from lunch.

.... 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.

Cheers,
Benoit