[eigen] Re: 2.0.10 on November 25?

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here's an update on 4x4 inverse.

In Eigen 2.0.9, the 4x4 inverse uses "Euler's trick" that is used in
all "fast" implementations of 4x4 inverse one can find around, and
that hadn't been properly checked for precision. As reported earlier
to this list, it was really not good enough.

I have rewritten it in both default and 2.0, keeping Euler's trick but
implementing it in a much more careful way, and added a
precision-oriented test. As a result precision is now much better, but
it's slower, too.

To be precise, it's now only 26% faster than the usual cofactors
algorithm (it used to be much faster). However there is room for
improvement as this Euler's trick algorithm is very suitable for
vectorization, contrary to the cofactors algorithm.

Precision-wise: the worst-case relative error is roughly 2x bigger
than with partial-pivoting LU and 3x bigger than with cofactors. In
practice that means that for Matrix4f/4d inversion, cofactors gives a
worst-case error of roughly 16*epsilon and our method gives roughly
48*epsilon. This is tested on many matrices, with arbitrarily bad
condition numbers.


2009/11/22 Benoit Jacob <jacob.benoit.1@xxxxxxxxx>:
> Hi,
> the 2.0.10 release is coming soon.
> Question about pkg-config: the installation dir for the .pc file was
> changed from lib/pkgconfig to share/pkgconfig. So to Rhys and Ingmar
> who contributed to that existing cmake code: please speak now if
> that's not ok with you!
> Benoit
> 2009/11/15 Benoit Jacob <jacob.benoit.1@xxxxxxxxx>:
>> Hi,
>> After looking at the night sky, i found that Nov. 25 would be the only
>> possible date to release 2.0.10.
>> As usual, testing, yada, yada...
>> Benoit

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