Re: [eigen] Non linear equations solver

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Hello Gael

If I were you I would be a good mathematician and programmer :-)

You and other people in Eigen's group are at least as good as Jorge Moré et al that developed Minpack in the Argonne National Laboratory years ago, a sample of robust and reliable software (

Something like this means many months of excelent design and programing effort from real experts.

Thomas Capricelli confirm me (and I think he is much better programmer than me) that this is too much difficult for us.

We prefer to offer Eigen's community in weeks a robust well tested library, better than to have in months or years a "best in class" library.

This way in only few weeks we can have something really useful. And we are sure we will do it. We think that re design Minpack from scratch is out of our capability.

Thak you

2009/8/10 Gael Guennebaud <gael.guennebaud@xxxxxxxxx>
my 2 cents:

if I were you, I'd start from Keir implementation, extend it to make
the underlying linear solver a template parameter so that one can use
LU, QR, SVD, LLT, etc. or any sparse solver when using sparse
matrices. Actually, we already discussed these things in another

Then you could have a look at cminpack implementation to see the
differences, and in particular to see whether there are some good
tricks to make the algorithm better (better convergence, more
accurate, etc.)

An in parallel to that, we could discuss the API design, in
particular, how to control the algorithm, how to specify the Jacobian
(user defined, AD, finite differences), etc.



On Mon, Aug 10, 2009 at 9:07 AM, Koldo Ramirez<koldo.ramirez@xxxxxxxxx> wrote:
> Hello Thomas
> I suppose Minpack 2 is based in version 1 as they present it as an
> improvement focusing in large scale problems and using Blas and Lapack..
> About the Octave reference is just to show that an important project like
> Octave has considered Minpack.
> Best regards
> Koldo
> 2009/8/8 Thomas Capricelli <orzel@xxxxxxxxxxxxxxx>
>> In data lunedì 27 luglio 2009 10:13:58, Koldo Ramirez ha scritto:
>> > It exists Minpack version 2. Between other advantages it uses BLAS and
>> > LAPACK. This is the presentation (
>> > or
>> >
>> It doesn't seem to be related to minpack actually. only the name is the
>> same,
>> i think it's not based on the minpack code. is it ?
>> >         ..., the old minpack code is gone. ...
>> >         Essentially the same method as in minpack is used - double
>> > dogleg
>> >         trust region steps with Broyden updating of the jacobian. For
>> > large
>> >         enough (no. of variables > 10) square and overdetermined(!)
>> > systems, the QR factorization of the jacobian is updated rather than the
>> > jacobian itself, avoiding costly re-factorizations. Broyden updating may
>> > be
>> > switched off by the user, yielding plain levenberg-marquardt method.
>> interesting to not, those are things we could do later on. I still prefer
>> considering minpack currently has it has a lot broader user test range.
>> Thomas
>> --
>> Thomas Capricelli <orzel@xxxxxxxxxxxxxxx>

Gaël Guennebaud
Iparla - INRIA Bordeaux
(+33)5 40 00 37 95

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