Re: [eigen] cppduals - dual number implementation with Eigen specializations

["Wood, Tobias" <tobias.wood@xxxxxxxxx>]

Thanks Michael – this sounds hopeful, which is a pleasant surprise as after discussing the issue on the Ceres mailing list yesterday I was ready to give up. Fortuitous timing!

 

I’ll take a look at your eigen-expokit and see if I can get that working.

 

Toby

 

From: Michael Tesch <tesch1@xxxxxxxxx>
Reply to: "eigen@xxxxxxxxxxxxxxxxxxx" <eigen@xxxxxxxxxxxxxxxxxxx>
Date: Wednesday, 4 December 2019 at 11:47
To: "eigen@xxxxxxxxxxxxxxxxxxx" <eigen@xxxxxxxxxxxxxxxxxxx>
Subject: Re: [eigen] cppduals - dual number implementation with Eigen specializations

 

Hi Toby,

 

Yes, that's literally my use case too - although I dont use Eigen's Pade' approximation, instead I have (partially, and admittedly somewhat sloppily) ported the great EXPOKIT to Eigen: https://gitlab.com/tesch1/eigen-expokit --  that padm() might work directly with ceres::Jet (but of course would be slower).  See https://gitlab.com/tesch1/cppduals/blob/master/tests/test_expm.cpp#L132 for an example.

 

To get Eigen's M.exp() to use the Pade approximant for a non-standard type, you might have to create some template trickery.  If you dont convince it that you actually want Pade, it silently falls back to the Sylvester's formula implementation, which I just checked doesn't work with cppduals (it compiles & runs but gives incorrect results - dunno why, didn't investigate).

 

As a side note, if you want really fast matrix exponential derivatives and have plenty of memory to throw at it:

- https://doi.org/10.1137/080716426

- https://github.com/scipy/scipy/blob/v0.14.0/scipy/linalg/_expm_frechet.py#L225

 

Cheers,

Michael

 

 

On Wed, Dec 4, 2019 at 11:35 AM Wood, Tobias <tobias.wood@xxxxxxxxx> wrote:

Hello Michael,

 

Would I be able to use the Eigen matrix functions, e.g. the matrix exponential, with your library? Literally in the last week I found that the ceres::Jet<> class does not work with the matrix exponential, due to issues with implicit conversions.

 

Thanks,

Toby