[eigen] LeastSquares, Pseudo Inverse & Geometry

[Thomas Capricelli <orzel@xxxxxxxxxxxxxxx>]

Hi all,

I feel uncomfortable with the name of the module "LeastSquares"
http://eigen.tuxfamily.org/dox-devel/group__LeastSquares__Module.html

It's nothing more than one function (and one variant) computing linear regression, which is I think a very special case of least squares. The API has a 'geometry' feeling more than an optimization or statistical one. (that's what i'm interested about, you'll have guessed).

What the (currently still unsupported) NonLinearOptimization module does is also least squares, in the non linear case.

Though even in the linear case, this is different from http://en.wikipedia.org/wiki/Least_squares, which also is something that I need. I dont really understand how far it's different, but at least the computation is different : the current LeastSquares module uses eigenvalue, while this article (and the stuff I do) uses pseudo-inverse.

Concerning the pseudo inverse, i think we need an implementation in eigen, and I'm happy Benoit has this planned.

So my questions are:
* what do you think of moving those two methods to the Geomerty module, and removing the LeastSquares module ? 
* should we provide methods for linear least squares (which is really nothing more than computing+applying a pseudo inverse ?)

++
Thomas
-- 
Thomas Capricelli <orzel@xxxxxxxxxxxxxxx>
http://www.freehackers.org/thomas