Re: [ublas] R: solving a linear system Ax=b with A singular

From: Gunter Winkler (guwi17_at_[hidden])
Date: 2007-06-04 03:56:28

On Monday 04 June 2007 09:25, Marchesi Mauro wrote:
> On Friday 01 June 2007 17:15, Gunter Winkler wrote:
> > If you are looking for solutions to over/underdetermined systems
> > you have to solve an auxiliary problem that has a unique solution.
> > [...] both can be done by using a QR decomposition and solving the
> > so called "normal equation" [...] QR is not included in ublas, yet
>
> Thank you for your answer, and for reminding me some issues about
> numerical linear algebra.
> However, maybe I didn't asked my question clearly: is there a way of
> solving an underdetermined system *by using the uBLAS library*?

The answer is twofold:

out of box: no
using additional tools: yes

uBLAS provides everything, except the QR-decomposition. Depending whether you 
have (small) dense or (large) sparse systems you have to call an external 
library (or contribute a qr decomposition).

LAPACK binding are available in the boost-sandbox SVN repository. Bindings to 
CXSparse are on my page: http://freenet-homepage.de/guwi17/ublas/

However, both only provide bindings to LU, but not QR decomposition.

mfg
Gunter