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

From: Karl Meerbergen (Karl.Meerbergen_at_[hidden])
Date: 2007-06-04 04:03:35

Gunter Winkler wrote:

>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
>  
>
>  
>

Gunter,

There are bindings to DGEQRF and ZGEQRF in the lapack bindings, as well 
as DORMQR and ZUNMQR, but they is rather technical to use.

Bindings to DGELS/ZGELS or DGELSD/ZGELSD should be added to solve any 
underdetermined or overdetermined linear system in a more user friendly 
way. Recall that DGELS uses QR, whereas DGELSD uses SVD (more reliable, 
but more expensive).

Karl

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