[R] underdetermined system

[Charles C. Berry]

On Tue, 16 Oct 2007, Ravi Varadhan wrote:

> QR is good for overdetermined LS problems, and I don't think that it can be
> used for "minimum norm" solution of underdetrmined LS problems.  You need
> LAPACK's Fortran routine DGELS.  I am not sure if this currently available
> in R.

It is in include/R_ext/Lapack.h around line 240 in R-2.6.0.

Chuck

>
> Ravi.
>
> ----------------------------------------------------------------------------
> -------
>
> Ravi Varadhan, Ph.D.
>
> Assistant Professor, The Center on Aging and Health
>
> Division of Geriatric Medicine and Gerontology
>
> Johns Hopkins University
>
> Ph: (410) 502-2619
>
> Fax: (410) 614-9625
>
> Email: rvaradhan at jhmi.edu
>
> Webpage:  http://www.jhsph.edu/agingandhealth/People/Faculty/Varadhan.html
>
>
>
> ----------------------------------------------------------------------------
> --------
>
>
> -----Original Message-----
> From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org] On
> Behalf Of yoooooo
> Sent: Tuesday, October 16, 2007 11:34 AM
> To: r-help at r-project.org
> Subject: [R] underdetermined system
>
>
> Hi, sorry, I'm an idiot.. and I know I'm missing something stupid..
>
> I thought if we solve an underdetermine system with QR, my soln is:
>
> min ||x|| (L2 sense)  such that Ax = b
>
> then say i have:
>
>> w <- matrix(c(1, 5), ncol=2)
>> sw = 2
>> qrW = qr(t(w) %*% w)
>> qr.coef(qrW, t(w) %*% sw)
>     [,1]
> [1,]    2
> [2,]   NA
>
> but we also have soln (0, 2/5) which obviously has a smaller distance in L2
> than (2, 0). Am I missing something very obvious? Thanks a lot!!!!
>
> - yoooooooooooooooooo
>
>
>
> -- 
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Charles C. Berry                            (858) 534-2098
                                             Dept of Family/Preventive Medicine
E mailto:cberry at tajo.ucsd.edu	            UC San Diego
http://famprevmed.ucsd.edu/faculty/cberry/  La Jolla, San Diego 92093-0901