Here is a more general R function to solve "any" linear system (under/over
determined):
ls.min <- function(x, y) {
# solves: x %*% b = y
d <- svd(x)
# min-norm solution
b.min <- d$v %*% diag(1/d$d, length(d$d)) %*% t(d$u) %*% y
return(b.min)
}
> # underdetermined case
> x <- matrix(c(2, -1, 4, 1, 4, 3), by=T, ncol=3)
> y <- c(8, -1)
> ls.min(x,y)
[,1]
[1,] 0.7511211
[2,] -1.3946188
[3,] 1.2757848
>
> # overdetermined case
> x <- matrix(c(2, -1, 4, 1, 4, 3), by=T, ncol=2)
> y <- c(2, -1, 5)
> ls.min(x,y)
[,1]
[1,] 0.26
[2,] 0.76
>
>
Best,
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 Ravi Varadhan
Sent: Tuesday, October 16, 2007 3:18 PM
To: 'yoooooo'; r-help at r-project.org
Subject: Re: [R] underdetermined system
Here is a solution using SVD:
w <- matrix(c(1, 5), ncol=2)
sw <- 2
w.svd <- svd(w)
sw %*% w.svd$u %*% diag(1/w.svd$d, length(w.svd$d)) %*% t(w.svd$v)
> sw %*% w.svd$u %*% diag(1/w.svd$d, length(w.svd$d)) %*% t(w.svd$v)
[,1] [,2]
[1,] 0.07692308 0.3846154
>
This, of course, has a smaller norm than (0, 0.4).
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 3:02 PM
To: r-help at r-project.org
Subject: Re: [R] underdetermined system
Turns out someone asked this before ;)
http://tolstoy.newcastle.edu.au/R/e2/devel/07/04/2981.html
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.
>
> 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
>
>
>
> --
> View this message in context:
> http://www.nabble.com/underdetermined-system-tf4634837.html#a13235711
> Sent from the R help mailing list archive at Nabble.com.
>
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
> http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
> http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>
>
--
View this message in context:
http://www.nabble.com/underdetermined-system-tf4634837.html#a13240230
Sent from the R help mailing list archive at Nabble.com.
______________________________________________
R-help at r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
______________________________________________
R-help at r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.