Yes, it can be formulated as an LSAP. It works just fine. I have checked it
with several 3 x 3 examples.
Here is another convincing example:
n <- 50
A <- matrix(rnorm(n*n), n, n)
> # Find P such that ||PA - C|| is minimum
vec <- sample(1:n, n, rep=FALSE) # a random permutation
C <- A[vec, ] # the target matrix is just a permutation of original matrix
B <- pMatrix.min(A, C)$A
> dist(B, C)
[1] 0
> dist(A, C)
[1] 69.60859
Ravi.
____________________________________________________________________
Ravi Varadhan, Ph.D.
Assistant Professor,
Division of Geriatric Medicine and Gerontology
School of Medicine
Johns Hopkins University
Ph. (410) 502-2619
email: rvarad...@jhmi.edu
----- Original Message -----
From: Erwin Kalvelagen <erwin.kalvela...@gmail.com>
Date: Saturday, January 16, 2010 1:36 pm
Subject: Re: [R] optimization problem
To: Ravi Varadhan <rvarad...@jhmi.edu>
Cc: r-h...@stat.math.ethz.ch
> I also have doubts this can be formulated correctly as a linear assignment
> problem. You may want to check the results with a small example.
>
> Erwin
>
> ----------------------------------------------------------------
> Erwin Kalvelagen
> Amsterdam Optimization Modeling Group
> er...@amsterdamoptimization.com
>
> ----------------------------------------------------------------
>
>
> On Sat, Jan 16, 2010 at 9:59 AM, Ravi Varadhan <rvarad...@jhmi.edu> wrote:
>
> >
> > Thanks, Erwin, for pointing out this mistake.
> >
> > Here is the correct function for Frobenius norm.
> >
> > Klaus - Just replace the old `dist' with the following one.
> >
> > dist <- function(A, B) {
> > # Frobenius norm of A - B
> > n <- nrow(A)
> > sqrt(sum((B - A)^2))
> > }
> >
> > Ravi.
> >
> > ____________________________________________________________________
> >
> > Ravi Varadhan, Ph.D.
> > Assistant Professor,
> > Division of Geriatric Medicine and Gerontology
> > School of Medicine
> > Johns Hopkins University
> >
> > Ph. (410) 502-2619
> > email: rvarad...@jhmi.edu
> >
> >
> > ----- Original Message -----
> > From: Erwin Kalvelagen <erwin.kalvela...@gmail.com>
> > Date: Saturday, January 16, 2010 2:35 am
> > Subject: Re: [R] optimization problem
> > To: r-h...@stat.math.ethz.ch
> >
> >
> > > Ravi Varadhan <rvaradhan <at> jhmi.edu> writes:
> > > > dist <- function(A, B) {
> > > > # Frobenius norm of A - B
> > > > n <- nrow(A)
> > > > sum(abs(B - A))
> > > > }
> > > >
> > >
> > > See for a definition of the
> > > Frobenius norm.
> > >
> > >
> > > Erwin
> > >
> > > ----------------------------------------------------------------
> > > Erwin Kalvelagen
> > > Amsterdam Optimization Modeling Group
> > > er...@amsterdamoptimization.com
> > >
> > >
> > > ______________________________________________
> > > R-help@r-project.org mailing list
> > >
> > > PLEASE do read the posting guide
> > > and provide commented, minimal, self-contained, reproducible code.
> >
______________________________________________
R-help@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.
