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.