Berend's point is well-taken. It's a lot of work to re-jig a code, especially one more than 30 years old.
On the other hand, nlmrt is all-R, and it does more or less work on underdetermined systems as I illustrated in a small script. The changes needed to treat the problem as Mike suggests are pretty easy, but they imply that some aspects of the modeling computations have to be omitted. Mike: If you give that a try, I'd be interested in outcomes, and am willing to answer questions on how the code works. Indeed, I want to include the sort of "diagnostics" that allow underdetermined systems in my packages, so that some results are replaced with NA or NULL and helpful warnings rather than "Failed m<n" are reported. Best, JN On 16-10-21 03:39 AM, Berend Hasselman wrote: > >> On 21 Oct 2016, at 06:00, Mike meyer <1101...@gmx.net> wrote: >> >> Let's take a different view of the problem. >> Given f=(f_1,...,f_m):R^n -> R^m we want to minimize ||f(x)||. >> >> What distinguishes this from a general minimization problem is that you know >> the structure of the >> objective function F(x)=||f(x)||² and have the individual constituents f_j. >> Make use of that information as appropriate. >> >> This is more general than trying to solve the system f(x)=0 or fitting a >> model to data. >> In this more general setting notions such as underdetermined/overdetermined >> system do not apply. >> >> The restricted view of model fitting serves only to confuse the issue. >> For that reason it is (in my view) a bad idea to force the user to set up >> his problem in >> R-model notation. >> > > I assume that you have been referring to the R package minpack.lm. > > I've had a look at the underlying Fortran code (from Minpack and developed by > More et.al. made in a distant past) as used by the package. > That underlying code returns an error when the condition: number of > functions (m) >= the number of independent variables (n) > is not satisfied i.e. when m < n. > > Making that more general would entail a lot of thinking and reworking of the > code. As far as I can see it is not possible to just remove the condition > m>=n from the underlying Fortran. More (possibly many) changes would be > required. Blaming R and/or the package author/maintainer is unfair. > > If you require a more general version of the algorithm or if you want > something else you will have to roll your own package/code. > If you don't feel that minpack.lm is appropriate for your application and you > want changes you'll have to discuss matters with Moré > (http://www.mcs.anl.gov/~more/) if I got the correct link. > > Berend > ______________________________________________ R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see 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.
