Note that we now have a constrained optimization problem in (n + 3) variables: y, A, B, and C; but we also have `n' constraints among these n+3 variables.
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: Ravi Varadhan <rvarad...@jhmi.edu> Date: Tuesday, October 5, 2010 11:48 am Subject: Re: [R] nonlinear curve fit of an implicit function To: "Schmitt, H. (Heike)" <h.schm...@uu.nl> Cc: r-help@r-project.org > You can solve this as a (nonlinearly) constrained optimization problem: > > Given: x, y.obs; both in R^n > Minimize the objective function: sum( (y - y.obs)^2 ) > where `y' is such that it satisfies the constraints: > (A+B+C)*log((B+C+y)/C)-A*log((B-y)/B)=(B+C)*D*x > > Do you have other constraints on A,B, and C, such as positivity, etc? > If so, you need to incorporate them as well. > > You can take a look at the package "alabama", which has 2 optimizers: > `auglag' and `constrOptim.nl'. > > > Hope this helps, > 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: "Schmitt, H. (Heike)" <h.schm...@uu.nl> > Date: Tuesday, October 5, 2010 11:10 am > Subject: [R] nonlinear curve fit of an implicit function > To: r-help@r-project.org > > > > Hello, > > > > I want to perform a nonlinear curve fit in order to obtain parameter > > estimates from experimentally determined data (y in dependence of > x), > > but with an implicit function, thus, a function of which I cannot > > isolate y on the left-hand side of the equation. As far as I understand, > > the functions I found up to now (nls, optim) all work only for explicit > > functions. > > > > My data looks like > > x<-c(4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37, 40, 43, 46, 49, > 52, > > 55, 58, 61) > > y<-c(0.0, -0.1, 0.0, 0.1, 0.5, 0.9, 1.4, 2.3, 3.1, 3.4, 3.8, 4.2, > 4.6, > > 4.9, 5.0, 5.1, 5.2, 5.3, 5.4, 5.5) > > > > > > > > My function is a sigmoidal growth function based on an integrated > form > > of the Monod function: > > > > (A+B+C)*log((B+C+y)/C)-A*log((B-y)/B)=(B+C)*D*x > > > > > > > > Your ideas would be greatly appreciated. > > > > > > > > Heike Schmitt > > > > Utrecht University > > > > > > > > > > [[alternative HTML version deleted]] > > > > ______________________________________________ > > 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 > > 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.
