[R] nonlinear curve fit of an implicit function
Ravi Varadhan
rvaradhan at jhmi.edu
Tue Oct 5 18:12:56 CEST 2010
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: rvaradhan at jhmi.edu
----- Original Message -----
From: Ravi Varadhan <rvaradhan at 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.Schmitt at uu.nl>
Cc: r-help at 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: rvaradhan at jhmi.edu
>
>
> ----- Original Message -----
> From: "Schmitt, H. (Heike)" <H.Schmitt at uu.nl>
> Date: Tuesday, October 5, 2010 11:10 am
> Subject: [R] nonlinear curve fit of an implicit function
> To: r-help at 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 at r-project.org mailing list
> >
> > PLEASE do read the posting guide
> > and provide commented, minimal, self-contained, reproducible code.
>
> ______________________________________________
> R-help at r-project.org mailing list
>
> PLEASE do read the posting guide
> and provide commented, minimal, self-contained, reproducible code.
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