nonlinear curve fitting on a torus
Have you tried plotting it, e.g., like the following:
npts = 51 # or some number
h = seq(0, ???, length=npts)
funh <- rep(NA, npts)
for(i in 1:npts)funh[i] <- fun(h[i])
plot(h, funh)
Hope this helps.
Spencer
Sungsu wrote:
Dear Spencer.
Thank you for your kind reply.
I have n data points observed on the surface of a torus. I am trying
to fit the geodesic line equation to these points on the surface:
the equation is
?u=h*integrate(((5+cos(v))*sqrt((5+cos(v))^2-h^2))^{-1}) from 0 to v?.
I wrote the following R code to make the above function.
fun<-function(h)
{
u<-h*integrate(((5+cos(y))*sqrt((5+cos(y))^2-h^2))^(-1)),lower=0,upper=v)$value
u
}
Then minimized the sum of
(1-cos(u-h**integrate(((5+cos(y))*sqrt((5+cos(y))^2-h^2))^(-1)),lower=0,upper=v)$value)
as:
nlminb(c(1),fun,lower=0,upper=9)
I did not get an error, but the estimated h is 9 or 0, these are just
boundaty values.
I would like to appreciate your help.
Sungsu
UCR
ps: you may use any sized two vectors for u and v with values from 0
to 2pi in the above equation.
---- Original message ----
*Date:* Sun, 13 Apr 2008 13:54:17 -0700
*From:* Spencer Graves <spencer.graves at pdf.com>
*Subject:* Re: [R] nonlinear curve fitting on a torus
*To:* Sungsu <skim033 at ucr.edu>
*Cc:* r-help at r-project.org
> Having seen no reply to this, I will offer a couple of comments
>that may or may not be useful. Googling for "geodesic equation on a
>torus" produced interesting hits, but RSiteSearch("geodesic
equation on
>a torus") found nothing. RSiteSearch("torus") returned 33 hits,
some of
>which referred to a package "geozoo".
>
> If you want a solution of a differential equation, you might
>consider lsoda {odesolve}. The 'fda' package may also be useful.
>
> To say more, I'd prefer to hear more specifics from you. PLEASE
>do read the posting guide
>and provide commented, minimal, self-contained, reproducible code.
>Doing so can make it much easier for people to understand what you
>want. If you provide code that doesn't quite work, someone who is
>interested can copy it from your email into R and try things,
possibly
>generating a solution to your problem. Without a self-contained
>example, you restrict the pool of possible respondents to people who
>have actually worked with a "geodesic equation on a torus" -- or to
>fools like me who are willing to expose their ignorance
commenting on
>something we know essentially nothing about.
>
> Hope this helps.
> Spencer Graves
>
>Sungsu wrote:
>> Dear R users.
>>
>> I have data observed on the surface of a torus, and
>> am trying to fit the nonlinear regression using
>>
>> the geodesic equation on a torus. Could anyone give
>> me a helpful advise on this problem? I would
>> definitely appreicate your reply.
>>
>> Sincerely,
>>
>> SUNGSU KIM
>>
>> [[alternative HTML version deleted]]
>>
>> ______________________________________________
>> R-help at 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. >>