Re: [R] nonlinear curve fitting on a torus

From: Sungsu <skim033_at_ucr.edu>
Date: Mon, 14 Apr 2008 05:53:36 -0700 (PDT)


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.

  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
  "http://www.R-project.org/posting-guide.html"
>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.
>>

        [[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. Received on Mon 14 Apr 2008 - 13:22:34 GMT

Archive maintained by Robert King, hosted by the discipline of statistics at the University of Newcastle, Australia.
Archive generated by hypermail 2.2.0, at Mon 14 Apr 2008 - 19:30:28 GMT.

Mailing list information is available at https://stat.ethz.ch/mailman/listinfo/r-help. Please read the posting guide before posting to the list.

list of date sections of archive