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@pdf.com>
  Subject: Re: [R] nonlinear curve fitting on a
  torus
  To: Sungsu <skim033@ucr.edu>
  Cc: r-help@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@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]]

