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
âu=h*integrate(((5+cos(v))*sqrt((5+cos(v))^2-h^2))^{-1})
from 0 to vâ.
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 <[EMAIL PROTECTED]>
Subject: Re: [R] nonlinear curve fitting on a
torus
To: Sungsu <[EMAIL PROTECTED]>
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]]
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