From: Moshe Olshansky <m_olshansky_at_yahoo.com>

Date: Tue, 03 Jun 2008 17:00:18 -0700 (PDT)

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 Wed 04 Jun 2008 - 00:02:49 GMT

Date: Tue, 03 Jun 2008 17:00:18 -0700 (PDT)

Since k_i(l,m,s) are known constants, you actually have a system of four non-linear equations with 4 unknowns.

One possibility is to use optim (check ?optim).

Another one is to use the very recently released package - look at https://stat.ethz.ch/pipermail/r-help/attachments/20080423/da0b7f6c/attachment.pl

- On Wed, 4/6/08, Jorge Ivan Velez <jorgeivanvelez_at_gmail.com> wrote:

*> From: Jorge Ivan Velez <jorgeivanvelez_at_gmail.com>
**> Subject: [R] How to solve a non-linear system of equations using R
**> To: "R mailing list" <r-help_at_r-project.org>
**> Received: Wednesday, 4 June, 2008, 7:09 AM
*

> Dear R-list members,

*>
**> I've had a hard time trying to solve a non-linear
**> system (nls) of equations
**> which structure for the equation i, i=1,...,4, is as
**> follows:
**>
**>
**> f_i(d_1,d_2,d_3,d_4)-k_i(l,m,s) = 0 (1)
**>
**>
**> In the expression above, both f_i and k_i are known
**> functions and l, m and s
**> are known constants. I would like to estimate the vector
**> d=(d_1,d_2,d_3,d_4)
**> which is solution of (1). Functions in R to estimate
**> f_i-k_i are at the end
**> of this message.
**>
**> Any help/suggestions/comments would be greatly appreciated.
**>
**> Thanks in advance,
**>
**> Jorge
**>
**>
**> # ------------------------------
**> # Constants
**> # ------------------------------
**>
**> l=1
**> m=0.4795
**> s=0.4795
**>
**> # ------------------------------
**> # Functions to estimate f_i-k_i
**> # ------------------------------
**>
**> f1=function(d){
**> d1=d[1]
**> d2=d[2]
**> d3=d[3]
**> d4=d[4]
**> res=2*d1+2*sqrt(2)*d1*d2+2*sqrt(3)*d2*d3+4*d3*d4-l*m*(1+d1^2+d2^2+d3^2+d4^2)
**> res
**> }
**>
**> f2=function(d){
**> d1=d[1]
**> d2=d[2]
**> d3=d[3]
**> d4=d[4]
**> res=2*sqrt(2)*d2+2*d1^2+2*sqrt(6)*d1*d3+4*d2^2+4*sqrt(3)*d2*d4+6*d3^2+8*d4^2-l*(m^2+m^3*s^(-1))*(1+d1^2+d2^2+d3^2+d4^2)
**> res
**> }
**>
**> f3=function(d){
**> d1=d[1]
**> d2=d[2]
**> d3=d[3]
**> d4=d[4]
**> res=6*d1+12*sqrt(2)*d1*d2+18*sqrt(3)*d2*d3+48*d3*d4+2*sqrt(6)*d3+4*sqrt(6)*d1*d4-l*(m^3+3*m^4*s^(-1)+3*m^6*s^(-2))*(1+d1^2+d2^2+d3^2+d4^2)
**> res
**> }
**>
**>
**> f4=function(d){
**> d1=d[1]
**> d2=d[2]
**> d3=d[3]
**> d4=d[4]
**> res=12*sqrt(2)*d2+12*d1^2+36*d2^2+72*d3^2+120*d4^2+20*sqrt(6)*d1*d3+56*sqrt(3)*d2*d4+4*sqrt(6)*d4-l*((m^4+6*m^6*s^(-1)+15*m^6*s^(-2)+15*m^7*s^(-3))-3*l^(2)*(m^2+m^3*s^(-1))^2)*(1+d1^2+d2^2+d3^2+d4^2)
**> res
**> }
**>
**> [[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.
*

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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 Wed 04 Jun 2008 - 00:02:49 GMT

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