Re: [R] How to solve a non-linear system of equations using R
Jorge,
You can use the package BB to try and solve this problem.
I have re-written your functions a little bit.
# --
# Constants
# --
l=1
m=0.4795
s=0.4795
# --
# Functions to estimate f_i-k_i
# --
myfn - function(d){
d1 - d[1]
d2 - d[2]
d3 - d[3]
d4 - d[4]
res - rep(NA, 4)
res[1] -
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[2] -
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[3] -
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[4] -
12*sqrt(2)*d2+12*d1^2+36*d2^2+72*d3^2+120*d4^2+20*sqrt(6)*d1*d3+56*sqrt(3)*d
2*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
}
myfn.opt - function(d){
# re-writing myfn to be used for minimization
d1 - d[1]
d2 - d[2]
d3 - d[3]
d4 - d[4]
res - rep(NA, 4)
res[1] -
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[2] -
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[3] -
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[4] -
12*sqrt(2)*d2+12*d1^2+36*d2^2+72*d3^2+120*d4^2+20*sqrt(6)*d1*d3+56*sqrt(3)*d
2*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)
sum(res^2)
}
library(BB)
p0 - runif(4, -1,0)
ans1 - dfsane(par=p0, fn=myfn)
ans2 - spg(par=p0, fn=myfn.opt)
ans1
ans2
Note that the above does not produce a redual of zero, so the system can't
be solved exactly. I tried a large number of random starting values without
improving upon the solution provided by spg. So, you may want to check
your system for its correctness.
Hope this helps,
Ravi.
-Original Message-
From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On
Behalf Of Jorge Ivan Velez
Sent: Tuesday, June 03, 2008 5:09 PM
To: R mailing list
Subject: [R] How to solve a non-linear system of equations using R
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)*d
1*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
}
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[R] How to solve a non-linear system of equations using R
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]]
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Re: [R] How to solve a non-linear system of equations using R
Hi Jorge,
Have you tried to use systemfit package. In this package, this is a
function call nlsystemfit . This might help.
Chunhao
Quoting Jorge Ivan Velez [EMAIL PROTECTED]:
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]]
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and provide commented, minimal, self-contained, reproducible code.
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Re: [R] How to solve a non-linear system of equations using R
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 [EMAIL PROTECTED] wrote:
From: Jorge Ivan Velez [EMAIL PROTECTED]
Subject: [R] How to solve a non-linear system of equations using R
To: R mailing list r-help@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]]
__
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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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