R help - Jun 2007 - finding roots of multivariate equation

Hello,
I want to find the roots of an equation in two variables.  I am aware of the
uniroot function, which can do this for a function with a single variable (as I
understand it...) but cannot find a function that does this for an equation
with more than one variable.  I am looking for something implementing similar
to a Newton-Raphson algorithm.
Thanks.

-- 
Bill Shipley
North American Editor for Annals of Botany
Subject Editor for Ecology
D?partement de biologie
Universit? de Sherbrooke
Sherbrooke (Qu?bec) J1K 2R9
Canada

R does not really have a dedicated solver for nonlinear systems of
equations, but instead you can use optim(), which is a minimizer.  Suppose
your system is F(x) = 0, where x \in R^p and F is a mapping from R^p to R^p,
then you minimize the norm of F.  The problem with this approach is that it
can sometimes yield local minima which are not the zeros of the original
system.  However, this can be easily remedied by using different starting
values.

Ravi.

----------------------------------------------------------------------------
-------

Ravi Varadhan, Ph.D.

Assistant Professor, The Center on Aging and Health

Division of Geriatric Medicine and Gerontology 

Johns Hopkins University

Ph: (410) 502-2619

Fax: (410) 614-9625

Email: rvaradhan at jhmi.edu

Webpage:  http://www.jhsph.edu/agingandhealth/People/Faculty/Varadhan.html

 

----------------------------------------------------------------------------
--------


-----Original Message-----
From: r-help-bounces at stat.math.ethz.ch
[mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of Bill Shipley
Sent: Wednesday, June 20, 2007 1:37 PM
To: r-help at stat.math.ethz.ch
Subject: [R] finding roots of multivariate equation

Hello,
I want to find the roots of an equation in two variables.  I am aware of the
uniroot function, which can do this for a function with a single variable
(as I
understand it...) but cannot find a function that does this for an equation
with more than one variable.  I am looking for something implementing
similar
to a Newton-Raphson algorithm.
Thanks.

-- 
Bill Shipley
North American Editor for Annals of Botany
Subject Editor for Ecology
D?partement de biologie
Universit? de Sherbrooke
Sherbrooke (Qu?bec) J1K 2R9
Canada

______________________________________________
R-help at stat.math.ethz.ch 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.

Hi All,

Replying to this and numerous other requests in the past has made me realize
that a nonlinear solver is very much needed for R users.  I have
successfully used a nonlinear solver based on the spectral gradient method,
in FORTRAN.  I can readily translate that to R and make it available as an R
function, but what I would really like to do is to make that into a package.
I can provide the R function and several test examples.  But I am not good
at creating a good/reliable package.  So, it would be ideal if one of the R
gurus is interested in collaborating with me on this project.  Any one
interested?

Ravi.
----------------------------------------------------------------------------
-------

Ravi Varadhan, Ph.D.

Assistant Professor, The Center on Aging and Health

Division of Geriatric Medicine and Gerontology 

Johns Hopkins University

Ph: (410) 502-2619

Fax: (410) 614-9625

Email: rvaradhan at jhmi.edu

Webpage:  http://www.jhsph.edu/agingandhealth/People/Faculty/Varadhan.html

 

----------------------------------------------------------------------------
--------

-----Original Message-----
From: r-help-bounces at stat.math.ethz.ch
[mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of Bill Shipley
Sent: Wednesday, June 20, 2007 1:37 PM
To: r-help at stat.math.ethz.ch
Subject: [R] finding roots of multivariate equation

Hello,
I want to find the roots of an equation in two variables.  I am aware of the
uniroot function, which can do this for a function with a single variable
(as I
understand it...) but cannot find a function that does this for an equation
with more than one variable.  I am looking for something implementing
similar
to a Newton-Raphson algorithm.
Thanks.

-- 
Bill Shipley
North American Editor for Annals of Botany
Subject Editor for Ecology
D?partement de biologie
Universit? de Sherbrooke
Sherbrooke (Qu?bec) J1K 2R9
Canada

______________________________________________
R-help at stat.math.ethz.ch 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.

Hi,

I have written a simple function to solve a system of nonlinear equations. I
have called it nlsolve().  It actually minimizes the squared-norm of the set
of functions by calling optim().  It uses the BFGS algorithm within optim().
Apart from this restriction, the user can pass all the arguments available
in optim().  All the control parameters can be passed as in the call to
optim().  I have attached a text file containing the source for nlsolve()
and also a number of test problems illustrating the use of nlsolve().  Any
feedback and suggestions to improve it are welcome.

Hope this is useful.

Best,
Ravi.

----------------------------------------------------------------------------
-------

Ravi Varadhan, Ph.D.

Assistant Professor, The Center on Aging and Health

Division of Geriatric Medicine and Gerontology 

Johns Hopkins University

Ph: (410) 502-2619

Fax: (410) 614-9625

Email: rvaradhan at jhmi.edu

Webpage:  http://www.jhsph.edu/agingandhealth/People/Faculty/Varadhan.html



----------------------------------------------------------------------------
--------

-----Original Message-----
From: r-help-bounces at stat.math.ethz.ch
[mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of Ravi Varadhan
Sent: Wednesday, June 20, 2007 5:23 PM
To: r-help at stat.math.ethz.ch
Subject: [R] Creatiing an R package for solving nonlinear system of
equations was: RE: finding roots of multivariate equation

Hi All,

Replying to this and numerous other requests in the past has made me realize
that a nonlinear solver is very much needed for R users.  I have
successfully used a nonlinear solver based on the spectral gradient method,
in FORTRAN.  I can readily translate that to R and make it available as an R
function, but what I would really like to do is to make that into a package.
I can provide the R function and several test examples.  But I am not good
at creating a good/reliable package.  So, it would be ideal if one of the R
gurus is interested in collaborating with me on this project.  Any one
interested?

Ravi.
----------------------------------------------------------------------------
-------

Ravi Varadhan, Ph.D.

Assistant Professor, The Center on Aging and Health

Division of Geriatric Medicine and Gerontology 

Johns Hopkins University

Ph: (410) 502-2619

Fax: (410) 614-9625

Email: rvaradhan at jhmi.edu

Webpage:  http://www.jhsph.edu/agingandhealth/People/Faculty/Varadhan.html



----------------------------------------------------------------------------
--------

-----Original Message-----
From: r-help-bounces at stat.math.ethz.ch
[mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of Bill Shipley
Sent: Wednesday, June 20, 2007 1:37 PM
To: r-help at stat.math.ethz.ch
Subject: [R] finding roots of multivariate equation

Hello,
I want to find the roots of an equation in two variables.  I am aware of the
uniroot function, which can do this for a function with a single variable
(as I
understand it...) but cannot find a function that does this for an equation
with more than one variable.  I am looking for something implementing
similar
to a Newton-Raphson algorithm.
Thanks.

-- 
Bill Shipley
North American Editor for Annals of Botany
Subject Editor for Ecology
D?partement de biologie
Universit? de Sherbrooke
Sherbrooke (Qu?bec) J1K 2R9
Canada

______________________________________________
R-help at stat.math.ethz.ch 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.

______________________________________________
R-help at stat.math.ethz.ch 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.

This seems useful, but it is important to note that the approach may not 
work well
unless the system of nonlinear equations is very well behaved and a good 
starting
point is chosen. A good explanation of the problems with this exact 
approach, that
is adding up the sums of squares of the individual functions,  is described
in Numerical Recipes for C, second edition, p 382 (see 
http://www.nrbook.com/a/bookcpdf.php)
Briefly there will often be a great number of local minima even when 
there is only a single
root of the original equations.

Rob





Ravi Varadhan wrote:
> Hi,
>
> I have written a simple function to solve a system of nonlinear equations.
I
> have called it nlsolve().  It actually minimizes the squared-norm of the
set
> of functions by calling optim().  It uses the BFGS algorithm within
optim().
> Apart from this restriction, the user can pass all the arguments available
> in optim().  All the control parameters can be passed as in the call to
> optim().  I have attached a text file containing the source for nlsolve()
> and also a number of test problems illustrating the use of nlsolve().  Any
> feedback and suggestions to improve it are welcome.
>
> Hope this is useful.
>
> Best,
> Ravi.
>
>
----------------------------------------------------------------------------
> -------
>
> Ravi Varadhan, Ph.D.
>
> Assistant Professor, The Center on Aging and Health
>
> Division of Geriatric Medicine and Gerontology 
>
> Johns Hopkins University
>
> Ph: (410) 502-2619
>
> Fax: (410) 614-9625
>
> Email: rvaradhan at jhmi.edu
>
> Webpage:  http://www.jhsph.edu/agingandhealth/People/Faculty/Varadhan.html
>
>
>
>
----------------------------------------------------------------------------
> --------
>
> -----Original Message-----
> From: r-help-bounces at stat.math.ethz.ch
> [mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of Ravi Varadhan
> Sent: Wednesday, June 20, 2007 5:23 PM
> To: r-help at stat.math.ethz.ch
> Subject: [R] Creatiing an R package for solving nonlinear system of
> equations was: RE: finding roots of multivariate equation
>
> Hi All,
>
> Replying to this and numerous other requests in the past has made me
realize
> that a nonlinear solver is very much needed for R users.  I have
> successfully used a nonlinear solver based on the spectral gradient method,
> in FORTRAN.  I can readily translate that to R and make it available as an
R
> function, but what I would really like to do is to make that into a
package.
> I can provide the R function and several test examples.  But I am not good
> at creating a good/reliable package.  So, it would be ideal if one of the R
> gurus is interested in collaborating with me on this project.  Any one
> interested?
>
> Ravi.
>
----------------------------------------------------------------------------
> -------
>
> Ravi Varadhan, Ph.D.
>
> Assistant Professor, The Center on Aging and Health
>
> Division of Geriatric Medicine and Gerontology 
>
> Johns Hopkins University
>
> Ph: (410) 502-2619
>
> Fax: (410) 614-9625
>
> Email: rvaradhan at jhmi.edu
>
> Webpage:  http://www.jhsph.edu/agingandhealth/People/Faculty/Varadhan.html
>
>
>
>
----------------------------------------------------------------------------
> --------
>
> -----Original Message-----
> From: r-help-bounces at stat.math.ethz.ch
> [mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of Bill Shipley
> Sent: Wednesday, June 20, 2007 1:37 PM
> To: r-help at stat.math.ethz.ch
> Subject: [R] finding roots of multivariate equation
>
> Hello,
> I want to find the roots of an equation in two variables.  I am aware of
the
> uniroot function, which can do this for a function with a single variable
> (as I
> understand it...) but cannot find a function that does this for an equation
> with more than one variable.  I am looking for something implementing
> similar
> to a Newton-Raphson algorithm.
> Thanks.
>
>   
> ------------------------------------------------------------------------
>
> ______________________________________________
> R-help at stat.math.ethz.ch 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.
>