# [R] Minimizing two non-linear functions with genoud - Trying to minimize or converge near zero

Fri Feb 5 00:54:36 CET 2010

```This works!

f=function(x) {

# x = c(0.16,80)
Vcmax = x
gi = x

# First dataset
f.1=(-(((Vcmax-0.89189)/gi)+164.6573+272.38*(1+21*10/165.82))+sqrt((((Vcmax-0.89189)/gi)+164.6573+272.38*(1+21*10/165.82))^2-4*(-1/gi)*(0.89189*(164.6573+272.38*(1+21*10/165.82))-Vcmax*(164.6573-(5*21/2.605459)))))/(-2/gi)

if (is.nan(f.1)) f.1 = 1e30

# Second data set
f.2= (-(((Vcmax-0.89189)/gi)+164.3077+272.38*(1+2*10/165.82))+sqrt((((Vcmax-0.89189)/gi)+164.3077+272.38*(1+2*10/165.82))^2-4*(-1/gi)*(0.89189*(164.3077+272.38*(1+2*10/165.82))-Vcmax*(164.3077-(5*2/2.605459)))))/(-2/gi)

if (is.nan(f.2)) f.2 = 1e30

# Values here are the measured values. f.1 and f.2 should be equal or close to the value on their left.
y.1 = 7.478327 - f.1
y.2 = 12.73134 - f.2

# This should be close to 0.
y = y.1^2 + y.2^2

return(y)
}

res <- optim(par=c(0.15,50), fn=f, lower=c(0,0), upper=c(1,250), method="L-BFGS-B")

>  f.1(res\$par)
 7.478115
>  f.2(res\$par)
 12.73143
>

Ravi.

____________________________________________________________________

Assistant Professor,
Division of Geriatric Medicine and Gerontology
School of Medicine
Johns Hopkins University

Ph. (410) 502-2619

----- Original Message -----
From: Guillaume Théroux Rancourt <Guillaume.Theroux-Rancourt at fsaa.ulaval.ca>
Date: Thursday, February 4, 2010 5:31 pm
Subject: Re: [R] Minimizing two non-linear functions with genoud - Trying to minimize or converge near zero
To: "r-help at r-project.org" <r-help at r-project.org>

> Thank you Ravi!
>
>  What I forgot to mention in my first post is that gi should be
> between [0,1], while Vcmax is usually between [0,150], but can be
> higher [0,250]. That was the Domains of the genoud function initially.
>
>  Also, in this example, f.1 should equal 7.478 and f.2 = 12.731 with
> the same Vcmax and gi.
>
>  Using optim, I see that it is very sensitive to the starting
> parameters. Using c(0.15, 100) give parameters close to what should be
> expected, but it is still not close enough to 7.478 for f.1 (for example).
>
>  Thank you for your help,
>
>  Guillaume
>
>  > I do not understand completely what you are trying to do, but may
> be this works for you!?
>  >
>  > f=function(x) {
>  >
>  > # x = c(0.16,80)
>  > Vcmax = x
>  > gi = x
>  >
>  > # First dataset
>  > f.1=function(x){
>  > (-(((Vcmax-0.89189)/gi)+164.6573+272.38*(1+21*10/165.82))+sqrt((((Vcmax-0.89189)/gi)+164.6573+272.38*(1+21*10/165.82))^2-4*(-1/gi)*(0.89189*(164.6573+272.38*(1+21*10/165.82))-Vcmax*(164.6573-(5*21/2.605459)))))/(-2/gi)
>  > }
>  >
>  > # Second data set
>  > f.2=function(x){
>  > (-(((Vcmax-0.89189)/gi)+164.3077+272.38*(1+2*10/165.82))+sqrt((((Vcmax-0.89189)/gi)+164.3077+272.38*(1+2*10/165.82))^2-4*(-1/gi)*(0.89189*(164.3077+272.38*(1+2*10/165.82))-Vcmax*(164.3077-(5*2/2.605459)))))/(-2/gi)
>  > }
>  >
>  > # Values here are the measured values. f.1 and f.2 should be equal
> or close to the value on their left.
>  > y.1 = abs(7.478327 - f.1(x))
>  > y.2 = abs(12.73134 - f.2(x))
>  >
>  > # This should be close to 0.
>  > y = (y.1 - y.2)^2
>  >
>  > return(y*y)
>  > }
>  >
>  > dom = matrix(c(0,0,200,1.5), 2, 2)
>  >
>  > res <-  optim(par=c(0.15,100), fn=f, method="BFGS")  # no need for
> "genoud" here
>  >
>  > # First dataset
>  > f.1=function(x){
>  > Vcmax = res\$par
>  > gi = res\$par
>  > (-(((Vcmax-0.89189)/gi)+164.6573+272.38*(1+21*10/165.82))+sqrt((((Vcmax-0.89189)/gi)+164.6573+272.38*(1+21*10/165.82))^2-4*(-1/gi)*(0.89189*(164.6573+272.38*(1+21*10/165.82))-Vcmax*(164.6573-(5*21/2.605459)))))/(-2/gi)
>  > }
>  >
>  > # Second data set
>  > f.2=function(x){
>  > Vcmax = res\$par
>  > gi = res\$par
>  > (-(((Vcmax-0.89189)/gi)+164.3077+272.38*(1+2*10/165.82))+sqrt((((Vcmax-0.89189)/gi)+164.3077+272.38*(1+2*10/165.82))^2-4*(-1/gi)*(0.89189*(164.3077+272.38*(1+2*10/165.82))-Vcmax*(164.3077-(5*2/2.605459)))))/(-2/gi)
>  > }
>  >
>  >
>  > f.1(res\$par)
>  > f.2(res\$par)
>  >
>  >
>  > Hope this is helpful,
>  > Ravi.
>  >
>  > ____________________________________________________________________
>  >
>  > Assistant Professor,
>  > Division of Geriatric Medicine and Gerontology
>  > School of Medicine
>  > Johns Hopkins University
>  >
>  > Ph. (410) 502-2619
>  > email: rvaradhan at jhmi.edu
>  >
>  >
>  > ----- Original Message -----
>  > From: Guillaume Théroux Rancourt <Guillaume.Theroux-Rancourt at fsaa.ulaval.ca>
>  > Date: Thursday, February 4, 2010 3:02 pm
>  > Subject: [R] Minimizing two non-linear functions with genoud -
> Trying to minimize or converge near zero
>  > To: "r-help at r-project.org" <r-help at r-project.org>
>  >
>  >
>  >> Hello R users,
>  >>
>  >> I am trying to minimize two functions with genoud. It is actually
> one
>  >> function with two sets of data, each of them having two unknown
>  >> variables (called Vcmax and gi) which have the same value in each
> of
>  >> the function. They are called f.1 and f.2 in the code below.
>  >>
>  >> My objective to minimize the functions in order to get the two
>  >> variables equal in each of the functions. Furthermore, I have a
>  >> measured comparison value for each of the function expression, and
> the
>  >> results of f.1 and f.2 should be very close or equal to their
> measured
>  >> value, so that  measured.1 - f.1 = 0.
>  >>
>  >> I have been able to run genoud with the code below. However, I
>  >> haven't been able to restrain the values of the difference between
> the
>  >> measured and estimated value to 0. I am fairly new at writing R
>  >> functions and I think there might be something I haven't written
> that
>  >> makes the output parameters of genoud not replicable.
>  >>
>  >> I have made several runs of this function and when comparing with
> the
>  >> measured value, I got answers between 1 and 12, where it should
> have
>  >> been very close to 7.47.
>  >>
>  >> This example has already been solved with the solver Excel add-in
> and
>  >> theh result are:
>  >> Vcmax = 104.32, gi = 0.11
>  >>
>  >> The values were also estimated using another approach and they are:
>  >> Vcmax = 64.48, gi = 0.28
>  >>
>  >>
>  >> Here is my code.
>  >>
>  >>
>  >> ######
>  >>
>  >> f=function(x) {
>  >>
>  >> x = c(0.16,80)
>  >> Vcmax = x
>  >> gi = x
>  >>
>  >> # First dataset
>  >> f.1=function(x){
>  >> (-(((Vcmax-0.89189)/gi)+164.6573+272.38*(1+21*10/165.82))+sqrt((((Vcmax-0.89189)/gi)+164.6573+272.38*(1+21*10/165.82))^2-4*(-1/gi)*(0.89189*(164.6573+272.38*(1+21*10/165.82))-Vcmax*(164.6573-(5*21/2.605459)))))/(-2/gi)
>  >> }
>  >>
>  >> # Second data set
>  >> f.2=function(x){
>  >> (-(((Vcmax-0.89189)/gi)+164.3077+272.38*(1+2*10/165.82))+sqrt((((Vcmax-0.89189)/gi)+164.3077+272.38*(1+2*10/165.82))^2-4*(-1/gi)*(0.89189*(164.3077+272.38*(1+2*10/165.82))-Vcmax*(164.3077-(5*2/2.605459)))))/(-2/gi)
>  >> }
>  >>
>  >> # Values here are the measured values. f.1 and f.2 should be equal
> or
>  >> close to the value on their left.
>  >> y.1 = (7.478327 - f.1(x))
>  >> y.2 = (12.73134 - f.2(x))
>  >>
>  >> # This should be close to 0.
>  >> y = y.1 - y.2
>  >>
>  >> return(y)
>  >> }
>  >>
>  >> dom = matrix(c(0,0,200,1.5), 2, 2)
>  >>
>  >> res = genoud(f, nvars=2, max=FALSE,Domains=dom,pop.size=5000,print.level=0)
>  >>
>  >>
>  >> # In order to test the results to see I the estimated variables
> make
>  >> the "test" function = 7.478327 or near.
>  >> # This is the same as f.1
>  >>
>  >> test=function(Vcmax, gi){
>  >> (-(((Vcmax-0.89189)/gi)+164.6573+272.38*(1+21*10/165.82))+sqrt((((Vcmax-0.89189)/gi)+164.6573+272.38*(1+21*10/165.82))^2-4*(-1/gi)*(0.89189*(164.6573+272.38*(1+21*10/165.82))-Vcmax*(164.6573-(5*21/2.605459)))))/(-2/gi)
>  >> }
>  >>
>  >> test(res\$par,res\$par)
>  >>
>  >> ## End
>  >>
>  >>
>  >> Thank you for your help!
>  >>
>  >>
>  >> Guillaume Théroux Rancourt
>  >> Ph.D. candidate --- Plant Biology
>  >> Université Laval, Québec, QC, Canada
>  >> guillaume.theroux-rancourt.1 at ulaval.ca
>  >>
>  >> ______________________________________________
>  >> R-help at r-project.org mailing list
>  >>