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

Thu Feb 4 21:49:46 CET 2010

```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[2]
gi = x[1]

# 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(1,1), fn=f, method="BFGS")  # no need for "genoud" here

# First dataset
f.1=function(x){
Vcmax = res\$par[1]
gi = res\$par[2]
(-(((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[1]
gi = res\$par[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)
}

f.1(res\$par)
f.2(res\$par)

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 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[2]
>  gi = x[1]
>
>  # 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[1],res\$par[2])
>
>  ## 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
>