[R] Simple question on a function

[Christoph Buser]

Dear Serguei

There might be more efficient ways, but this should work:	

## Define function that you want to optimize. In your case I
## copied your code, but included freq as a second argument:
fun <- function(x, freq)
{
  (freq[1]-(1-x[1])*(1-x[2])-x[3]*sqrt(x[1]*(1-x[1])*x[2]*(1-x[2])))^2/freq[1]+
    (freq[2]-(1-x[1])*x[2]+x[3]*sqrt(x[1]*(1-x[1])*x[2]*(1-x[2])))^2/freq[2]+
      (freq[3]-x[1]*(1-x[2])+x[3]*sqrt(x[1]*(1-x[1])*x[2]*(1-x[2])))^2/freq[3]+
        (freq[4]-x[1]*x[2]-x[3]*sqrt(x[1]*(1-x[1])*x[2]*(1-x[2])))^2/freq[4]
}

## Define mat with values for freq (your code)
mat<-matrix(c(0.4,0.1,0.1,0.4), byrow=TRUE, nrow=10, ncol=4)

## Use apply on mat
apply(mat, 1, function(freq, start) optim(start, fun,
method="BFGS", freq = freq)$par, start = c(0.1,0.1,0.1))

You still can use t() to transpose the matrix if you want the
solutions by row instead of columns.


Please remark that in general optim returns a list, including
several arguments, e.g. convergence that indicates if optim has
converge.
Since you wanted a matrix I only returned optim(...)$par. This
might be dangerous since the additional information gets
lost. Maybe it is better to save the output in a list. You can
try:  

apply(mat, 1, function(freq, start) optim(start, fun,
method="BFGS", freq = freq), start = c(0.1,0.1,0.1))

to see the difference.

Hope this helps

Christoph

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Christoph Buser <buser at stat.math.ethz.ch>
Seminar fuer Statistik, LEO C13
ETH Zurich	8092 Zurich	 SWITZERLAND
phone: x-41-44-632-4673		fax: 632-1228
http://stat.ethz.ch/~buser/
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Serguei Kaniovski writes:
 > I would like to apply the following function to the rows of the matrix 
 > "mat", so that freq[1],...,freq[4] are the four elements of each row.
 > 
 > min_chi2<-function(freq){
 > 
 > obj<-function(x){
 > (freq[1]-(1-x[1])*(1-x[2])-x[3]*sqrt(x[1]*(1-x[1])*x[2]*(1-x[2])))^2/freq[1]+
 > (freq[2]-(1-x[1])*x[2]+x[3]*sqrt(x[1]*(1-x[1])*x[2]*(1-x[2])))^2/freq[2]+
 > (freq[3]-x[1]*(1-x[2])+x[3]*sqrt(x[1]*(1-x[1])*x[2]*(1-x[2])))^2/freq[3]+
 > (freq[4]-x[1]*x[2]-x[3]*sqrt(x[1]*(1-x[1])*x[2]*(1-x[2])))^2/freq[4]
 > }
 > 
 > optim(c(0.1,0.1,0.1),obj,NULL,method="BFGS")$par
 > }
 > 
 > mat<-matrix(c(0.4,0.1,0.1,0.4), byrow=TRUE, nrow=10, ncol=4)
 > 
 > Questions:
 > 1. How to do this using the "apply" function?
 > 2. Can "opmit" be used directly, i.e. without needing to define the 
 > function "min_chi2"?
 > 3. How to pass the vector of initial conditions (c(0.1,0.1,0.1)) as an 
 > argument to "apply"?
 > 
 > The output should be a 10x3 matrix containing 0.5 0.5 0.6 in each row.
 > 
 > Thanks a lot,
 > Serguei
 > -- 
 > ___________________________________________________________________
 > 
 > Austrian Institute of Economic Research (WIFO)
 > 
 > Name: Serguei Kaniovski			P.O.Box 91
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 > Mail: Serguei.Kaniovski at wifo.ac.at
 > 
 > http://www.wifo.ac.at/Serguei.Kaniovski
 > 
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