[Rd] problem with function 'optimise' (PR#9438)

[karsten_krug at gmx.net]

Full_Name: Karsten Krug
Version: 2.4.0
OS: Open Suse 10.0, Windows XP
Submission from: (NULL) (88.134.13.50)



I found a problem in the 'optimise' function for one dimensional optimisation.


Example 1:
Try to find a maximum of the function below with the use of 'optimise' in the
interval [0,0.5]. The function follows a parabola and has two local maxima
located at the margins of the interval [0,0.5]. Please try the following code
which performs this optimisation, produces a plot of the function within the
given interval and adds the computed maximum returned by 'optimise()' 

ex1 <- function(x) log(4 * x^2 - 2 * x + 0.5)
opt1 <- optimise(ex1, lower=0, upper=0.5, maximum=T)
x <- seq(0,0.5,0.001)
plot(x, ex1(x), type="l")
abline(v=opt1$maximum, col="red")

The returned value of the maximum is 0.309017 which is definitely wrong.


Example 2:
The next function has also two equivalent maxima this time not located at the
margins of the interval [0, 9/41]. Thus, the maxima are real analytic extrema.
The function 'optimise()' again returns a wrong value.    

ex2 <- function(x) log((18/41) * x - 2 * x^2) + 16 *  log(4 * x^2 - (36/41) * x
+ (9/41)) + 24 * log((23/82) +  (18/41) * x - 2 * x^2)
opt2 <- optimise(ex2, lower=0, upper=(9/41), maximum=T)
x <- seq(0,9/41,0.001)
plot(x,ex2(x),type="l")
abline(v=opt2$maximum, col="red")


The two functions are not only of theoretical interest but have to be optimised
as likelihood functions when dealing with SNP data. 

I observed this problem on Windows XP and Open Suse 10.0. Other platforms have
to be tested.


Some informations:

Open Suse 10.0

platform       i686-pc-linux-gnu
arch           i686
os             linux-gnu
system         i686, linux-gnu
status
major          2
minor          4.0
year           2006
month          10
day            03
svn rev        39566
language       R
version.string R version 2.4.0 (2006-10-03)

Windows XP:

platform       i386-pc-mingw32             
arch           i386                        
os             mingw32                     
system         i386, mingw32               
status                                     
major          2                           
minor          4.0                         
year           2006                        
month          10                          
day            03                          
svn rev        39566                       
language       R                           
version.string R version 2.4.0 (2006-10-03)



With best regards,

Karsten Krug
Student at University of Leipzig