[R] Taking Integral and Optimization using Integrate, Optim and maxNR

[Berend Hasselman]

Dear All, Hello!

I have some questoins in R programming as follows:

Question 1- How to take the integral of this function with respect to y,
such that x would appear in the output after taking integral.

f(x,y)=(0.1766*exp(-exp(y+lnx))*-exp(y+lnx))/(1-exp(-exp(y+lnx))) y in
(-6.907,-1.246)

It is doable in maple but not in R. At least I could not find the way.

p.s: result from maple is:

g(x)=dilog*exp(0.001000755564*x)+0.5*ln(exp(0.001000755564*x))^2-dilog*(exp(0.2876531111*x))-0.5*ln(exp(0.2876531111*x))^2

Where dilog=integral(log(t)/(1-t)) for t in (1,x)

Question 2- Then I want to optimize (maximize) the answer of the above
integral for x. Assum x in (0,100)

The answer should be something between 26 and 27.

What I did is: got answer of integral(f(x,y)) from maple which is g(x), and
then applied it in R. The code is as follows:

##In the case n=1

library(stats)
require(graphics)
integrand=function(t){(log(t))/(1-t)}
#dilog=integrate(integrand, lower=1, upper=x)
fr <- function(x){(integrate(integrand, lower=1,
upper=x)$value)*(exp(0.001000755564*x))+0.5*log(exp(0.001000755564*x))^2-(integrate(integrand,
lower=1,
upper=x)$value)*(exp(0.2876531111*x))-0.5*log(exp(0.2876531111*x))^2}

optim(20, fr, NULL, method = "BFGS")

Question 2-1-Default by optim is to minimize a function, how I can use it to
maximization?

Question 2-2- The above code faced with errors, and did not work. What I
guess is there is something wrong with taking integral. The output of
integrate function in R is some sort of thing. I had to somehow tell it,
just take the value and forget about the others. But I guess it is still
something wrong with it. I also tried maxNR, but is didn't work either.

/quote>

The integral of dilog (should) exist (according to the books).

dilog <- function(t) log(t)/(1-t)

integrate(dilog,1,2)
-0.822467 with absolute error < 9.1e-15

Now if you do:

z <- integrate(dilog,1.000,2)

str(z)

you will see that z is a list:

List of 5
 $ value       : num -0.822
 $ abs.error   : num 9.13e-15
 $ subdivisions: int 1
 $ message     : chr "OK"
 $ call        : language integrate(f = dilog, lower = 1, upper = 2)
 - attr(*, "class")= chr "integrate"

If you need the result of integrate then it is standard  R to use z$value to
get the value of the integral.

Berend



--
View this message in context: http://r.789695.n4.nabble.com/Taking-Integral-and-Optimization-using-Integrate-Optim-and-maxNR-tp3577923p3580456.html
Sent from the R help mailing list archive at Nabble.com.