R help - Jun 2011 - Taking Integral and Optimization using Integrate, Optim and maxNR

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.



Question 2-3- Thoes above are the easiest case of my problem. Assume the case
that I have summation of f(x1,y)+f(x2,y)+...+f(x12,y)



The article have done it by E04JAF-NAG Fortran Library Routine Document. But I
want to do it in R.

Thanx all.



Cheers,

Maryam

	[[alternative HTML version deleted]]

On 06.06.2011 20:14, MARYAM ZOLGHADR wrote:
> 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?

If you want to maximize f, either minimize -f or read ?optim and find 
that it tells us:
"By default this function performs minimization, but it will maximize if 
control$fnscale is negative. "

> 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.
If you integrate  log(t)/(1-t) from t=1 (as you specified in your 
code!), then at t=1 the value is undefined ...


Uwe Ligges


> Question 2-3- Thoes above are the easiest case of my problem. Assume the
case that I have summation of f(x1,y)+f(x2,y)+...+f(x12,y)
>
>
>
> The article have done it by E04JAF-NAG Fortran Library Routine Document.
But I want to do it in R.
>
> Thanx all.
>
>
>
> Cheers,
>
> Maryam
>
> 	[[alternative HTML version deleted]]
>
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.

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



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