R help - Jul 2005 - using integrate with optimize nested in the integration

Hi guys
im having a problem getting R to numerically integrate for some function, 
say f(bhat)*optimize(G(bhat)), over bhat. Where id like to integrate this over
some finite range, so that here as we integrate over bhat optimize would return
a different optimum.
 
For instance consider this simple example for which I cannot get R to return the
desired result:
 
f <- function(bhat) exp(bhat)
g <- function(bhat) optimize(f,c(0,15),maximum=TRUE)$maximum*bhat
integrate(g,lower=0,upper=5)
which returns:
187.499393759 with absolute error < 2.1e-12

However this is an approximation of : 15*(5^2/2 - 0)=187.5, not what I intended
on getting. Its not identifying that f is a function of bhat ... any advice or
ways I can get integrate to not treat this as a constant?

Any help is appreciated.
 
Gregoy Gentlemen

__________________________________________________



	[[alternative HTML version deleted]]

In your example, f is a function, but
optimize(f,c(0,15),maximum=TRUE)$maximum is just a number (the point at
which f reaches its maximum value). I'm not sure what you want, but if you
had say

f <- function(x,y) x^3 + yx + 1

and defined

g <- function(y) optimize(f,c(0,5),maximum=TRUE,y)$maximum

then g(t) is the x-value at which the function f(x,t) (over x in (0,5))
reaches its maximum for this fixed t. That could then be integrated. 

Reid Huntsinger

-----Original Message-----
From: r-help-bounces at stat.math.ethz.ch
[mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of Gregory Gentlemen
Sent: Thursday, July 28, 2005 3:58 PM
To: r-help at stat.math.ethz.ch
Subject: [R] using integrate with optimize nested in the integration


Hi guys
im having a problem getting R to numerically integrate for some function, 
say f(bhat)*optimize(G(bhat)), over bhat. Where id like to integrate this
over some finite range, so that here as we integrate over bhat optimize
would return a different optimum.
 
For instance consider this simple example for which I cannot get R to return
the desired result:
 
f <- function(bhat) exp(bhat)
g <- function(bhat) optimize(f,c(0,15),maximum=TRUE)$maximum*bhat
integrate(g,lower=0,upper=5)
which returns:
187.499393759 with absolute error < 2.1e-12

However this is an approximation of : 15*(5^2/2 - 0)=187.5, not what I
intended on getting. Its not identifying that f is a function of bhat ...
any advice or ways I can get integrate to not treat this as a constant?

Any help is appreciated.
 
Gregoy Gentlemen

__________________________________________________



	[[alternative HTML version deleted]]

______________________________________________
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https://stat.ethz.ch/mailman/listinfo/r-help
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http://www.R-project.org/posting-guide.html

Gregory Gentlemen wrote:
> Hi guys
> im having a problem getting R to numerically integrate for some function, 
> say f(bhat)*optimize(G(bhat)), over bhat. Where id like to integrate this
over some finite range, so that here as we integrate over bhat optimize would
return a different optimum.
>  
> For instance consider this simple example for which I cannot get R to
return the desired result:
>  
> f <- function(bhat) exp(bhat)
> g <- function(bhat) optimize(f,c(0,15),maximum=TRUE)$maximum*bhat
> integrate(g,lower=0,upper=5)
> which returns:
> 187.499393759 with absolute error < 2.1e-12
> 
> However this is an approximation of : 15*(5^2/2 - 0)=187.5, not what I
intended on getting. Its not identifying that f is a function of bhat ... any
advice or ways I can get integrate to not treat this as a constant?
> 
> Any help is appreciated.
>  
> Gregoy Gentlemen
> 
Hi, Gregory,

Your example is not very useful here since the optimize function is 
constant.

I think you want something more like:

f <- function(bhat, x) {
   exp(bhat * x)
}
g <- function(bhat) {
   o <- vector("numeric", length(bhat))
   for(i in seq(along = bhat))
     o[i] <- optimize(f, c(0,15), maximum = TRUE, x = bhat[i])$maximum
   bhat * o
}
integrate(g, lower = 0, upper = 5)

Because of the way "integrate" works, "g(bhat)" will always
return a vector.

HTH,

--sundar

Integrate needs a vectorized function. For your example,
 
> integrate(function(x) sapply(x,g),lower=0,upper=5)
187.4994 with absolute error < 2.1e-12

Reid Huntsinger
-----Original Message-----
From: Gregory Gentlemen [mailto:gregory_gentlemen@yahoo.ca] 
Sent: Thursday, July 28, 2005 4:37 PM
To: Huntsinger, Reid; r-help@stat.math.ethz.ch
Subject: RE: [R] using integrate with optimize nested in the integration


Thanks for the prompt reply.
Your right, that was a weak example.
Consider this one though:
 
f <- function(n,x) (x-2.5)^2*n
g <- function(y) optimize(f,c(0,15), maximum=TRUE,x=y)$maximum*y
 
then if you try:
integrate(g,lower=0,upper=5)
it produces:
Error in optimize(f, c(0, 15), maximum = TRUE, x = y) : 
        invalid function value in 'optimize'

Any ideas? 
My problem is a similar more complex function in which optimizaiton depends
on the value of the integrator.

"Huntsinger, Reid" <reid_huntsinger@merck.com> wrote:

In your example, f is a function, but
optimize(f,c(0,15),maximum=TRUE)$maximum is just a number (the point at
which f reaches its maximum value). I'm not sure what you want, but if you
had say

f <- function(x,y) x^3 + yx + 1

and defined

g <- function(y) optimize(f,c(0,5),maximum=TRUE,y)$maximum

then g(t) is the x-value at which the function f(x,t) (over x in (0,5))
reaches its maximum for this fixed t. That could then be integrated. 

Reid Huntsinger

-----Original Message-----
From: r-help-bounces@stat.math.ethz.ch
[mailto:r-help-bounces@stat.math.ethz.ch] On Behalf Of Gregory Gentlemen
Sent: Thursday, July 28, 2005 3:58 PM
To: r-help@stat.math.ethz.ch
Subject: [R] using integrate with optimize nested in the integration


Hi guys
im having a problem getting R to numerically integrate for some function, 
say f(bhat)*optimize(G(bhat)), over bhat. Where id like to integrate this
over some finite range, so that here as we integrate over bhat optimize
would return a different optimum.

For instance consider this simple example for which I cannot get R to return
the desired result:

f <- function(bhat) exp(bhat)
g <- function(bhat) optimize(f,c(0,15),maximum=TRUE)$maximum*bhat
integrate(g,lower=0,upper=5)
which returns:
187.499393759 with absolute error < 2.1e-12

However this is an approximation of : 15*(5^2/2 - 0)=187.5, not what I
intended on getting. Its not identifying that f is a function of bhat ...
any advice or ways I can get integrate to not treat this as a constant?

Any help is appreciated.

Gregoy Gentlemen

__________________________________________________



[[alternative HTML version deleted]]

______________________________________________
R-help@stat.math.ethz.ch mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide!
http://www.R-project.org/posting-guide.html





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