# [R] using integrate with optimize nested in the integration

Sundar Dorai-Raj sundar.dorai-raj at pdf.com
Thu Jul 28 22:27:25 CEST 2005

```
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

```