[R] numerical integration of a ftn of 2 variables

[Paul Smith]

On Tue, Feb 19, 2008 at 11:07 PM, Chris Rhoads
<c-rhoads at northwestern.edu> wrote:
>  To start, let me confess to not being an experienced programmer, although I have used R fairly
>  extensively in my work as a
>  graduate student in statistics.
>
>  I wish to find the root of a function of two variables that is defined by an integral which must be
>  evaluated numerically.
>
>  So the problem I want to solve is of the form:  Find k such that f(k)=0, where f(y) = int_a^b
>  g(x,y) dx.  Again, the integral
>  involved must be done numerically.
>
>  I'm told by a friend who knows programming, but not R, that what I need to do is create something
>  like a "local environment"
>  within which I could create a placeholder for x.  So I want to make something like the following work.
>
>  f(var) <- function(var) {
>
>  cons <- var
>
>  g <- function(x,cons) {h(x,cons)}
>
>  ret <- function(cons) integrate(g(x,cons),a,b)$value
>  ret
>  }
>
>  I could then use (e.g.) a Newton Raphson algorithm to find the root of the function"f".

Can you Chris provide us an example with concrete functions? To us, it
would be easier to think about a concrete example.

Paul