R help - Aug 2007 - Clarification: Expedite scalar f(x) evaluation over vectors

Please note clarifications in <<>> below.  My apologies for any
confusion.
Thanks again,
Scott

---------- Forwarded message ----------
From: Scott Stark <stark.sc@gmail.com>
Date: Aug 23, 2007 1:03 PM
Subject: Expedite scalar f(x) evaluation over vectors
To: r-help@lists.r-project.org

Dear R community,

I am trying to code a fairly complex equation for optim().  My current
approach is too slow for optim().

I have a function that takes a double integral (hopefully correctly) across
two terms, e.g.,

<<note replacement of example function by hypothetical f(x,y)>>

 doubleint <- function(c1,c2) {integrate(function(y) {
   sapply(y, function(y) {
   integrate(function(x) {f(x,y)}, boundsx[1], boundsx[2])$value
   })
   }, boundsy[1],boundsy[2])
   }

<<I do not have a closed form for the real function>>

I would like to rapidly evaluate this function over vectors c1 and c2 of
equal length where the double integral is calculated for each (matching)
element c1_i & c2_i.  At present I get length mismatch errors.  Furthermore,
mapply() takes too long.  Can I expedite this evaluation or do I need to
reformulate my approach?

Thanks in advance for your help,
Scott C. Stark
University of Arizona

	[[alternative HTML version deleted]]

On Thu, Aug 23, 2007 at 03:44:36PM -0700, Scott Stark
wrote:
> Please note clarifications in <<>> below.  My apologies for any
confusion.
> Thanks again,
> Scott
> 
> ---------- Forwarded message ----------
> From: Scott Stark <stark.sc at gmail.com>
> Date: Aug 23, 2007 1:03 PM
> Subject: Expedite scalar f(x) evaluation over vectors
> To: r-help at lists.r-project.org
> 
> Dear R community,
> 
> I am trying to code a fairly complex equation for optim().  My current
> approach is too slow for optim().
> 
> I have a function that takes a double integral (hopefully correctly) across
> two terms, e.g.,
> 
> <<note replacement of example function by hypothetical f(x,y)>>
> 
>  doubleint <- function(c1,c2) {integrate(function(y) {
>    sapply(y, function(y) {
>    integrate(function(x) {f(x,y)}, boundsx[1], boundsx[2])$value
>    })
>    }, boundsy[1],boundsy[2])
>    }
> 
> <<I do not have a closed form for the real function>>
I assume you're trying to find the optimal c1 and c2. You could try
varying the tolerance to integrate, initially allowing a rough
approximation of your integral for the first steps until you get near
an optimum, and then re-running the optimize on a much higher
tolerance.

For example, set your maximum subdivisions to 10, run the optimize,
then set to 20 and run the optimize from the endpoint of the last
run. When the optimal point stops moving, call it good??

The next approach I'd try is to be more fancy about your mathematics,
by finding an approximate closed form for your function that was
analytically integrable, perhaps in a computer algebra system like
maxima.

-- 
Daniel Lakeland
dlakelan at street-artists.org
http://www.street-artists.org/~dlakelan