[R] optim with gradient
Laurent Gautier
laurent at genome.cbs.dtu.dk
Wed Mar 20 17:42:31 CET 2002
On Wed, Mar 20, 2002 at 02:31:03PM +0100, Göran Broström wrote:
> I want to maximise a function using 'optim' with a method that requires
> the gradient, so I supply two functions, 'fun' for the function value
> and 'd.fun' for its gradient. My question is: Since some calculations are
> common to the two functions, is it possible to save time by feeding
> 'd.fun' with some of the calculations made in 'fun'? That would require
> (at least) that it is guaranteed that each time 'd.fun' is evaluated, it
> is done immediately after a call to 'fun' at the same parameter value.
> The help page says:
>
> "It is guaranteed that `gr' will be called immediately after a
> call to `fn' at the same parameter values."
>
> which is not exactly the same. However, look at this trivial example:
>
> prov <- function(x.start = 0){
> fun <- function(x) {
> e.x <- exp(-x)
> x * e.x
> }
> d.fun <- function(x) {
> e.x <- exp(-x)
> e.x * (1 - x)
> }
> optim(x.start, fun, d.fun, method = "BFGS",
> control = list(fnscale = -1))
> }
>
> > prov(2)$counts
> function gradient
> 19 9
>
> This contradicts the help page info, since that implies that the gradient
> is called at least as many times as the function.
>
> Q1: What is the correct guarantee? Is it what I need?
>
> Q2: If so, How do I share calculations between the two functions? In my
> trivial example, exp(-x) is calculated in both.
>
> Thanks for any enlightenment! (Brian?)
>
> Göran
> --
> Göran Broström tel: +46 90 786 5223
> professor fax: +46 90 786 6614
> Department of Statistics http://www.stat.umu.se/egna/gb/
> Umeå University
> SE-90187 Umeå, Sweden e-mail: gb at stat.umu.se
>
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Here is a (proposal of) reply for Q2:
Storing and accessing the result of the 'shared calculation' in a given environment could be a workaround.
Hopin' it helps,
Laurent
--------------------------------------------------------------
Laurent Gautier CBS, Building 208, DTU
PhD. Student D-2800 Lyngby,Denmark
tel: +45 45 25 24 85 http://www.cbs.dtu.dk/laurent
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