# [R] getting variable length numerical gradient

Dimitris Rizopoulos dimitris.rizopoulos at med.kuleuven.be
Mon Sep 26 16:16:51 CEST 2005

```Randall,

thanks for your comments; however, you have to take into account what
is the purpose of the function here! The goal is to approximate
*partial* derivatives numerically, using in fact the definition of the
partial derivatives. If you recall this definition I hope that you can
see why I change the ith element of the x vector and not the whole
one. You could also test your approach with the original one in the
logistic regression example and see the difference.

I hope it is more clear now.

Best,
Dimitris

----
Dimitris Rizopoulos
Ph.D. Student
Biostatistical Centre
School of Public Health
Catholic University of Leuven

Tel: +32/(0)16/336899
Fax: +32/(0)16/337015
Web: http://www.med.kuleuven.be/biostat/
http://www.student.kuleuven.be/~m0390867/dimitris.htm

----- Original Message -----
From: "Randall R Schulz" <rschulz at sonic.net>
To: "R Help" <R-Help at stat.math.ethz.ch>
Sent: Monday, September 26, 2005 3:53 PM
Subject: Re: [R] getting variable length numerical gradient

Dimitris,

I'm new to R programming, and I'm trying to learn the proper way to do
certain things. E.g., I had a piece of code with explicit iteration to
apply some computations to a vector. It was pretty slow. I found a way
to utilize R's built-in vectorization and it was sped up considerably.

(By the way, this message is best viewed using a mono-spaced font.)

On Sunday 25 September 2005 04:07, Dimitris Rizopoulos wrote:
> maybe you can find the following function useful (any comments are
> greatly appreciated):
>
> fd <- function(x, f, scalar = TRUE, ..., eps =
> sqrt(.Machine\$double.neg.eps)){
>     f <- match.fun(f)
>     out <- if(scalar){
>         ...
>     } else{
>         n <- length(x)
>         res <- array(0, c(n, n))
>         f0 <- f(x, ...)
>         ex <- pmax(abs(x), 1)
>         for(i in 1:n){

This (following) statement will create a copy of the entire "x" vector
on each iteration. It doesn't look like that's what you would want to
do:

>             x. <- x

The computation described by this statement could be vectorized
outside
the loop:

>             x.[i] <- x[i] + eps * ex[i]

>             res[, i] <- c(f(x., ...) - f0) / (x.[i] - x[i])
>         }
>         res
>     }
>     out
> }

Offhand, I cannot tell for sure if the last line of that loop is
vectorizable, but I have a hunch it is.

So at a minimum, it seems this fragment of your code:

for(i in 1:n){
x. <- x
x.[i] <- x[i] + eps * ex[i]
res[, i] <- c(f(x., ...) - f0) / (x.[i] - x[i])
}

Could be more efficiently and succinctly replaced with this:

x. <- x + eps * ex
for (in in 1:n)
res[, i] <- c(f(x., ...) - f0) / (x.[i] - x[i])

Could your someone else with R programming experience comment?

Thanks.

Randall Schulz

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