[Rd] symbollic differentiation in R

[Gabor Grothendieck]

On 5/13/07, Gabor Grothendieck <ggrothendieck at gmail.com> wrote:
> On 5/13/07, Andrew Clausen <clausen at econ.upenn.edu> wrote:
> > Hi all,
> >
> > I wrote a symbollic differentiation function in R, which can be downloaded
> > here:
> >
> >        http://www.econ.upenn.edu/~clausen/computing/Deriv.R
> >        http://www.econ.upenn.edu/~clausen/computing/Simplify.R
> >
> > It is just a prototype.  Of course, R already contains two differentiation
> > functions: D and deriv.  However, these functions have several limitations.
> > They can probably be fixed, but since they are written in C, this would
> > require a lot of work.  Limitations include:
> >  * The derivatives table can't be modified at runtime, and is only available
> > in C.
> >  * The output of "deriv" can not be differentiated again.
>
> Try this:
>
> > D(D(quote(x^3), "x"), "x")
> 3 * (2 * x)
>
> >  * Neither function can substitute function calls.  eg:
> >       f <- function(x, y) x + y; deriv(f(x, x^2), "x")
>
> Try Ryacas package:

I had omitted one line.  f has to be registered with yacas:

>
> > library(Ryacas)
> > x <- Sym("x")
> > f <- function(x)x^2

yacas(f)

> > deriv(f(x^3))
> expression(6 * x^5)
>
> >  * They can't differentiate vector-valued functions (although my code also
> > can't do this yet)
>
> > library(Ryacas)
> > x <- Sym("x")
> > deriv(List(x, x^2))
> expression(list(1, 2 * x))
>
>
> >
> > I think these limitations are fairly important.  As it stands, it's rather
> > difficult to automatically differentiate a likelihood function.  Ideally, I
> > would like to be able to write
> >
> >        ll <- function(mean, sd)
> >                -sum(log(dnorm(x, mean, sd)))
> >
> >        ll.deriv <- Deriv.function(ll)
> >
> > I can't get this to work with my code since:
> >  * since sum can't add a list of vectors (although I could easily write a sum
> > replacement.)
> >  * "x" is assumed to be a scalar in this contect.  I'm not sure if there's a
> > good way to generalize.
> >
> > The above code would work right now if there were one parameter (so
> > sum doesn't screw it up) and one scalar data point "x".
> >
> > Is there an existing way of doing this that is close to being this convenient?
> > Is it really much easier to solve the limitations I listed with a fresh
> > R implementation?
> >
> > Cheers,
> > Andrew
> >
> > ______________________________________________
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> > https://stat.ethz.ch/mailman/listinfo/r-devel
> >
>