[Rd] symbollic differentiation in R

[Gabor Grothendieck]

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:

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