[Rd] Extending deriv3()

[Prof Brian Ripley]

On Mon, 15 Oct 2007, Thomas Yee wrote:

> Hello,
>
> I was wondering if the functions deriv3(), deriv() etc. could be extended
> to handle psigamma() and its special cases (digamma(), trigamma()
> etc.). From the error message it seems that 'psigamma' needs to be
> added to the derivatives table.
> This might be easy since psigamma() has a deriv argument.

If you look at ?deriv you will see that it only knows about functions *of 
one argument* and operators.  So it would be easy to add digamma(x) and 
psigamma(x) (and I will do so shortly), it would not be so easy to add 
psigamma(x, deriv).

> Additionally, this error message is also obtained when requesting for
> the Hessian of the gamma and lgamma functions:
>
> d3 = deriv(~  gamma(y), namev="y", hessian= TRUE)
> d3 = deriv(~ lgamma(y), namev="y", hessian= TRUE)
>
> Another class of special functions worth adding are the Bessel functions.

Well, you can always submit a patch ....

Note that deriv() in R differs from that in S in being done in C and hence 
not being user-extensible.  A long time ago that had an advantage: S's 
deriv could be very slow and take a lot of memory by the standards of the 
early 1990's.  Rather than work on adding yet more special cases it would 
seem better to work on making it user-extensible.

-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595