[R] Automatic differentiation in R

[Prof. John C Nash]

 >> Gabor G. wrote
 >>  "R does not currently have AD (except for the Ryacas package
 >>  which can do true AD for certain simple one line functions, i..e.
 >>  input the function and output a function representing its
 >>  derivative); however, for specific problems one can get close
 >>  using deriv and associated functions or the approach explained
 >>  below using rSymPy:
 >> ...

As the instigator of Finlay's participation in this work, I probably 
didn't express clearly enough the contribution Gabor has made to get as 
far as he has with Ryacas and rSympy, which may show another pathway for 
AD/Symbolic diff. development. At UseR all conversations seemed more 
rushed than I'd like.

Gabor showed Ravi Varadhan and I a way to get some derivatives via his 
tools that "worked". We need to play with this a bit more to see how 
general it could be -- Gabor is very fair in his post that some work is 
needed for each instance. On the other hand, if analytic gradients were 
straightforward, we wouldn't be exchanging posts about them.

The clear issue in my mind is that users who need gradients/Jacobians 
for R want to be able to send a function X to some process that will 
return another function gradX or JacX that computes analytic 
derivatives. This has to be "easy", which implies a very simple command 
or GUI interface. I am pretty certain the users have almost no interest 
in the mechanism, as long as it works. Currently, most use numerical 
derivatives, not realizing the very large time penalty and quite large 
loss in accuracy that can compromise some optimization and differential 
equation codes. I'll try to prepare a few examples to illustrate this 
and post them somewhere in the next few weeks. Time, as always, ...

However, the topic does appear to be on the table.

JN