🚀 go-pugleaf

In article <l71d15INNakq@almaak.usc.edu> ajayshah@almaak.usc.edu (Ajay Shah)
   writes:
>A few days ago I asked for information on software to do
>"automatic differentiation".  For the uninitiated, this is a way to
>get exact derivatives of any order without needing to analytically
>evaluate the formulas for the derivatives.
>..........
>It looks like the best way to do automatic differentiation is to use
>C++.  What follows gives you some pointers to software available.
>It looks like the people who write matrix libraries in C++ have not
>talked a lot with the people who do automatic differentiation in C++
>:-)  Please do so!

Could you explain the connection with matrix packages a little more.

To do symbolic manipulation in C++ you will probably want to use the kind of
representation I use in my matrix package, Newmat. Of course the basic
concept in that representation is taken from the reading I have done about
symbolic manipulation.

The problem is that actually evaluating the expressions you get will be quite
slow because the computer will have to interpret the representation of the
expression as well as do the arithmetic. This is not a problem with your
main function (if you are doing maximisation or solving) because you can
use templates to get both the symbolic representation and an efficiently
compiled expression. But with the derivatives you are stuck with the symbolic
expressions. Of course if your variables are matrices rather than reals,
then the efficiency is not a problem because the matrix computation times
will overwhelm the interpret times.

So there are at least two connections with matrices - is this what you had in
mind.

Now for a short comnmercial break:

I agree that C++ is almost an ideal language for doing this kind of thing;
having the structure to do both symbolic manipulation and numerical
manipulations.

But much work with equations will involve powers (the fortran ** operator)
and at the moment C++ does not have the power operator.

I am still interested in putting the case together for a power operator if
no-one else will do it and would be interested if people interested in
symbolic manipulation have any comments.


Thanks for your list of responses and references.

Robert