Re: [eigen] AutoDiffScalar

2009/10/20 Björn Piltz <bjornpiltz@xxxxxxxxxxxxxx>

I've done some more testing and got the class to work for
fixed/dynamic/sparse cases 1st and 2nd derivatives.
There are some minor bugs in the code and I had to rewrite
CompressedStorage to handle non-POD data types(evil memcpy's).
You are obviously still working on the code, so I was wondering how I
should submit any fixes.
Clone the repository and submit a patch queue/pull request?

excellent!

I also have a couple of local changes improving the supports for second order derivatives so I think currently the best is that you create a fork on bitbucket and push your changes into it and then I'll do the merge(s).

There is also the question of performance. For second and higher order
derivatives There is a need to differentiate the type Scalar from the
underlying primitive type. let's call it Real for now.

E.g.

typedef AutoDiffScalar<Matrix<double, Dynamic, 1> > D1;
typedef AutoDiffScalar<Matrix<Fad1 , Dynamic, 1> > D2;

D1::Scalar == double
D1::Real == double

D2::Scalar == D1
D2::Real == double

Then the overloads should be
AutoDiffScalar OP AutoDiffScalar::Real
instead of
AutoDiffScalar OP AutoDiffScalar::Scalar

That should lead to resize()/zero() being called significantly less often.

yes I agree. To make that working we have to specialize struct ei_scalar_product_traits<A,B> for Real/AutoDiffScalar pairs such that Eigen knows the return type of this product.

Also I found that our scalar multiple functors stored the scalar factor by value. However, when the scalar type is an AutoDiffScalar, this led to many useless memory allocations and matrix copies.