Re: [eigen] AutoDiffScalar

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2009/10/15 Björn Piltz <bjornpiltz@xxxxxxxxxxxxxx>
Hi all,
I've been following the work on the cminpack branch with interest and
right now I'm looking at AutoDiffScalar.
I've written some tests and seen that it has the potential to be very
efficient, mainly thanks to the lazy evaluation I guess, but I have
some questions.
The fixed size implementation already seems to be mostly done, but
there are some problems with the dynamic version.
Look for example at the implementation of addition:

template<typename OtherDerType>
inline const AutoDiffScalar<CwiseBinaryOp<ei_scalar_sum_op<Scalar>,DerType,OtherDerType>
operator+(const AutoDiffScalar<OtherDerType>& other) const
   return AutoDiffScalar<CwiseBinaryOp<ei_scalar_sum_op<Scalar>,DerType,OtherDerType>
   m_value + other.value(),
   m_derivatives + other.derivatives());

This implementation crashes when "other" was initialized through c'tor
AutoDiffScalar(const Scalar& value) and other.derivatives() is of size

Oh I see, but do you have a use case for that ? I mean this happens only when you convert a constant to an active scalar type, and I think this could be avoided in most cases. For instance,

Scalar sum = 0;
for(i=0 ...) sum += v[i];

can be changed to:

Scalar sum = v[0];
for(i=1....) sum += v[i];

So following this idea, I guess we should also add overloads for "AutoDiffScalar + constant" and similars....

Anyway, can you retry with the devel branch, I've just committed a fix which resize and set to zero the derivatives of one argument if the other is a null Matrix. Yes I know this is not optimal but I don't know how to do it more efficiently.
The fix is not obvious to me since we need to return a binary
_expression_ and just m_derivatives won't do.
I could check the size of other.m_derivatives and fill it up with
zeros, when appropriate, but I would have to do that check at compile
time since "OtherDerType" could also be a binary _expression_ or
something similar. I haven't found a way at compilation to check if an
type is a "normal matrix" or some kind of an _expression_.

I hope somebody has an idea of how to resolve this, because a fast
forward differentiation implementation with _expression_ templates
supporting dynamic size vectors would be a really cool feature. I've
compared this implementation to Sacado, the only other good template
implementation I could find out there, and this one compares very

I did not know about Sacado, but I'm glad we are already faster :) I've seen it is part of the trilineos framework. This framework really provide a lot of features !

btw, about this module, there is still a work in progress AutoDiffVector class. Its goal is to efficiently representing a vector of active variables. Basically it will behave like a Matrix<AutoDiffScalar,Size,1> but internally it will directly store the Jacobian matrix allowing much higher performances, and ease of use (directly initialize the Jacobian to the identity, directly get the Jacobian as a matrix, etc...).



Any feedback will be appreciated

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