[eigen] const-correctness in Eigen 3.0

[Jim Bosch <talljimbo@xxxxxxxxx>]

I've been following the occasional discussions regarding the 
const-incorrectness of Map (and Block, Transpose, etc.) with interest; I 
once put a lot of effort into getting this right in my own 
template-based multidimensional array library, and I'd love to see this 
get fixed in Eigen.

I'd be happy to put some effort into fixing this in Eigen 3.0, but as a 
relatively new face (well, I've been lurking a long time!) tackling a 
fairly widely-dispersed issue, I wanted to get some discussion going 
instead of just going out and making a giant patch.

First off, here's what I think the solution should look like:

 - Matrix and Array (and other PlainObjectBase subclasses) should 
pretty much behave as they do currently.

 - Map, Block, Transpose, and anything else that does not own its data 
but supports direct access should come in both const and non-const 
versions (probably just partial specializations).  The non-const version 
should be implicitly convertible to the const version.

 - Calling block() or transpose() on a const reference to Matrix should 
return a const Block or const Transpose(), etc.

What I think this implies:

 - MatrixBase, ArrayBase, DenseBase, DenseCoeffsBase, and EigenBase 
should also have partial specializations for const and non-const; the 
non-const version should probably inherit from the const version in some 
cases for code reuse, just adding non-const accessors and augmented 
assignment operators.

 - PlainObjectBase should inherit from a non-const base class.

 - Expressions that don't have direct access should inherit from the 
const MatrixBase or ArrayBase.

 - There should probably be a flag for constness on every Eigen class.


I anticipate these changes would be fairly straightforward, but they are 
very extensive.  I don't seen any easier way to get const-correctness in 
place in a consistent way, however, and I think doing it now will pay 
off in the long run.

Any thoughts?

Jim Bosch