[eigen] Implementing a custom-matrix product

[Manoj Rajagopalan <rmanoj@xxxxxxxxx>]

Hi,

   I have a basic implementation of a SymmetricMatrix class that stores only 
the lower triangle in Rectangular Full Packed Format (RFPF) from a LAWN 
reference that Gael mentioned a little while ago.

   I would like to implement a SymmetricMatrix * Matrix product. How do I go 
about it? Here are my preliminary issues:

- classes like DiagonalWrapper and TriangularView return a custom class like 
DiagonalProduct and TriangularProduct when the pre-multiplication operator * 
(member function) is called. But then, someone mentioned ReturnByValue in a 
different context but that also seems to serve a similar purpose. I am a 
little confused. How do these concepts relate? Are they mutually exclusive?

- I am not able to identify which member of the dense matrix class hierarchy 
actually performs the evaluation of the product into a matrix with 
dense-storage. Even DenseStorageBase seems to be passing this off to its base 
class operator=() or some _set() method.

- There are coeff() methods that return Scalar, and there are packet() methods 
that return PacketScalar. I am guessing the latter is used when the 
expression is vectorizable. How and where is this decided?

- The product that I am interested in shouldn't have to worry about 
PacketScalar etc. because it reduces to a sequence of high-level Eigen TRMM 
and GEMM calls. This is due to the layout - the triangular part is stored as 
two sub-triangles (one is adjoint-ed) and one rectangular block, all packed 
so that they form a rectangular array of total size N*(N+1)/2. When the 
product evaluation is triggered, the most efficient operation would be with 
these triangular/rectangular blocks as opposed to coeff() or packet() access 
which would be expensive. How can this be ensured?

Thanks,
Manoj