Overload dot

Hi all,

I believe block-wise linear algebra operations such as dot default to the implementation for AbstractArray instead of doing the operation block by block and then adding the results. This is highly inefficient since searching for the block index every single time. I would understand this behavior for mixed arrays, but I think there should be specialized implementations for operations between block-arrays. Also, this limits BlockArray to contain sub-arrays that are indexable. This is quite a heavy restriction, since there might be objects implementing the whole LinearAlgebra API without being indexable (for instance, parallel arrays).

In summary, I would like someone to explain the though process behind why these choices have been made instead of leveraging the block-wise structure of BlockArray.

Thanks,
Jordi

No files or tests are named. Start by tracing how dot dispatches for BlockArray and AbstractArray, then review the relevant block-wise operation code. Done means clarifying the dispatch rationale and defining the specialized behavior needed for block arrays, including support for non-indexable subarrays.