Re: [eigen] Sparse Matrix Support

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Ok, since that's a standard approach it's probably good to support
though I doubt it's the most efficient way of doing this. I plane to
simply provide a template Tripplet<Scalar,Index> class and then let
the user takes its favorite container like std::vector<Tripplet>.

I would argue for a lower level interface with three arrays/iterators instead of one, as this would allow for easy interface with cholmod_triplet and matlab.

 > And last but not the least, have you given any thought to supporting
> block sparse matrices?

This is very tricky and I'm still not sure how to implement it the
most efficient and simple way. Indeed, the idea is of course to reuse
the SparseMatrix class and let it stores small fixed size dense Matrix
for the scalar type. For instance, let's assume a 300x300 block matrix
represented as a 100x100 standard sparse matrix of Matrix3d. The pb is
that depending on the context, sometimes we want to see it as a
300x300 matrix of double, and sometimes as a 100x100 matrix of
Matrix3d blocks. So this probably requires a lot of work to get it

Block sparse matrices have two uses. One as Trevor pointed out and I had forgotten, ease of representation for problems coming from PDEs. So we should see if we can allow for building sparse matrices out of a list of triplets just like we do for  scalars.

The other is high performance operations. One way would indeed be to store the matrix as a collection of dense blocks and then represent matrix vector products as operations on these blocks using dense BLAS operations.

But this does not necessarily require uniform block sizes. For example in the problem of interest to me, I am interested in storing block sparse jacobians where different blocks are of different size and the matrix itself is extremely rectangular.  

In those cases, we could just store i,j, row_size, col_size, double* or a block CSR or CSC version of it and that leads to a 2-3 times speedup over storing it has a generic sparse matrix.

Designing a good API for this will require some effort, but I think its worth it.



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