Single node sparse matrix structures

[tbetcke]

Implement CSR sparse matrix structures on a single node.

• Very useful in their own right.
• Allow us to test data structures for a later full MPI implementation.

The following features should be available:

• Defining CSR matrices
• Import/Export of CSR matrices (via Serde?)
• Simple iterative solvers

[jedbrown]

Do you have a vision of the traits that would allow writing a function that is agnostic over whether its input matrices are sparse or dense? I see your traits like MatMul are specialized on dense/strided storage.

[tbetcke]

I should rather call the MatMul trait a DenseMatMul trait. Still experimenting with traits for sparse matrices. But it will likely come down to something like the scipy operator interface, or more involved, the Trilinos Thyra interfaces.

[jedbrown]

SciPy LinearOperator doesn't support sparse-sparse products, as in $P^T A P$ needed for multigrid. I think the same restriction applies to Thyra LinearOpBasi.

PETSc has a dynamic multiple dispatch system for heterogeneous matrix-matrix operations, but it's based on strings and function pointers. In Rust, that would naturally use a HashMap and Any::type_id to locate the fully resolved implementation. I struggle to see how to avoid without creating a closed world. There is an open sum technique that might be useful, though it's hard for me to see how to use it effectively and I'm not sure it's better than the HashMap.