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youngdae avatar youngdae commented on June 8, 2024 1

For batched operations on small matrices, I think it might be more efficient to perform dense operations and get rid of all the sorting and selection routines. This means that we no longer compute an incomplete Cholesky factorization. Instead, we will compute a fully scaled and shifted Cholesky factorization (shifted: we need to deal with indefinite cases as well), since we do not need to save memory in this case. This would make the implementation much simpler and more efficient. This may also resolve the getindex() and setindex() issue as well.

For larger matrices, we may still need to do sparse linear algebra. But, I think it might be more helpful if we separate this case from the batched case, i.e., having a different implementation for that case.

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frapac avatar frapac commented on June 8, 2024

I agree. At the moment, all sparse algebra related operations depend on TronSparseMatrixCSC (https://github.com/exanauts/ExaTron/blob/main/src/dssyax.jl#L3). I think it would be nice to add a new type TronDenseMatrix and implement all dense operations in its interface. Then, we would only have to rely on multiple dispatch in the remaining of the code.

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