Performance: Explore possibilities for memoization

[ranocha]

substitute needs to iterate over the partition forests and skeletons of trees. Currently, these are constructed on the fly each time substitute is called. Since this is likely the most expensive part, it might make sense to store values that are already computed.

Some links:

• https://github.com/JuliaCollections/LRUCache.jl

[ketch]

There is an older Python library for working with B-series, and the author used memoization in several places:

https://github.com/henriksu/pybs

[ranocha]

Did you compare its performance to your BSeries package?

[ketch]

No, not yet. I discovered it long after I had written my own package.

[ketch]

Another relevant package is Valentin Dallerit's code: https://gitlab.com/v_dallerit/orderconditions
Docs: https://v_dallerit.gitlab.io/orderconditions/

He has the composition and substitution rules implemented based on the Butcher product, which (I think) implicitly uses memoization since all results on a given tree are built up from subtrees.