Design of Julia libraries

This document is a collection of thoughts on how to design Julia libraries.

• TensorCrossInterpolation.jl (no ITensor dependence)
• QuanticsTCI.jl
  TCI for quantics. QFT MPOs are implemented as well.
• TCIAlgorithms.jl
  Advanced algorithms for TCI. But, we currently implement only adaptive patching + TCI. Rename to something else? Such as AdaptivePatchingTCI.jl?
• ProjMPSs.jl (rename to PartitionedMPSs.jl, PartitionedMPS, SubDomainMPS)
  This library implements adaptive patching of MPSs. We use ITensorMPS.MPS as an internal data structure. In the future, we may implement operations using TCI. ITensorMPS.ProjMPS exists, need to be renamed.
• FastMPOContractions.jl
  This library implements a set of functionalities missing in ITensorMPS.jl such as MPO-MPO contractions. We use ITensorMPS.MPS and ITensorMPS.MPO as internal data structures. In the future, we may implement operations using TCI.
• Quantics.jl
  Many things related to quantics. But, it is already messy.
  • automul
    Element-wise multiplication or matrix multiplication. The current implemtation assumes quantics, but can be generalized.
  • makediagonal, extractdiagonal
  • utility functions for quantics tags, e.g., x=1, x=2.