General einsum prototype

[dcharbon]

Assumptions

• Focus on a simple end-to-end example in einsum. We will produce Python AST as the initial target.
• We won't do distributed or other sophisticated targets until after we've evaluated the result of the simplest initial end-to-end pass.

  Questions to be answered

• What needs to be done in the back-end to support an initial einsum prototype?
  • Need to figure out how an einsum is represented in our MoA implementation.
  • Need to figure out how the MoA representation is transformed into Python for evaluation.
• What needs to be done in the MoA model to support an initial einsum prototype?
• Can we implement and demonstrate both a MoA einsum over the backend and an override/escape to an optimized einsum in the backend from a uarray einsum call?

https://python-moa.readthedocs.io/en/latest/roadmap.html

• [X] arbitrary transpose
• [X] reduction
• [X] inner product (not as full featured as tensor contractions)
• [ ] high level einsum what would the moa representation be (need inner product similar to outer) Still needs thought

[costrouc]

Performance of numpy vs numba moa was due to loop ordering