Calculate FOI without for loops

[ethho]

Problem

Force of infection calculation is implemented with naive for looping in the BruteForceCythonFOI process: https://github.com/eho-tacc/episimlab/blob/e888ae7d7f1d1773c271c53320a7ea8a341b40d4/episimlab/foi/bf_cython.py#L15

This wraps the lower level Cython API bf_cython_engine._brute_force_foi: https://github.com/eho-tacc/episimlab/blob/e888ae7d7f1d1773c271c53320a7ea8a341b40d4/episimlab/foi/bf_cython_engine.pyx#L69

It is relatively straightforward to perform this arithmetic on arrays directly using numpy (or xarray, which uses numpy backend): https://github.com/eho-tacc/episimlab/blob/e888ae7d7f1d1773c271c53320a7ea8a341b40d4/episimlab/foi/bf_cython_engine.pyx#L156

Objective

• Write and test a new process LooplessFOI that produces the same outputs as BruteForceCythonFOI in unit tests, but has no nested for loop structure.
• Preferable implementation is to perform matrix math in xarray, but numpy implementation would also work as a first pass. No Cython.
• New process should live in a dedicated module episimlab.foi.loopless
• Testing: new pytest module at tests/test_foi/test_loopless.py that checks the following:
  • Can initialize the method and run the run_step method error-free, as in https://github.com/eho-tacc/episimlab/blob/e888ae7d7f1d1773c271c53320a7ea8a341b40d4/tests/test_foi/test_bf_cython_foi.py#L10
  • Can exactly recapitulate the outputs of process BruteForceCythonFOI, as in https://github.com/eho-tacc/episimlab/blob/e888ae7d7f1d1773c271c53320a7ea8a341b40d4/tests/test_foi/test_bf_cython_foi.py#L33

[ethho]

Prototype implementation in https://github.com/eho-tacc/episimlab-markov/

[ethho]

Migrated prototype notebook to markov branch on this repo: https://github.com/eho-tacc/episimlab/blob/markov/notebooks/20210731_markov_sandbox.ipynb. Process FOI in this notebook implements the above requested LooplessFOI in its foi method. foi method is confirmed to produce equivalent output to the (current) brute force method in brute_force_foi.

[ethho]

Fixed in v2 (#40)