FIX: support_enumeration: Use _numba_linalg_solve

[oyamad]

• It turned out that the workaround in item 3 in game_theory: Add support_enumeration #263 (comment) did not work properly in all cases.
• This fix replaces "SVD + linalg.solve" with _numba_linalg_solve, which calls directly Numba internal numba_xgesv.
• As a bonus, this leads to about 9x speedup.

ns = [8, 9, 10, 11]
seed = 1234
for n in ns:
    g = gt.random_game((n, n), random_state=seed)
    %timeit gt.support_enumeration(g)

• Current version:

  • n = 8: 99.1 ms
  • n = 9: 391 ms
  • n = 10: 1.58 s
  • n = 11: 6.56 s

• This PR:

  • n = 8: 11.6 ms
  • n = 9: 43 ms
  • n = 10: 179 ms
  • n = 11: 727 ms

numba.__version__
'0.30.1'

[coveralls]

Coverage increased (+0.8%) to 91.978% when pulling b283cbd on fix_supp_enum into 34b628b on master.

[coveralls]

Coverage increased (+1.0%) to 92.124% when pulling e7bcb02 on fix_supp_enum into 34b628b on master.

[mmcky]

@oyamad is it standard convention to return the solution in b and not explicitly return the solution and a status code from the function as a tuple?

[oyamad]

I am not sure if I understand your question, but here is where this is used, where it is check whether matrix A is nonsingular (instead of try-except which is not available in nopython mode), and in case A is singular I don't know what is in there in b.

[mmcky]

ah. I see. In the code example b is out and it is modified in place (rather than returned). Thanks @oyamad

[mmcky]

Thanks @oyamad. I just have one inline question/comment.

This is looking great. I will leave this open for one day and then merge tomorrow.