TODO

   1 1. Make it work on a cartesian product of cones in the correct order.
   2
   3 2. Make it work on a cartesian product of cones in the wrong order
   4    (apply a perm utation before/after).
   5
   6 3. Make sure we have the dimensions of the PSD cone correct.
   7
   8 4. Come up with a fast heuristic (like making nu huge and taking e1 as
   9    our point) that finds a primal feasible point.
  10
  11 12. Investigate this test failure too. It looks like it was really
  12     close to being solved, but we would have needed a fudge factor
  13     of three instead of two.
  14
  15     ERROR: test_positive_operator_value (test.symmetric_linear_game_test
  16                                          .SymmetricLinearGameTest)
  17     ----------------------------------------------------------------------
  18     Traceback (most recent call last):
  19       File "/home/mjo/src/dunshire/test/symmetric_linear_game_test.py",
  20       line 550, in test_positive_operator_value
  21         self.assertTrue(G.solution().game_value() >= -options.ABS_TOL)
  22       File "/home/mjo/src/dunshire/dunshire/games.py", line 515, in solution
  23         raise GameUnsolvableException(self, soln_dict)
  24     dunshire.errors.GameUnsolvableException: Solution failed with result
  25     "unknown."
  26     The linear game (L, K, e1, e2) where
  27       L = [8.0814704 3.5584693]
  28           [3.9986814 9.3381562],
  29       K = Nonnegative orthant in the real 2-space,
  30       e1 = [1.3288182]
  31            [0.7458942],
  32       e2 = [0.6814326]
  33            [3.3799082],
  34       Condition((L, K, e1, e2)) = 41.093597.
  35     CVXOPT returned:
  36       dual infeasibility: 2.368640021750079e-06
  37       dual objective: -7.867137172157051
  38       dual slack: 1.1314089173606103e-07
  39       gap: 1.1404410161224882e-06
  40       iterations: 6
  41       primal infeasibility: 1.379959981010593e-07
  42       primal objective: -7.867137449574777
  43       primal slack: 1.0550559882036034e-08
  44       relative gap: 1.4496264027827932e-07
  45       residual as dual infeasibility certificate: 0.12711103707156543
  46       residual as primal infeasibility certificate: None
  47       s:
  48         [1.4674968]
  49         [0.0000000]
  50         [1.4055364]
  51         [0.0000000]
  52       status: unknown
  53       x:
  54         [ 7.8671374]
  55         [ 1.4674968]
  56         [-0.0000000]
  57       y:
  58         [7.8671372]
  59       z:
  60         [ 0.0000001]
  61         [14.0707905]
  62         [ 0.0000002]
  63         [ 1.3406728]
  64
  65 13. Add a test to ensure that if we solve the same game twice, we get the
  66     same answer back.