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 7. Figure out why this happens, too:
  12
  13   FAIL: test_scaling_icecream (test.symmetric_linear_game_test
  14                                .SymmetricLinearGameTest)
  15   ----------------------------------------------------------------------
  16   Traceback (most recent call last):
  17     File "/home/mjo/src/dunshire/test/symmetric_linear_game_test.py",
  18     line 336, in test_scaling_icecream
  19       self.assert_scaling_works(L, K, e1, e2)
  20     File "/home/mjo/src/dunshire/test/symmetric_linear_game_test.py",
  21     line 318, in assert_scaling_works
  22       self.assert_within_tol(alpha*value1, value2)
  23     File "/home/mjo/src/dunshire/test/symmetric_linear_game_test.py",
  24     line 254, in assert_within_tol
  25       self.assertTrue(abs(first - second) < options.ABS_TOL)
  26   AssertionError: False is not true
  27
  28
  29   FAIL: test_translation_orthant (test.symmetric_linear_game_test
  30                                   SymmetricLinearGameTest)
  31   ----------------------------------------------------------------------
  32   Traceback (most recent call last):
  33     File "/home/mjo/src/dunshire/test/symmetric_linear_game_test.py",
  34     line 374, in test_translation_orthant
  35       self.assert_translation_works(L, K, e1, e2)
  36     File "/home/mjo/src/dunshire/test/symmetric_linear_game_test.py",
  37     line 366, in assert_translation_works
  38       self.assert_within_tol(value2, inner_product(M*x_bar, y_bar))
  39     File "/home/mjo/src/dunshire/test/symmetric_linear_game_test.py",
  40     line 254, in assert_within_tol
  41       self.assertTrue(abs(first - second) < options.ABS_TOL)
  42   AssertionError: False is not true
  43
  44
  45 12. Investigate this test failure too. It looks like it was really
  46     close to being solved, but we would have needed a fudge factor
  47     of three instead of two.
  48
  49     ERROR: test_positive_operator_value (test.symmetric_linear_game_test
  50                                          .SymmetricLinearGameTest)
  51     ----------------------------------------------------------------------
  52     Traceback (most recent call last):
  53       File "/home/mjo/src/dunshire/test/symmetric_linear_game_test.py",
  54       line 550, in test_positive_operator_value
  55         self.assertTrue(G.solution().game_value() >= -options.ABS_TOL)
  56       File "/home/mjo/src/dunshire/dunshire/games.py", line 515, in solution
  57         raise GameUnsolvableException(self, soln_dict)
  58     dunshire.errors.GameUnsolvableException: Solution failed with result
  59     "unknown."
  60     The linear game (L, K, e1, e2) where
  61       L = [8.0814704 3.5584693]
  62           [3.9986814 9.3381562],
  63       K = Nonnegative orthant in the real 2-space,
  64       e1 = [1.3288182]
  65            [0.7458942],
  66       e2 = [0.6814326]
  67            [3.3799082],
  68       Condition((L, K, e1, e2)) = 41.093597.
  69     CVXOPT returned:
  70       dual infeasibility: 2.368640021750079e-06
  71       dual objective: -7.867137172157051
  72       dual slack: 1.1314089173606103e-07
  73       gap: 1.1404410161224882e-06
  74       iterations: 6
  75       primal infeasibility: 1.379959981010593e-07
  76       primal objective: -7.867137449574777
  77       primal slack: 1.0550559882036034e-08
  78       relative gap: 1.4496264027827932e-07
  79       residual as dual infeasibility certificate: 0.12711103707156543
  80       residual as primal infeasibility certificate: None
  81       s:
  82         [1.4674968]
  83         [0.0000000]
  84         [1.4055364]
  85         [0.0000000]
  86       status: unknown
  87       x:
  88         [ 7.8671374]
  89         [ 1.4674968]
  90         [-0.0000000]
  91       y:
  92         [7.8671372]
  93       z:
  94         [ 0.0000001]
  95         [14.0707905]
  96         [ 0.0000002]
  97         [ 1.3406728]
  98
  99 13. Add a test to ensure that if we solve the same game twice, we get the
 100     same answer back.