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 5. Fix the solve failures that we get in the translation tests. For example,
  12
  13   ERROR: test_translation_orthant (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 374, in test_translation_orthant
  19       self.assert_translation_works(L, K, e1, e2)
  20     File "/home/mjo/src/dunshire/test/symmetric_linear_game_test.py",
  21       line 361, in assert_translation_works
  22       value2 = game2.solution().game_value()
  23     File "/home/mjo/src/dunshire/dunshire/games.py", line 458, in solution
  24       raise GameUnsolvableException(self, soln_dict)
  25   dunshire.errors.GameUnsolvableException: Solution failed with result
  26   "unknown."
  27   The linear game (L, K, e1, e2) where
  28     L = [352.0763359 267.0812248 300.8004888 307.8135853]
  29         [429.8303135 324.8322824 361.6866231 372.1748983]
  30         [390.6592961 286.8039007 320.7409227 330.1854235]
  31         [316.0538913 247.7440818 276.9063990 274.9871772],
  32     K = Nonnegative orthant in the real 4-space,
  33     e1 = [7.7040001]
  34          [9.4324457]
  35          [8.3882819]
  36          [6.8908420],
  37     e2 = [8.5054325]
  38          [6.4738132]
  39          [7.2452437]
  40          [7.3307357].
  41   CVXOPT returned:
  42     dual infeasibility: 0.053819211766446585
  43     dual objective: -5.369636805607942
  44     dual slack: 2.105806354638527e-17
  45     gap: 2.6823510532777825e-16
  46     iterations: 11
  47     primal infeasibility: 4.71536776301359e-15
  48     primal objective: -5.3799616179161
  49     primal slack: 1.0328930392495263e-17
  50     relative gap: 4.985818196816016e-17
  51     residual as dual infeasibility certificate: 0.18587493201993227
  52     residual as primal infeasibility certificate: None
  53     s:
  54       [0.0115539]
  55       [0.0000000]
  56       [0.0000000]
  57       [0.1230066]
  58       [0.4837410]
  59       [0.0000000]
  60       [0.0000000]
  61       [0.4044349]
  62     status: unknown
  63     x:
  64       [ 5.3799616]
  65       [ 0.0115539]
  66       [-0.0000000]
  67       [-0.0000000]
  68       [ 0.1230066]
  69     y:
  70       [5.3696368]
  71     z:
  72       [0.0000000]
  73       [0.4176330]
  74       [0.6007564]
  75       [0.0000000]
  76       [0.0000000]
  77       [0.0889310]
  78       [0.0191076]
  79       [0.0000000]
  80
  81
  82 7. Figure out why this happens, too:
  83
  84   FAIL: test_scaling_icecream (test.symmetric_linear_game_test
  85                                .SymmetricLinearGameTest)
  86   ----------------------------------------------------------------------
  87   Traceback (most recent call last):
  88     File "/home/mjo/src/dunshire/test/symmetric_linear_game_test.py",
  89     line 336, in test_scaling_icecream
  90       self.assert_scaling_works(L, K, e1, e2)
  91     File "/home/mjo/src/dunshire/test/symmetric_linear_game_test.py",
  92     line 318, in assert_scaling_works
  93       self.assert_within_tol(alpha*value1, value2)
  94     File "/home/mjo/src/dunshire/test/symmetric_linear_game_test.py",
  95     line 254, in assert_within_tol
  96       self.assertTrue(abs(first - second) < options.ABS_TOL)
  97   AssertionError: False is not true
  98
  99
 100   FAIL: test_translation_orthant (test.symmetric_linear_game_test
 101                                   SymmetricLinearGameTest)
 102   ----------------------------------------------------------------------
 103   Traceback (most recent call last):
 104     File "/home/mjo/src/dunshire/test/symmetric_linear_game_test.py",
 105     line 374, in test_translation_orthant
 106       self.assert_translation_works(L, K, e1, e2)
 107     File "/home/mjo/src/dunshire/test/symmetric_linear_game_test.py",
 108     line 366, in assert_translation_works
 109       self.assert_within_tol(value2, inner_product(M*x_bar, y_bar))
 110     File "/home/mjo/src/dunshire/test/symmetric_linear_game_test.py",
 111     line 254, in assert_within_tol
 112       self.assertTrue(abs(first - second) < options.ABS_TOL)
 113   AssertionError: False is not true
 114
 115
 116 12. Investigate this test failure too. It looks like it was really
 117     close to being solved, but we would have needed a fudge factor
 118     of three instead of two.
 119
 120     ERROR: test_positive_operator_value (test.symmetric_linear_game_test
 121                                          .SymmetricLinearGameTest)
 122     ----------------------------------------------------------------------
 123     Traceback (most recent call last):
 124       File "/home/mjo/src/dunshire/test/symmetric_linear_game_test.py",
 125       line 550, in test_positive_operator_value
 126         self.assertTrue(G.solution().game_value() >= -options.ABS_TOL)
 127       File "/home/mjo/src/dunshire/dunshire/games.py", line 515, in solution
 128         raise GameUnsolvableException(self, soln_dict)
 129     dunshire.errors.GameUnsolvableException: Solution failed with result
 130     "unknown."
 131     The linear game (L, K, e1, e2) where
 132       L = [8.0814704 3.5584693]
 133           [3.9986814 9.3381562],
 134       K = Nonnegative orthant in the real 2-space,
 135       e1 = [1.3288182]
 136            [0.7458942],
 137       e2 = [0.6814326]
 138            [3.3799082],
 139       Condition((L, K, e1, e2)) = 41.093597.
 140     CVXOPT returned:
 141       dual infeasibility: 2.368640021750079e-06
 142       dual objective: -7.867137172157051
 143       dual slack: 1.1314089173606103e-07
 144       gap: 1.1404410161224882e-06
 145       iterations: 6
 146       primal infeasibility: 1.379959981010593e-07
 147       primal objective: -7.867137449574777
 148       primal slack: 1.0550559882036034e-08
 149       relative gap: 1.4496264027827932e-07
 150       residual as dual infeasibility certificate: 0.12711103707156543
 151       residual as primal infeasibility certificate: None
 152       s:
 153         [1.4674968]
 154         [0.0000000]
 155         [1.4055364]
 156         [0.0000000]
 157       status: unknown
 158       x:
 159         [ 7.8671374]
 160         [ 1.4674968]
 161         [-0.0000000]
 162       y:
 163         [7.8671372]
 164       z:
 165         [ 0.0000001]
 166         [14.0707905]
 167         [ 0.0000002]
 168         [ 1.3406728]
 169
 170 13. Add a test to ensure that if we solve the same game twice, we get the
 171     same answer back.