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 6. Fix the math domain errors that sometimes pop up:
  83
  84   ERROR: 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 317, in assert_scaling_works
  93       value2 = game2.solution().game_value()
  94     File "/home/mjo/src/dunshire/dunshire/games.py", line 428, in solution
  95       soln_dict = solvers.conelp(c, G, h, C.cvxopt_dims(), A, b)
  96     File "/usr/lib64/python3.4/site-packages/cvxopt/coneprog.py", line 1395,
  97     in conelp
  98       misc.update_scaling(W, lmbda, ds, dz)
  99     File "/usr/lib64/python3.4/site-packages/cvxopt/misc.py", line 510,
 100     in update_scaling
 101       ln = jnrm2(lmbda, n = m, offset = ind)
 102     File "/usr/lib64/python3.4/site-packages/cvxopt/misc.py", line 856, in jnrm2
 103       return math.sqrt(x[offset] - a) * math.sqrt(x[offset] + a)
 104   ValueError: math domain error
 105
 106
 107 7. Figure out why this happens, too:
 108
 109   FAIL: test_scaling_icecream (test.symmetric_linear_game_test
 110                                .SymmetricLinearGameTest)
 111   ----------------------------------------------------------------------
 112   Traceback (most recent call last):
 113     File "/home/mjo/src/dunshire/test/symmetric_linear_game_test.py",
 114     line 336, in test_scaling_icecream
 115       self.assert_scaling_works(L, K, e1, e2)
 116     File "/home/mjo/src/dunshire/test/symmetric_linear_game_test.py",
 117     line 318, in assert_scaling_works
 118       self.assert_within_tol(alpha*value1, value2)
 119     File "/home/mjo/src/dunshire/test/symmetric_linear_game_test.py",
 120     line 254, in assert_within_tol
 121       self.assertTrue(abs(first - second) < options.ABS_TOL)
 122   AssertionError: False is not true
 123
 124
 125   FAIL: test_translation_orthant (test.symmetric_linear_game_test
 126                                   SymmetricLinearGameTest)
 127   ----------------------------------------------------------------------
 128   Traceback (most recent call last):
 129     File "/home/mjo/src/dunshire/test/symmetric_linear_game_test.py",
 130     line 374, in test_translation_orthant
 131       self.assert_translation_works(L, K, e1, e2)
 132     File "/home/mjo/src/dunshire/test/symmetric_linear_game_test.py",
 133     line 366, in assert_translation_works
 134       self.assert_within_tol(value2, inner_product(M*x_bar, y_bar))
 135     File "/home/mjo/src/dunshire/test/symmetric_linear_game_test.py",
 136     line 254, in assert_within_tol
 137       self.assertTrue(abs(first - second) < options.ABS_TOL)
 138   AssertionError: False is not true
 139
 140
 141 12. Investigate this test failure too. It looks like it was really
 142     close to being solved, but we would have needed a fudge factor
 143     of three instead of two.
 144
 145     ERROR: test_positive_operator_value (test.symmetric_linear_game_test
 146                                          .SymmetricLinearGameTest)
 147     ----------------------------------------------------------------------
 148     Traceback (most recent call last):
 149       File "/home/mjo/src/dunshire/test/symmetric_linear_game_test.py",
 150       line 550, in test_positive_operator_value
 151         self.assertTrue(G.solution().game_value() >= -options.ABS_TOL)
 152       File "/home/mjo/src/dunshire/dunshire/games.py", line 515, in solution
 153         raise GameUnsolvableException(self, soln_dict)
 154     dunshire.errors.GameUnsolvableException: Solution failed with result
 155     "unknown."
 156     The linear game (L, K, e1, e2) where
 157       L = [8.0814704 3.5584693]
 158           [3.9986814 9.3381562],
 159       K = Nonnegative orthant in the real 2-space,
 160       e1 = [1.3288182]
 161            [0.7458942],
 162       e2 = [0.6814326]
 163            [3.3799082],
 164       Condition((L, K, e1, e2)) = 41.093597.
 165     CVXOPT returned:
 166       dual infeasibility: 2.368640021750079e-06
 167       dual objective: -7.867137172157051
 168       dual slack: 1.1314089173606103e-07
 169       gap: 1.1404410161224882e-06
 170       iterations: 6
 171       primal infeasibility: 1.379959981010593e-07
 172       primal objective: -7.867137449574777
 173       primal slack: 1.0550559882036034e-08
 174       relative gap: 1.4496264027827932e-07
 175       residual as dual infeasibility certificate: 0.12711103707156543
 176       residual as primal infeasibility certificate: None
 177       s:
 178         [1.4674968]
 179         [0.0000000]
 180         [1.4055364]
 181         [0.0000000]
 182       status: unknown
 183       x:
 184         [ 7.8671374]
 185         [ 1.4674968]
 186         [-0.0000000]
 187       y:
 188         [7.8671372]
 189       z:
 190         [ 0.0000001]
 191         [14.0707905]
 192         [ 0.0000002]
 193         [ 1.3406728]
 194
 195
 196 13. Add game payoff(x,y) method to check solutions.