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 8. Fix floating point comparisons in the doctest output.
 142
 143
 144 12. Investigate this test failure too. It looks like it was really
 145     close to being solved, but we would have needed a fudge factor
 146     of three instead of two.
 147
 148     ERROR: test_positive_operator_value (test.symmetric_linear_game_test
 149                                          .SymmetricLinearGameTest)
 150     ----------------------------------------------------------------------
 151     Traceback (most recent call last):
 152       File "/home/mjo/src/dunshire/test/symmetric_linear_game_test.py",
 153       line 550, in test_positive_operator_value
 154         self.assertTrue(G.solution().game_value() >= -options.ABS_TOL)
 155       File "/home/mjo/src/dunshire/dunshire/games.py", line 515, in solution
 156         raise GameUnsolvableException(self, soln_dict)
 157     dunshire.errors.GameUnsolvableException: Solution failed with result
 158     "unknown."
 159     The linear game (L, K, e1, e2) where
 160       L = [8.0814704 3.5584693]
 161           [3.9986814 9.3381562],
 162       K = Nonnegative orthant in the real 2-space,
 163       e1 = [1.3288182]
 164            [0.7458942],
 165       e2 = [0.6814326]
 166            [3.3799082],
 167       Condition((L, K, e1, e2)) = 41.093597.
 168     CVXOPT returned:
 169       dual infeasibility: 2.368640021750079e-06
 170       dual objective: -7.867137172157051
 171       dual slack: 1.1314089173606103e-07
 172       gap: 1.1404410161224882e-06
 173       iterations: 6
 174       primal infeasibility: 1.379959981010593e-07
 175       primal objective: -7.867137449574777
 176       primal slack: 1.0550559882036034e-08
 177       relative gap: 1.4496264027827932e-07
 178       residual as dual infeasibility certificate: 0.12711103707156543
 179       residual as primal infeasibility certificate: None
 180       s:
 181         [1.4674968]
 182         [0.0000000]
 183         [1.4055364]
 184         [0.0000000]
 185       status: unknown
 186       x:
 187         [ 7.8671374]
 188         [ 1.4674968]
 189         [-0.0000000]
 190       y:
 191         [7.8671372]
 192       z:
 193         [ 0.0000001]
 194         [14.0707905]
 195         [ 0.0000002]
 196         [ 1.3406728]
 197
 198
 199 13. Add game payoff(x,y) method to check solutions.