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 10. Sometimes our Lyapunov-like tests over the ice cream cone are
 144     failing badly. For example,
 145
 146   FAIL: test_lyapunov_icecream (test.symmetric_linear_game_test
 147                                 .SymmetricLinearGameTest)
 148   ----------------------------------------------------------------------
 149   Traceback (most recent call last):
 150     File "/home/mjo/src/dunshire/test/symmetric_linear_game_test.py",
 151     line 620, in test_lyapunov_icecream
 152       self.assert_lyapunov_works(G)
 153     File "/home/mjo/src/dunshire/test/symmetric_linear_game_test.py",
 154     line 578, in assert_lyapunov_works
 155       self.assertTrue(negative_stable)
 156   AssertionError: False is not true
 157
 158
 159     We should have a matrix L that is negative stable, but its eigenvalues
 160     are actually,
 161
 162       [0.8991268260361707,
 163        0.8991268260361707,
 164        -1.4648148562918966,
 165        3.2630685083642352,
 166        0.8991268260361712]
 167
 168 11. Complete the unit tests for the matrices module. We still need to
 169     document it, and finish adding all of the tests.
 170
 171 12. Investigate this test failure too. It looks like it was really
 172     close to being solved, but we would have needed a fudge factor
 173     of three instead of two.
 174
 175     ERROR: test_positive_operator_value (test.symmetric_linear_game_test
 176                                          .SymmetricLinearGameTest)
 177     ----------------------------------------------------------------------
 178     Traceback (most recent call last):
 179       File "/home/mjo/src/dunshire/test/symmetric_linear_game_test.py",
 180       line 550, in test_positive_operator_value
 181         self.assertTrue(G.solution().game_value() >= -options.ABS_TOL)
 182       File "/home/mjo/src/dunshire/dunshire/games.py", line 515, in solution
 183         raise GameUnsolvableException(self, soln_dict)
 184     dunshire.errors.GameUnsolvableException: Solution failed with result
 185     "unknown."
 186     The linear game (L, K, e1, e2) where
 187       L = [8.0814704 3.5584693]
 188           [3.9986814 9.3381562],
 189       K = Nonnegative orthant in the real 2-space,
 190       e1 = [1.3288182]
 191            [0.7458942],
 192       e2 = [0.6814326]
 193            [3.3799082],
 194       Condition((L, K, e1, e2)) = 41.093597.
 195     CVXOPT returned:
 196       dual infeasibility: 2.368640021750079e-06
 197       dual objective: -7.867137172157051
 198       dual slack: 1.1314089173606103e-07
 199       gap: 1.1404410161224882e-06
 200       iterations: 6
 201       primal infeasibility: 1.379959981010593e-07
 202       primal objective: -7.867137449574777
 203       primal slack: 1.0550559882036034e-08
 204       relative gap: 1.4496264027827932e-07
 205       residual as dual infeasibility certificate: 0.12711103707156543
 206       residual as primal infeasibility certificate: None
 207       s:
 208         [1.4674968]
 209         [0.0000000]
 210         [1.4055364]
 211         [0.0000000]
 212       status: unknown
 213       x:
 214         [ 7.8671374]
 215         [ 1.4674968]
 216         [-0.0000000]
 217       y:
 218         [7.8671372]
 219       z:
 220         [ 0.0000001]
 221         [14.0707905]
 222         [ 0.0000002]
 223         [ 1.3406728]
 224
 225
 226 13. Add game payoff(x,y) method to check solutions.