1. Make it work on a cartesian product of cones in the correct order. 2. Make it work on a cartesian product of cones in the wrong order (apply a perm utation before/after). 3. Make sure we have the dimensions of the PSD cone correct. 4. Come up with a fast heuristic (like making nu huge and taking e1 as our point) that finds a primal feasible point. 7. Figure out why this happens, too: FAIL: test_scaling_icecream (test.symmetric_linear_game_test .SymmetricLinearGameTest) ---------------------------------------------------------------------- Traceback (most recent call last): File "/home/mjo/src/dunshire/test/symmetric_linear_game_test.py", line 336, in test_scaling_icecream self.assert_scaling_works(L, K, e1, e2) File "/home/mjo/src/dunshire/test/symmetric_linear_game_test.py", line 318, in assert_scaling_works self.assert_within_tol(alpha*value1, value2) File "/home/mjo/src/dunshire/test/symmetric_linear_game_test.py", line 254, in assert_within_tol self.assertTrue(abs(first - second) < options.ABS_TOL) AssertionError: False is not true FAIL: test_translation_orthant (test.symmetric_linear_game_test SymmetricLinearGameTest) ---------------------------------------------------------------------- Traceback (most recent call last): File "/home/mjo/src/dunshire/test/symmetric_linear_game_test.py", line 374, in test_translation_orthant self.assert_translation_works(L, K, e1, e2) File "/home/mjo/src/dunshire/test/symmetric_linear_game_test.py", line 366, in assert_translation_works self.assert_within_tol(value2, inner_product(M*x_bar, y_bar)) File "/home/mjo/src/dunshire/test/symmetric_linear_game_test.py", line 254, in assert_within_tol self.assertTrue(abs(first - second) < options.ABS_TOL) AssertionError: False is not true 12. Investigate this test failure too. It looks like it was really close to being solved, but we would have needed a fudge factor of three instead of two. ERROR: test_positive_operator_value (test.symmetric_linear_game_test .SymmetricLinearGameTest) ---------------------------------------------------------------------- Traceback (most recent call last): File "/home/mjo/src/dunshire/test/symmetric_linear_game_test.py", line 550, in test_positive_operator_value self.assertTrue(G.solution().game_value() >= -options.ABS_TOL) File "/home/mjo/src/dunshire/dunshire/games.py", line 515, in solution raise GameUnsolvableException(self, soln_dict) dunshire.errors.GameUnsolvableException: Solution failed with result "unknown." The linear game (L, K, e1, e2) where L = [8.0814704 3.5584693] [3.9986814 9.3381562], K = Nonnegative orthant in the real 2-space, e1 = [1.3288182] [0.7458942], e2 = [0.6814326] [3.3799082], Condition((L, K, e1, e2)) = 41.093597. CVXOPT returned: dual infeasibility: 2.368640021750079e-06 dual objective: -7.867137172157051 dual slack: 1.1314089173606103e-07 gap: 1.1404410161224882e-06 iterations: 6 primal infeasibility: 1.379959981010593e-07 primal objective: -7.867137449574777 primal slack: 1.0550559882036034e-08 relative gap: 1.4496264027827932e-07 residual as dual infeasibility certificate: 0.12711103707156543 residual as primal infeasibility certificate: None s: [1.4674968] [0.0000000] [1.4055364] [0.0000000] status: unknown x: [ 7.8671374] [ 1.4674968] [-0.0000000] y: [7.8671372] z: [ 0.0000001] [14.0707905] [ 0.0000002] [ 1.3406728] 13. Add a test to ensure that if we solve the same game twice, we get the same answer back.