+ def test_solutions_dont_change_orthant(self):
+ """
+ If we solve the same game twice over the nonnegative orthant,
+ then we should get the same solution both times. The solution to
+ a game is not unique, but the process we use is (as far as we
+ know) deterministic.
+ """
+ G = random_orthant_game()
+ self.assert_solutions_dont_change(G)
+
+ def test_solutions_dont_change_icecream(self):
+ """
+ If we solve the same game twice over the ice-cream cone, then we
+ should get the same solution both times. The solution to a game
+ is not unique, but the process we use is (as far as we know)
+ deterministic.
+ """
+ G = random_icecream_game()
+ self.assert_solutions_dont_change(G)
+
+ def assert_solutions_dont_change(self, G):
+ """
+ Solve ``G`` twice and check that the solutions agree.
+ """
+ soln1 = G.solution()
+ soln2 = G.solution()
+ p1_diff = norm(soln1.player1_optimal() - soln2.player1_optimal())
+ p2_diff = norm(soln1.player2_optimal() - soln2.player2_optimal())
+ gv_diff = abs(soln1.game_value() - soln2.game_value())
+
+ p1_close = p1_diff < options.ABS_TOL
+ p2_close = p2_diff < options.ABS_TOL
+ gv_close = gv_diff < options.ABS_TOL
+
+ self.assertTrue(p1_close and p2_close and gv_close)
+
+
+ def assert_player1_start_valid(self, G):
+ """
+ Ensure that player one's starting point satisfies both the
+ equality and cone inequality in the CVXOPT primal problem.
+ """
+ x = G.player1_start()['x']
+ s = G.player1_start()['s']
+ s1 = s[0:G.dimension()]
+ s2 = s[G.dimension():]
+ self.assert_within_tol(norm(G.A()*x - G.b()), 0)
+ self.assertTrue((s1, s2) in G.C())
+
+
+ def test_player1_start_valid_orthant(self):
+ """
+ Ensure that player one's starting point is feasible over the
+ nonnegative orthant.
+ """
+ G = random_orthant_game()
+ self.assert_player1_start_valid(G)
+
+
+ def test_player1_start_valid_icecream(self):
+ """
+ Ensure that player one's starting point is feasible over the
+ ice-cream cone.
+ """
+ G = random_icecream_game()
+ self.assert_player1_start_valid(G)
+
+
+ def assert_player2_start_valid(self, G):
+ """
+ Check that player two's starting point satisfies both the
+ cone inequality in the CVXOPT dual problem.
+ """
+ z = G.player2_start()['z']
+ z1 = z[0:G.dimension()]
+ z2 = z[G.dimension():]
+ self.assertTrue((z1, z2) in G.C())
+
+
+ def test_player2_start_valid_orthant(self):
+ """
+ Ensure that player two's starting point is feasible over the
+ nonnegative orthant.
+ """
+ G = random_orthant_game()
+ self.assert_player2_start_valid(G)
+
+
+ def test_player2_start_valid_icecream(self):
+ """
+ Ensure that player two's starting point is feasible over the
+ ice-cream cone.
+ """
+ G = random_icecream_game()
+ self.assert_player2_start_valid(G)
+