+ 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)
+
+