+ self.assert_within_tol(soln.game_value(), expected)
+
+ def test_solution_exists_nonnegative_orthant(self):
+ """
+ Every linear game has a solution, so we should be able to solve
+ every symmetric linear game over the NonnegativeOrthant. Pick
+ some parameters randomly and give it a shot. The resulting
+ optimal solutions should give us the optimal game value when we
+ apply the payoff operator to them.
+ """
+ ambient_dim = randint(1, 10)
+ K = NonnegativeOrthant(ambient_dim)
+ e1 = [uniform(0.1, 10) for idx in range(K.dimension())]
+ e2 = [uniform(0.1, 10) for idx in range(K.dimension())]
+ L = [[uniform(-10, 10) for i in range(K.dimension())]
+ for j in range(K.dimension())]
+ self.assert_solution_exists(L, K, e1, e2)
+
+ def test_solution_exists_ice_cream(self):
+ """
+ Like :meth:`test_solution_exists_nonnegative_orthant`, except
+ over the ice cream cone.
+ """
+ # Use a minimum dimension of two to avoid divide-by-zero in
+ # the fudge factor we make up later.
+ ambient_dim = randint(2, 10)
+ K = IceCream(ambient_dim)
+ e1 = [1]
+ e2 = [1]
+ # If we choose the rest of the components of e1,e2 randomly
+ # between 0 and 1, then the largest the squared norm of the
+ # non-height part of e1,e2 could be is the 1*(dim(K) - 1). We
+ # need to make it less than one (the height of the cone) so
+ # that the whole thing is in the cone. The norm of the
+ # non-height part is sqrt(dim(K) - 1), and we can divide by
+ # twice that.
+ fudge_factor = 1.0 / (2.0*sqrt(K.dimension() - 1.0))
+ e1 += [fudge_factor*uniform(0, 1) for idx in range(K.dimension() - 1)]
+ e2 += [fudge_factor*uniform(0, 1) for idx in range(K.dimension() - 1)]
+ L = [[uniform(-10, 10) for i in range(K.dimension())]
+ for j in range(K.dimension())]
+ self.assert_solution_exists(L, K, e1, e2)
+