-
-
-class SymmetricLinearGameTest(TestCase):
- """
- Tests for the SymmetricLinearGame and Solution classes.
- """
-
- def assert_within_tol(self, first, second):
- """
- Test that ``first`` and ``second`` are equal within our default
- tolerance.
- """
- self.assertTrue(abs(first - second) < options.ABS_TOL)
-
-
- def assert_solution_exists(self, L, K, e1, e2):
- """
- Given the parameters needed to construct a SymmetricLinearGame,
- ensure that that game has a solution.
- """
- G = SymmetricLinearGame(L, K, e1, e2)
- soln = G.solution()
- L_matrix = matrix(L).trans()
- expected = inner_product(L_matrix*soln.player1_optimal(),
- soln.player2_optimal())
- 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] # Set the "height" of e1 to one
- e2 = [1] # And the same for e2
-
- # 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)
-