-def _random_square_matrix(dims):
+def _random_matrix(dims):
"""
Generate a random square (``dims``-by-``dims``) matrix,
represented as a list of rows. This is used only by the
"""
return [[uniform(-10, 10) for i in range(dims)] for j in range(dims)]
+def _random_nonnegative_matrix(dims):
+ """
+ Generate a random square (``dims``-by-``dims``) matrix with
+ nonnegative entries, represented as a list of rows. This is used
+ only by the :class:`SymmetricLinearGameTest` class.
+ """
+ L = _random_matrix(dims)
+ return [[abs(entry) for entry in row] for row in L]
+
+def _random_diagonal_matrix(dims):
+ """
+ Generate a random square (``dims``-by-``dims``) matrix with nonzero
+ entries only on the diagonal, represented as a list of rows. This is
+ used only by the :class:`SymmetricLinearGameTest` class.
+ """
+ return [[uniform(-10, 10)*int(i == j) for i in range(dims)]
+ for j in range(dims)]
def _random_orthant_params():
"""
K = NonnegativeOrthant(ambient_dim)
e1 = [uniform(0.5, 10) for idx in range(K.dimension())]
e2 = [uniform(0.5, 10) for idx in range(K.dimension())]
- L = _random_square_matrix(K.dimension())
+ L = _random_matrix(K.dimension())
return (L, K, e1, e2)
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 = _random_square_matrix(K.dimension())
+ L = _random_matrix(K.dimension())
return (L, K, e1, e2)
"""
(L, K, e1, e2) = _random_icecream_params()
self.assert_orthogonality(L, K, e1, e2)
+
+
+ def test_positive_operator_value(self):
+ """
+ Test that a positive operator on the nonnegative orthant gives
+ rise to a a game with a nonnegative value.
+
+ This test theoretically applies to the ice-cream cone as well,
+ but we don't know how to make positive operators on that cone.
+ """
+ (_, K, e1, e2) = _random_orthant_params()
+
+ # Ignore that L, we need a nonnegative one.
+ L = _random_nonnegative_matrix(K.dimension())
+
+ game = SymmetricLinearGame(L, K, e1, e2)
+ self.assertTrue(game.solution().game_value() >= -options.ABS_TOL)