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):
"""
- If we solve the same problem twice, we should get
- the same answer both times.
+ Solve ``G`` twice and check that the solutions agree.
"""
soln1 = G.solution()
soln2 = G.solution()
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())
+ self.assertTrue((s1, s2) in G.C())
def test_player1_start_valid_orthant(self):
"""
- Ensure that player one's starting point is in the orthant.
+ 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 in the ice-cream cone.
+ 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())
+ self.assertTrue((z1, z2) in G.C())
def test_player2_start_valid_orthant(self):
"""
- Ensure that player two's starting point is in the orthant.
+ 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 in the ice-cream cone.
+ Ensure that player two's starting point is feasible over the
+ ice-cream cone.
"""
G = random_icecream_game()
self.assert_player2_start_valid(G)
of the game by the same number.
"""
(alpha, H) = random_nn_scaling(G)
- value1 = G.solution().game_value()
- value2 = H.solution().game_value()
- modifier = 4*max(abs(alpha), 1)
+ soln1 = G.solution()
+ soln2 = H.solution()
+ value1 = soln1.game_value()
+ value2 = soln2.game_value()
+ modifier1 = G.tolerance_scale(soln1)
+ modifier2 = H.tolerance_scale(soln2)
+ modifier = max(modifier1, modifier2)
self.assert_within_tol(alpha*value1, value2, modifier)
(alpha, H) = random_translation(G)
value2 = H.solution().game_value()
- modifier = 4*max(abs(alpha), 1)
+ modifier = G.tolerance_scale(soln1)
self.assert_within_tol(value1 + alpha, value2, modifier)
# Make sure the same optimal pair works.
value that is the negation of the original game. Comes from
some corollary.
"""
- # This is the "correct" representation of ``M``, but
- # COLUMN indexed...
- M = -G.L().trans()
-
- # so we have to transpose it when we feed it to the constructor.
+ # Since L is a CVXOPT matrix, it will be transposed automatically.
# Note: the condition number of ``H`` should be comparable to ``G``.
- H = SymmetricLinearGame(M.trans(), G.K(), G.e2(), G.e1())
+ H = SymmetricLinearGame(-G.L(), G.K(), G.e2(), G.e1())
soln1 = G.solution()
x_bar = soln1.player1_optimal()
y_bar = soln1.player2_optimal()
soln2 = H.solution()
- # The modifier of 4 is because each could be off by 2*ABS_TOL,
- # which is how far apart the primal/dual objectives have been
- # observed being.
- self.assert_within_tol(-soln1.game_value(), soln2.game_value(), 4)
+ modifier = G.tolerance_scale(soln1)
+ self.assert_within_tol(-soln1.game_value(),
+ soln2.game_value(),
+ modifier)
# Make sure the switched optimal pair works. Since x_bar and
# y_bar come from G, we use the same modifier.
- self.assert_within_tol(soln2.game_value(), H.payoff(y_bar, x_bar), 4)
+ self.assert_within_tol(soln2.game_value(),
+ H.payoff(y_bar, x_bar),
+ modifier)
ip1 = inner_product(y_bar, G.L()*x_bar - value*G.e1())
ip2 = inner_product(value*G.e2() - G.L().trans()*y_bar, x_bar)
- # Huh.. well, y_bar and x_bar can each be epsilon away, but
- # x_bar is scaled by L, so that's (norm(L) + 1), and then
- # value could be off by epsilon, so that's another norm(e1) or
- # norm(e2). On the other hand, this test seems to pass most of
- # the time even with a modifier of one. How about.. four?
- self.assert_within_tol(ip1, 0, 4)
- self.assert_within_tol(ip2, 0, 4)
+ modifier = G.tolerance_scale(soln)
+ self.assert_within_tol(ip1, 0, modifier)
+ self.assert_within_tol(ip2, 0, modifier)
def test_orthogonality_orthant(self):
negative_stable = all([eig < options.ABS_TOL for eig in eigs])
self.assertTrue(negative_stable)
- # The dual game's value should always equal the primal's.
- # The modifier of 4 is because even though the games are dual,
- # CVXOPT doesn't know that, and each could be off by 2*ABS_TOL.
dualsoln = G.dual().solution()
- self.assert_within_tol(dualsoln.game_value(), soln.game_value(), 4)
+ mod = G.tolerance_scale(soln)
+ self.assert_within_tol(dualsoln.game_value(), soln.game_value(), mod)
def test_lyapunov_orthant(self):
projects / dunshire.git / blobdiff