X-Git-Url: https://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=test%2Fsymmetric_linear_game_test.py;h=cf305f0ae133699a1be00a3dce8c27c72c9f2a7c;hb=dd58b25641f37f52b7327b1b779a606c33e230eb;hp=b6bd9b89abdbf9ebb10820c9701faee5fadd240c;hpb=e41ad668f4f16d8948181ae307cb98430b37ed1d;p=dunshire.git diff --git a/test/symmetric_linear_game_test.py b/test/symmetric_linear_game_test.py index b6bd9b8..cf305f0 100644 --- a/test/symmetric_linear_game_test.py +++ b/test/symmetric_linear_game_test.py @@ -43,17 +43,28 @@ class SymmetricLinearGameTest(TestCase): # pylint: disable=R0904 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() @@ -69,17 +80,22 @@ class SymmetricLinearGameTest(TestCase): # pylint: disable=R0904 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) @@ -87,12 +103,42 @@ class SymmetricLinearGameTest(TestCase): # pylint: disable=R0904 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()) + + + 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) + + def test_condition_lower_bound(self): """ Ensure that the condition number of a game is greater than or @@ -114,9 +160,13 @@ class SymmetricLinearGameTest(TestCase): # pylint: disable=R0904 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) @@ -155,7 +205,7 @@ class SymmetricLinearGameTest(TestCase): # pylint: disable=R0904 (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. @@ -185,27 +235,25 @@ class SymmetricLinearGameTest(TestCase): # pylint: disable=R0904 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) @@ -240,13 +288,9 @@ class SymmetricLinearGameTest(TestCase): # pylint: disable=R0904 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): @@ -302,11 +346,9 @@ class SymmetricLinearGameTest(TestCase): # pylint: disable=R0904 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):