X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=test%2Fsymmetric_linear_game_test.py;h=1e7194b6bf08e50c1739539469a36279d866f8c1;hb=e22adb2af08288282c3f085eb7a43ab131577bfe;hp=936a7e869283b4fd9ee2e82ddccefa5ef7253658;hpb=96a9491fcc4c7df4c73f9617f2185586b0226b78;p=dunshire.git diff --git a/test/symmetric_linear_game_test.py b/test/symmetric_linear_game_test.py index 936a7e8..1e7194b 100644 --- a/test/symmetric_linear_game_test.py +++ b/test/symmetric_linear_game_test.py @@ -4,32 +4,14 @@ Unit tests for the :class:`SymmetricLinearGame` class. from unittest import TestCase -from dunshire.cones import NonnegativeOrthant from dunshire.games import SymmetricLinearGame -from dunshire.matrices import eigenvalues_re, inner_product +from dunshire.matrices import eigenvalues_re, inner_product, norm from dunshire import options -from .randomgen import (RANDOM_MAX, random_icecream_game, - random_ll_icecream_game, random_ll_orthant_game, - random_nn_scaling, random_orthant_game, - random_positive_orthant_game, random_translation) +from .randomgen import (random_icecream_game, random_ll_icecream_game, + random_ll_orthant_game, random_nn_scaling, + random_orthant_game, random_positive_orthant_game, + random_translation) -EPSILON = (1 + RANDOM_MAX)*options.ABS_TOL -""" -This is the tolerance constant including fudge factors that we use to -determine whether or not two numbers are equal in tests. - -Often we will want to compare two solutions, say for games that are -equivalent. If the first game value is low by ``ABS_TOL`` and the second -is high by ``ABS_TOL``, then the total could be off by ``2*ABS_TOL``. We -also subject solutions to translations and scalings, which adds to or -scales their error. If the first game is low by ``ABS_TOL`` and the -second is high by ``ABS_TOL`` before scaling, then after scaling, the -second could be high by ``RANDOM_MAX*ABS_TOL``. That is the rationale -for the factor of ``1 + RANDOM_MAX`` in ``EPSILON``. Since ``1 + -RANDOM_MAX`` is greater than ``2*ABS_TOL``, we don't need to handle the -first issue mentioned (both solutions off by the same amount in opposite -directions). -""" # Tell pylint to shut up about the large number of methods. class SymmetricLinearGameTest(TestCase): # pylint: disable=R0904 @@ -52,24 +34,38 @@ class SymmetricLinearGameTest(TestCase): # pylint: disable=R0904 modifier : float A scaling factor (default: 1) applied to the default - ``EPSILON`` for this comparison. If you have a poorly- + tolerance for this comparison. If you have a poorly- conditioned matrix, for example, you may want to set this greater than one. """ - self.assertTrue(abs(first - second) < EPSILON*modifier) + self.assertTrue(abs(first - second) < options.ABS_TOL*modifier) + + def test_solutions_dont_change_orthant(self): + G = random_orthant_game() + self.assert_solutions_dont_change(G) + + def test_solutions_dont_change_icecream(self): + G = random_icecream_game() + self.assert_solutions_dont_change(G) - def assert_solution_exists(self, G): + def assert_solutions_dont_change(self, G): """ - Given a SymmetricLinearGame, ensure that it has a solution. + If we solve the same problem twice, we should get + the same answer both times. """ - soln = G.solution() + soln1 = G.solution() + soln2 = G.solution() + p1_diff = norm(soln1.player1_optimal() - soln2.player1_optimal()) + p2_diff = norm(soln1.player2_optimal() - soln2.player2_optimal()) + gv_diff = abs(soln1.game_value() - soln2.game_value()) - expected = inner_product(G._L*soln.player1_optimal(), - soln.player2_optimal()) - self.assert_within_tol(soln.game_value(), expected, G.condition()) + p1_close = p1_diff < options.ABS_TOL + p2_close = p2_diff < options.ABS_TOL + gv_close = gv_diff < options.ABS_TOL + self.assertTrue(p1_close and p2_close and gv_close) def test_condition_lower_bound(self): @@ -87,40 +83,6 @@ class SymmetricLinearGameTest(TestCase): # pylint: disable=R0904 self.assertTrue(G.condition() >= 1.0) - def test_solution_exists_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. - """ - G = random_orthant_game() - self.assert_solution_exists(G) - - - def test_solution_exists_icecream(self): - """ - Like :meth:`test_solution_exists_nonnegative_orthant`, except - over the ice cream cone. - """ - G = random_icecream_game() - self.assert_solution_exists(G) - - - def test_negative_value_z_operator(self): - """ - Test the example given in Gowda/Ravindran of a Z-matrix with - negative game value on the nonnegative orthant. - """ - K = NonnegativeOrthant(2) - e1 = [1, 1] - e2 = e1 - L = [[1, -2], [-2, 1]] - G = SymmetricLinearGame(L, K, e1, e2) - self.assertTrue(G.solution().game_value() < -options.ABS_TOL) - - def assert_scaling_works(self, G): """ Test that scaling ``L`` by a nonnegative number scales the value @@ -129,7 +91,8 @@ class SymmetricLinearGameTest(TestCase): # pylint: disable=R0904 (alpha, H) = random_nn_scaling(G) value1 = G.solution().game_value() value2 = H.solution().game_value() - self.assert_within_tol(alpha*value1, value2, H.condition()) + modifier = 4*max(abs(alpha), 1) + self.assert_within_tol(alpha*value1, value2, modifier) def test_scaling_orthant(self): @@ -167,12 +130,11 @@ class SymmetricLinearGameTest(TestCase): # pylint: disable=R0904 (alpha, H) = random_translation(G) value2 = H.solution().game_value() - self.assert_within_tol(value1 + alpha, value2, H.condition()) + modifier = 4*max(abs(alpha), 1) + self.assert_within_tol(value1 + alpha, value2, modifier) # Make sure the same optimal pair works. - self.assert_within_tol(value2, - inner_product(H._L*x_bar, y_bar), - H.condition()) + self.assert_within_tol(value2, H.payoff(x_bar, y_bar), modifier) def test_translation_orthant(self): @@ -200,25 +162,26 @@ class SymmetricLinearGameTest(TestCase): # pylint: disable=R0904 """ # This is the "correct" representation of ``M``, but # COLUMN indexed... - M = -G._L.trans() + M = -G.L().trans() # so we have to transpose it when we feed it to the constructor. # Note: the condition number of ``H`` should be comparable to ``G``. - H = SymmetricLinearGame(M.trans(), G._K, G._e2, G._e1) + H = SymmetricLinearGame(M.trans(), G.K(), G.e2(), G.e1()) soln1 = G.solution() x_bar = soln1.player1_optimal() y_bar = soln1.player2_optimal() soln2 = H.solution() - self.assert_within_tol(-soln1.game_value(), - soln2.game_value(), - H.condition()) + # 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) + + # 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) - # Make sure the switched optimal pair works. - self.assert_within_tol(soln2.game_value(), - inner_product(M*y_bar, x_bar), - H.condition()) def test_opposite_game_orthant(self): @@ -249,11 +212,16 @@ class SymmetricLinearGameTest(TestCase): # pylint: disable=R0904 y_bar = soln.player2_optimal() value = soln.game_value() - ip1 = inner_product(y_bar, G._L*x_bar - value*G._e1) - self.assert_within_tol(ip1, 0, G.condition()) + 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) - ip2 = inner_product(value*G._e2 - G._L.trans()*y_bar, x_bar) - self.assert_within_tol(ip2, 0, G.condition()) + # 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) def test_orthogonality_orthant(self): @@ -298,22 +266,22 @@ class SymmetricLinearGameTest(TestCase): # pylint: disable=R0904 # # See :meth:`assert_within_tol` for an explanation of the # fudge factors. - eigs = eigenvalues_re(G._L) + eigs = eigenvalues_re(G.L()) - if soln.game_value() > EPSILON: + if soln.game_value() > options.ABS_TOL: # L should be positive stable positive_stable = all([eig > -options.ABS_TOL for eig in eigs]) self.assertTrue(positive_stable) - elif soln.game_value() < -EPSILON: + elif soln.game_value() < -options.ABS_TOL: # L should be negative stable 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(), - G.condition()) + self.assert_within_tol(dualsoln.game_value(), soln.game_value(), 4) def test_lyapunov_orthant(self):